Baffle Step as a Pressure Director, Not Booster:

While baffle step doesn’t create an overall gain in sound pressure, it acts like a pressure director, concentrating sound waves in the forward direction (towards the listener) for frequencies above the baffle step frequency. This can be visualized as:

At low frequencies the sound wavelength is large compared to the baffle size:
Sound from the driver radiates freely in all directions (think of a sphere),resulting in omnidirectional radiation (4π steradians).

When frequency increases and the wavelength becomes comparable to the baffle dimensions:

• The cabinet dimensions start to influence the sound radiation pattern and pass the radiation to 4π to 2π leading to a pressure increase in the forward direction due to a more focused radiation pattern (generaly +6dB SPL).

• Diffraction around the edges creates additional wavefronts at transition from 4π to 2π that interfere with the original waves from the driver. These interferences will causes cancellations or sommations at transition. Diffraction and Standing Waves article goes deep in these two concepts.

This combined effect leads to a global pressure increase in the forward axis from a frequency related to baffle dimensions and a beam of sound at transition.

The Energy point of view

While the baffle analogy is helpful, it’s important to remember that baffle step doesn’t create a uniform gain of +6dB SPL.

We take here as landmark the dB SPL (so in front of the speaker) in 4π, some parameters as woofer sensitivity are given in 2π on a big ISO baffle, so from this point of view, if we take SPL in 2π as landmark it’s no more +6dB SPL but -6dB SPL.

This difference of front pressure is in fact more a 6dB delta due to a difference in energy distribution than a plus or minus, to the energy point of view there is no loss or gain, the energy remain the same, only the his direction is changing, creating a energy focusing effect.

How to simulate it

The pressure increase in the forward direction is gradual and depends on the specific baffle size and frequency, as we can simulate it in VituixCAD with the Diffraction tool:

Analogy, Baffle Step as a 180-degree Horn:

The analogy of a 180-degree horn is apt. Similar to a horn, the baffle acts to channel and focus sound waves in a specific direction. However, unlike a true horn that uses its shape to progressively increase pressure by loading and acoustic loading, the baffle doesn’t create new energy. It simply redirects existing energy.

Addressing the Decrease in Other Directions:

The pressure increase in the forward direction comes at the expense of sound pressure radiating to the sides and back. This decrease happens because:

• The diffracted waves also travel sideways and backwards, but they might not be perfectly in phase with the original waves, leading to destructive interference and a decrease in pressure in those directions.

• The reduction in radiation area from 4π steradians (omnidirectional) to 2π steradians (forward direction) inherently represents a increased sound pressure in a spedific direction, to the listener, so it will be attached to a decrease sound pressure off axis.

Analogy, The Water Fountain:

Imagine your speaker as a water fountain:

• At low frequencies: The water sprays out in all directions, like a big sphere (think of a beach ball filled with water spraying everywhere). This is similar to how sound behaves at low frequencies from a speaker without a baffle step effect.

• As the water pressure increases (higher frequencies): The water starts to travel further, but the edges of the fountain (like the edges of the speaker cabinet) restrict the spray. This makes the water shoot out more in the forward direction (towards you) and less to the sides and back.

This is similar to what happens with baffle step:

• Higher frequencies are “focused” more towards the listener. This can sound a little louder in the front compared to the sides, especially for sounds just below the baffle step frequency.

• However, the total amount of sound energy doesn’t necessarily change. It’s just distributed differently, with more emphasis on the front.

Baffle mistakes and solutions

For tweeter without waveguide, put it in an asymetrical position in the baffle is a good solution for dispatch the baffle diffraction (beaming), but by keeping the medium (if there is one) perfectly vertical to the tweeter.

The worst baffle step is given by “vintage” way to do, provoking a lot of diffraction impacting both on and off-axis:

As seen in the midrange narrowing article, a big baffle will not necessarily solve the problem with a horn, as we have to pass from the profile acceleration of the horn to a 180° flat no acceleration surface, we have to accelerate then decelerate slowly for reach the big flat surface (it can be a wall in in-wall). The size of the panel, if he is not infinite (wall), will just put the problem further to the point of view of edge diffraction.

For waveguide or horns it’s always better to have an continuous profile to never create a flat area between the horn and the edges, as seen here with a X-shape X25:

Additional Considerations:

• The specific frequency response of the baffle step depends on the size and shape of the cabinet. A wider baffle will have a lower baffle step frequency compared to a narrower one.

• The proximity of the speaker to walls and other boundaries can further complicate the pressure distribution due to additional reflections.

By understanding the interplay between diffraction, constructive interference, and radiation patterns, we gain a deeper appreciation for the complexities of baffle step and its impact on speaker performance.

This text delves into how ITDG (Initial Time Delay Gap), EDT (Early Decay), critical distance, radiation coverage, and speaker directivity all influence the perception of space and sound clarity within a real room, focusing on aspects relevant to living rooms and home theaters.

Understanding ITDG

ITDG refers to the time difference between the arrival of the direct sound from a source (speaker, instrument, voice, etc.) and the arrival of the first significant reflections of that sound bouncing off the walls, ceiling, and floor.

ITDG and the Perception of Clarity

A room’s ITDG plays a crucial role in how clear the sound feels. Here’s the impact:

• Short ITDG (less than 20ms): While a very short ITDG can enhance clarity to some extent, it can also create an unnaturally dry and sterile sound, lacking the richness of natural reverberation.

• Optimal ITDG Range (20ms - 50ms): This range is generally considered ideal for good clarity in rooms like living rooms and home theaters. Early reflections arrive soon enough to reinforce the direct sound and improve intelligibility, but not so soon that they create an overly dry or “in-your-face” listening experience.

• Long ITDG (over 50ms): As you pointed out, longer ITDGs can lead to a decrease in clarity by creating noticeable echoes and muddying the sound. This can be particularly detrimental for speech intelligibility, especially in dialogue-heavy content.

Note: range and value can vary from one author or research to another and about preferences.

Critical Distance and Radiation Coverage

• Critical Distance: This is the distance from a sound source where the direct sound and the first reflections arrive at the listener’s ears with roughly equal intensity. Within this distance, the ITDG has a significant impact on perceived clarity. Beyond the critical distance, the influence of the room’s reflections becomes less prominent.

• Radiation Coverage: This refers to the area effectively covered by a speaker’s sound dispersion pattern. It’s important to consider the radiation coverage of your speakers in relation to the listening distance and room shape.

Relationship to ITDG and Directivity

• Speaker Directivity: Speakers with a wider directivity pattern (less focused sound dispersion) tend to create a larger critical distance. This means that ITDG plays a more significant role in shaping the perceived clarity at greater listening distances.

• Adapting Radiation Coverage: By strategically placing speakers with appropriate constant directivity speakers adapted to listening distance, you can influence the ITDG experienced within the room..

Early Decay Time (EDT) and its Impact

EDT is the time it takes for the sound level in a room to decrease by 60 dB after the source has stopped emitting sound. This decay is primarily caused by the absorption of sound by the room’s surfaces (walls, ceiling, floor, furniture, acoustics, etc.).

The Relationship Between EDT and ITDG

While ITDG is influenced by the room’s shape, size, and the placement of sound sources and listeners, the absorption characteristics of the room (reflected in the EDT) also play a significant role:

• High Absorption, Short EDT: If a room has a high absorption coefficient (meaning it absorbs sound waves efficiently), the first reflections will arrive weaker and decay more rapidly. This can lead to a shorter ITDG because the gap between the direct sound and the remaining reflections becomes smaller.

• Low Absorption, Long EDT: Conversely, in a room with low absorption (meaning sound waves reflect more readily), the first reflections will be stronger and take longer to decay. This can contribute to a longer ITDG as the first significant reflection arrives later, increasing the time difference between it and the direct sound.

Optimizing for Clarity: Balancing ITDG and EDT

When aiming for good acoustics in a living room or home theater, it’s important to consider both ITDG and EDT:

• Balancing ITDG: As discussed previously, an optimal ITDG range (around 20ms-50ms) is desirable for clear sound.

• Managing EDT: A moderate EDT (around 0.5s-1.0s for living rooms and home theaters) helps control unwanted reverberation without creating an overly dry and sterile sound.

Optimizing Your Room’s Acoustics

When optimizing ITDG and sound clarity in your living room or home theater, consider these points:

When aiming for optimal Initial Time Delay Gap (ITDG) and sound clarity in your living room or home theater, consider these key factors:

• Speaker Selection: Choose speakers with directivity patterns that suit your listening distance and room acoustics. Wider directivity create a larger critical distance (where direct sound and early reflections have similar intensity), influencing how ITDG affects perceived clarity, especially at greater distances.

• Strategic Speaker Placement: Strategically position speakers based on their directivity and desired ITDG. Avoid placing them too close to side walls, as this can negatively impact sound quality.

  While a slight “toe-in” angle can sometimes improve focus at larger listening distances, use it cautiously. Excessive toe-in narrows the “sweet spot” and can reduce overall clarity. This is because it increases directivity too much, leading to tonal imbalance. Additionally, over-toe-in cannot compensate for a large variation in Direct-to-Reverberant Energy Ratio (DI, for Directivity Index).

• Absorption Acoustic Treatment: Utilize sound-absorbing materials like acoustic panels, thick curtains, or carpets on walls and ceilings. This helps soak up unwanted reflections, shorten ITDG, and improve overall clarity.

• Diffusion Acoustic Treatment: Consider incorporating diffusers to scatter sound more evenly throughout the room. This can reduce the impact of strong direct reflections and further enhance overall clarity.

In most cases, proper acoustic treatment combined with speakers that offer constant directivity with a coverage adapted to your listening distance, oriented to the central listening position, will provide the more effective solution.

Constant Directivity

While constant directivity speakers (those that radiate sound uniformly across frequencies) can offer some advantages:

Consistent ITDG: Constant directivity speakers can help maintain a more consistent ITDG across the listening area, regardless of the frequency content of the sound. This can be beneficial for achieving a more uniform and predictable sound experience.

C20 and C50 Integration Times Explained:

The Time Period of Integration (TPI) represents the time window during which our auditory system fuses sound reflections with the direct sound, perceiving them as a single event rather than distinct echoes. This “fusion effect” is crucial for spatial perception and clarity. The TPI varies with frequency, distance, and other factors such as sound complexity, listening environment, and listener age. To understand how TPI influences our perception and room acoustics, see the detailed explanation at Critical Distance — Time Period of Integration (TPI).

In the context of EDT measurement using the exponential sine sweep method, C20 and C50 represent different integration times used when calculating the decay curve. These integration times essentially filter the measured data to focus on specific frequency ranges:

• C20: This integration time emphasizes the decay of mid-range frequencies (around 200 Hz to 4 kHz) which are particularly important for speech intelligibility.

• C50: This integration time considers a broader frequency range (around 50 Hz to 10 kHz) and provides a more holistic picture of the room’s overall reverberation characteristics.

By analyzing the decay curve using both C20 and C50 integration times, acoustic professionals can gain a more comprehensive understanding of the room’s absorption properties at different frequencies, which ultimately influences both ITDG and overall sound clarity.

Conclusion

By understanding ITDG, critical distance, radiation coverage, and speaker directivity, you can achieve a more comprehensive approach to optimizing the acoustics in your living room or home theater. By considering these factors alongside the previously mentioned techniques, you can create a space with clear, well-balanced sound that enhances your listening experience.

What is Critical Distance ?

In sound reproduction, achieving a balanced listening experience depends on the interaction between the direct sound from the speakers and the reflected sound bouncing around the room (often referred to as the diffuse field).

This ideal balance is often described as a 50/50 ratio of direct to reverberated sound. However, this is a guideline, and preferences can vary depending on the music and your personal taste, with some favoring a 60/40 or 40/60 mix.

The critical distance is the distance from the speakers where the direct and reflected sound levels become roughly equal. It’s influenced by some key factors:

• Room Acoustics (Sabine Absorption): Sabine absorption refers to the total amount of sound energy absorbed in a room, calculated using the Sabine equation, which relates reverberation time to the room’s volume and absorption properties. Higher absorption reduces reverberation, while lower absorption increases it.

  Mathematically, rooms with lower absorption (more reflective surfaces, low alpha sabine) should have a longer critical distance, as the direct sound needs to travel farther before reaching a 50/50 balance with the reverberant field.

  However, in practice, the opposite effect is often observed because the reverberant field is primarily sustained by sidewall reflections, while absorption is typically concentrated on the front and/or rear walls and not on side wall to preserve the Listener envelopment, altering the distribution of reflections and increasing the effective critical distance.

• Speaker Directivity Factor: Speakers with a wider dispersion pattern (spreading sound over a larger area) generally have a shorter critical distance when a narrower ones has a longer one. This is because the off-axis sound increasing sound energy by bouncing off walls and other surfaces.

  • Wider Dispersion: Speakers with a wider dispersion pattern (spreading sound over a larger area) generally have a shorter critical distance. This is because they excite a larger portion of the room with off-axis direct sound, leading to a higher overall level of sound energy reaching the listener even at closer distances. However, these speakers also tend to contribute more to the reverberated field due to the increased sound energy bouncing off walls and other surfaces.
    Generally 90° constant directivity horn are adapted from 2/2m50 to 5/6m.

  • Narrower Dispersion: In contrast, speakers with a narrower dispersion pattern focus sound energy within a more concentrated cone. This means that a smaller portion of the room is directly excited, requiring a longer listening distance to achieve a similar level of sound energy compared to wider dispersion speakers. While they contribute less to the overall reverberated sound due to the focused sound direction, achieving a balanced sound experience with these speakers might necessitate sitting further away.
    Generally 80/70° constant directivity horn are used after 5/6m.

Additional Considerations:

• Frequency and Directivity: The balance between direct and reverberated sound can also vary with frequency due to speaker directivity. Speakers with constant directivity help to maintain a more consistent balance across the listening area.

• Speaker Placement: While not directly related to critical distance, proper speaker placement can enhance the sound experience. Avoid placing the listening position (sofa) directly against the wall. This ensures the listener isn’t too close to the wall, affecting the ideal balance of direct and reflected sound. Additionally, maintaining some space between the seating area and the walls promotes better sound dispersion throughout the room. Angling the speakers slightly towards the listening area can create a more focused and engaging soundstage.

The formula can be found in Appendix A.

Why Respect It?

Respecting critical distance, along with using constant directivity devices and proper acoustic treatment when possible, allows us to achieve an optimal sound balance in the listening room. This translates to several benefits:

More Neutral and Faithful Sound: By achieving a balanced mix of direct and reflected sound, we hear the audio closer to how it was intended to be heard by the artist or sound engineer. The sound becomes more natural and accurate, avoiding unwanted coloration.

Increased Listening Volume Without Fatigue: Our hearing is generally more sensitive and find their limit at the most sensitive part of our ears. When the critical distance is not respected, especially in rooms with low absorption, reflections can cause an excess of high-frequency energy. This creates a fatiguing and harsh sound, forcing us to listen at lower volumes.

By adapting directivity to our listening distance, we can achieve two key benefits:

• Controlled High Frequencies: The speaker’s directivity helps focus high-frequency sound towards the listener, reducing uncontrolled reflections and preventing high frequencies from becoming harsh or fatiguing. This targeted approach allows for a more balanced energy spectrum across all frequencies. The highs won’t overpower the lows, resulting in a more natural,faithful and detailed listening experience.

• Improved Lower Frequency Presence and higher volume listening: With a balanced energy spectrum, we can listen at higher volumes without experiencing ear fatigue caused by excessive high frequencies, critical distance plays a role in how we perceive the low frequencies in comparaison to the high ones when they are controlled according to listening distance and with constant directivity behavior.
  When the balance is right, the low frequencies will have a stronger presence without overpowering the rest of the sound.

In simpler terms, respecting critical distance helps us achieve a more natural, balanced, and enjoyable listening experience at higher volumes without listener fatigue.

Modern Speaker Design: Beyond the 120-Degree Coverage Myth

Nowadays, many loudspeakers prioritize achieving a strict 120-degree sound dispersion (directivity) across all frequencies.

However, this “one-120°-coverage-fits-all” approach ignores psychoacoustics (how we hear) and the great impact of listening distance.

In most rooms, a 90-degree horizontal constant directivity provides a more even distribution of sound energy, creating a well-balanced listening experience.

This approach recognizes the concept of critical distance. Conversely, 120 degree dispersion in a typical listening environment will excite the sidewalls too much (creating too much reflected sound) and will make the sound less and less balanced and more and more aggressive the further we go away to the speakers.

Here is a guide for listening distance and type of horn with coverage (most of our horns are availables in several coverage) we can use:

Direct, Reverberated Field and Modal regime

Understanding the behavior of sound waves in a room is crucial for achieving a good listening experience. Here, we’ll differentiate between two key concepts and explore some additional factors influencing low-frequency response:

Direct and Reverberated Field

• Direct Field: This refers to the sound that travels directly from the source (speakers) to the listener without any reflections from walls or other surfaces. The intensity of the direct field decreases with distance following the inverse square law, meaning it weakens by 6 dB for each doubling of distance. This is why sound gets progressively quieter as you move further away from the speakers.

• Diffuse or Reverberated Field: A diffuse sound field is one that is homogeneous and isotropic (exhibits the same properties in all directions) throughout the volume of a room at any given time. It is made up of an infinite number of plane waves propagating in all directions. There are no major room-related anomalies to be observed in the measurements. Unlike the direct field, the diffuse field level is considered relatively constant within the listening area. This is because the sound has reflected numerous times and reached the listener from various directions, averaging out any distance-related variations.

It’s important to note: While the diffuse field is considered relatively constant within the listening zone, the overall sound pressure level (SPL) in a room, including the contribution from the diffuse field, will still decrease with distance from the speakers following the inverse square law. This decrease is primarily caused by the direct sound attenuating with distance, while the diffuse field level remains more stable within the listening area.

Modal Regime and Modes:

In addition to the concepts above, two other factors significantly influence how sound behaves in a room, particularly at lower frequencies:

• Modal Regime: This refers to a situation where reflections are very important but localized and resonate at specific frequencies. These localized reflections coexist with absorptions at nearby frequencies, leading to a chaotic response, especially noticeable in the low frequencies (30-80Hz) of typical living rooms.

• Modes: These chaotic responses manifest as large peaks and dips (typically +/- 15dB) in the sound pressure level at specific frequencies. They arise because the room dimensions create resonances where sound waves are reflected back and forth, reinforcing certain frequencies and cancelling others.

The consequence of these modes is the creation of resonance frequencies and a type of reverberation that’s specific to the room itself. Even small changes in speaker position can significantly alter this response.

Schroeder Frequency:

The Schroeder frequency is a critical transition zone, often with a wide range, that separates the modal regime from the diffuse field. Below the Schroeder frequency, the modal regime dominates, leading to the chaotic response described earlier. Above the Schroeder frequency, the diffuse field becomes more prominent, with sound reflecting more randomly throughout the room and creating a smoother response.

Room Size and Schroeder Frequency: The size of the room significantly impacts the Schroeder frequency. Larger rooms have a lower Schroeder frequency. In very large rooms, the Schroeder frequency can even fall outside the audible range of human hearing. This means that even low frequencies will exhibit a more diffuse character, which is often considered ideal for listening experiences. In these large rooms, the density of modes in the low frequencies becomes high enough to create a diffuse response.

The formula can be found in Appendix B.

Time Period of Integration (TPI), the brain interpretation:

The time period of integration (TPI) is the time window within which our auditory system perceives sound reflections as part of the direct sound rather than distinct echoes. This phenomenon is known as the “fusion effect.”

• If a reflection (Diffuse Field) arrives within a certain time delay (TPI), it merges with the direct sound, creating a single auditory event.
• If the delay exceeds the TPI, the reflection is perceived as a separate echo.

The TPI depends on several factors:

• Frequency: TPI is generally longer at lower frequencies and shorter at higher frequencies.
• Distance: The TPI increases with the distance between the sound source and the listener.
• Head size: The TPI is slightly affected by the size of the listener’s head.

Additional Factors:

The TPI is influenced by various factors beyond the distance and frequency:

• Sound type: Complex sounds like speech have longer TPIs than pure tones.
• Listening environment: TPI can be longer in noisy environments.
• Listener’s age: TPI tends to increase with age.
• Level difference between direct sound and reflections: Higher level differences lead to shorter TPIs.

Thévenot’s Fusion Curve:

This curve illustrates the relationship between the TPI and the level difference between the direct sound and its reflection.
A higher level difference allows for a longer TPI, meaning that reflections can arrive later without being perceived as echoes.

The formula can be found in Appendix C.

Haas Effect

The Haas effect is a psychoacoustic phenomenon related to the TPI.

If two identical sounds arrive very close together (under 35 milliseconds), our brains perceive them as a single sound coming from the direction of the first sound to arrive.

This allows sound engineers to increase sound level in the back of a room without affecting perceived sound direction by using delaying signal sent to a relay speaker.

In room accoustics in our reverberated field the early reflection on the near wall can create another “virtual” source and enter in Haas effect, it can be negative if the amplitude of this virtual source is too high.

Conclusion and additional considerations:

The critical distance formula is most accurate in ideal conditions with a well-established diffuse sound field (even distribution of sound throughout the room). In real rooms, this might not always be the case.

The formula is also only strictly valid if the listening position is directly on the speaker axis.

There’s no one-size-fits-all solution. Experiment, consider the factors mentioned, and personalize your listening experience, there is no golden rule because every room acoustics is different, but we often see:

• 90° constant directivity horn: 2/2m50 to 5/6m
• 80/70° constant directivity horn: 5/6m and more
• Line array: very long distance outdoors (large festivals, no obstavle), the distance between the center of the first speaker and the center of the last speaker must be equal to or greater than the wavelength of the lowest frequency reproduced, knowing that 80hz is a wavelength of 4m25.
  The main goal of line array is in fact to maintain SPL for everybody at distance, nor really the directivity.

Appendix A: Calculating Your Ideal Listening Distance

Experiment with different listening distances to find the sweet spot that sounds best to you.
Consider the size of your room and the type of speakers you have.
Take into account your personal preferences for a more direct or spacious sound.

Critical Distance Formula:

The critical distance, which is the theoretical distance for achieving a 50/50 balance, can be calculated using the following formula:

dc = √(αQ / 50)

Where:

dc is the critical distance in meters
α is the Sabine absorption equivalent in m²/s (explained below)
Q is the directivity factor of the speaker (a value representing how the speaker spreads sound)

Directivity factor represents the speaker’s tendency to focus sound in specific directions compared to an ideal omnidirectional source radiating sound equally in all directions.

High Q: Indicates a more directional speaker, concentrating sound energy in a narrower beam.
Low Q: Indicates a more omnidirectional speaker, radiating sound more evenly.

Understanding Q is crucial in the formula as it influences the critical distance (dc):

Higher Q (more directional): Leads to a greater critical distance. This means you can sit further away from the speaker and still maintain a good balance between direct and reflected sound (50/50 ratio).
Lower Q (less directional): Results in a shorter critical distance. You need to sit closer to the speaker to achieve the desired balance.

Remember:

• Q is usually measured in decibels (dB).

• It often varies with frequency.

• Speaker design significantly impacts directivity.

Sabine Absorption Equivalent (α):

The Sabine absorption equivalent (α) represents the total sound-absorbing capacity of a room. It essentially measures how effectively a room absorbs sound energy and prevents reflections. A higher α value indicates greater sound absorption, leading to a shorter reverberation time (less echo) and a potentially quieter environment. Conversely, a lower α value means more reflections and a longer reverberation time, resulting in a noisier and potentially less comfortable space.

Calculating Sabine Absorption:

The total Sabine absorption of a room can be calculated by summing the product of the surface area of each material and its corresponding sound absorption coefficient (SAC).

Total Absorption (α) = Σ (Surface Area x Sound Absorption Coefficient)

Σ (sigma) represents the summation over all materials in the room.

Sound Absorption Coefficient (SAC):

The sound absorption coefficient (SAC) is a value between 0 (perfectly reflective) and 1 (perfectly absorbent) that specifies how well a particular material absorbs sound at different frequencies. Different materials have different SAC values, and understanding these values is crucial for calculating the total Sabine absorption of a room.

Appendix B: Schroeder frequency formula

Fs = 2000 * √(T/V)

Where:

Fs is the Schroeder frequency in Hertz (Hz)
T is the reverberation time of the room in seconds (s)
V is the volume of the room in cubic meters (m³)

Appendix C: TPI formula

The TPI can be estimated using various formulas, including:

Schroeder’s Formula: TPI = 0.6 * (c / f) * (1 + (d / r))
Blauert’s Formula: TPI = 1.5 * (c / f) * (1 + (d / r))^0.5
Houtgast’s Formula: TPI = 4.2 * (c / f) * (1 + (d / r))^0.4

Where:

c is the speed of sound (approximately 343 m/s)
f is the sound frequency in Hertz (Hz)
d is the distance between the sound source and the listener (in meters)
r is the radius of the listener’s head (approximately 0.0875 m)

Wavefront Basics and Challenges:

Sound travels in waves, and the shape of the wavefront determines how the sound propagates in horns. Ideally, the wavefront should smoothly follow the horn’s curvature for optimal constant directivity (controlled sound dispersion).

However, horns with diagonal sections pose a challenge. A wavefront, while traveling at the speed of sound, inherently wants to maintain a 90-degree angle to its edges.

This tendency is crucial when the wavefront encounters sudden geometry changes, like those found in diagonal horn sections.

These rapid transitions can “pull” and deform the wavefront in some points, causing a phenomenon called diffraction (bending and spread out).

The Problem: Cross Syndrome in Horns or Waveguides

When a round waveguide transitions too quickly to a square or rectangular shape, bypassing the elliptical stage or another smooth way to do, it creates a sudden change in the wavefront’s edges expansion rate.

This rapid change causes diffraction primarily at the diagonals, disrupting the wavefront in high frequencies. This phenomenon can be named “cross syndrome” as the wavefront will form a cross shape.

Why We Hear It: Audibility

Even subtle changes in the direct sound caused by diffraction will be audible due to how we listen in rooms.

Most listening happens within the “critical distance” where both direct sound from the speaker and reflected sound bouncing off walls contribute significantly in a ratio close to 50/50.

This means even diffraction effects off axis become noticeable even when listening directly in front of the speakers.

These compromised wavefront are audible and present in your listening experience. This will lead to a:

• “Floating” sensation: The compromised wavefront might seem disconnected from the rest of the soundstage, creating an unnatural spatial impression.

• Shifting power response: As the off-axis sound degrades with increasing frequency due to diffraction, the perceived balance of the sound can change, making it seem less powerful or detailed at higher frequencies.

A proper wavefront should be round or elliptical, not cross shaped. The horn mouth is not in cause, it’s the overall profile.

Why some measurement don’t detect it

A horizontal polar is done at a 0° vertical position, and a vertical polar is done at a 0° horizontal position. This means that the measurement is valid on two 2D planes.

Some designs that can suffer from cross wavefront syndrome, such as MEH/synergy horns, should be measured diagonally, and a diagonal polar plot should be provided.

We also need to pay attention to scale. A “half-space” option in VituixCAD displays the polar response over 180° instead of 360°. If we stay in the 360° mode, the scale is affected, and the polar response may appear more consistent than it actually is.

The same issue exists with the color scale, where using solid colors for a 2 or 3 dB range instead of a gradient can hide certain problems.

Lastly, an even simpler issue is with polar maps that start at 0 dB or use the same color for ranges like +6 dB to -2 or -3 dB (and sometimes even down to -6 dB). This completely obscures the true response of the horn.

AudioHorn Solution

X-Shape horns and PureShape tweeter waveguide address this problem by focusing on the diagonal transitions.

Using advanced Finite Element Analysis (FEA), a specific diagonal profile is designed to ensure the wavefront maintains its integrity, even along these critical axes.

This allows the wavefront to smoothly follow the curvature without encountering drastic changes in geometry, removing diffraction as we can see here with a polar of the X-Shape diagonal (the worst place to measure a horn) :

In the world of sound manipulation, both delay and acoustic phase play a vital role, influencing how we hear and experience audio. While often used interchangeably, understanding the distinction between them is key to achieving desired sonic effects.

Delay: A Controlled Time Shift

Delay, in the context of Digital Signal Processing (DSP), refers to the intentional postponement of a sound signal by a specific time interval. Think of a sound wave reaching your ears. With delay, a copy of that wave is electronically held back for a fraction of a second before being released. This creates an echo effect, a delayed replica following the original sound.

Acoustic Phase: The Timing Within the Wave

Acoustic phase, on the other hand, is an inherent property of sound waves themselves. Every sound wave has a cyclical pattern of peaks and troughs, representing areas of high and low pressure. Acoustic phase refers to the specific point within this cycle at which the sound wave begins. Consider two identical sound waves playing simultaneously. If their peaks (or troughs) line up perfectly, they are considered “in phase.” Conversely, if one wave’s peak coincides with the other’s trough, they are “out of phase.”

The Combined Effect on Sound Perception

The interaction between delay and acoustic phase significantly influences how we perceive sound. In-phase sounds tend to reinforce each other, leading to a louder and fuller perception. Out-of-phase sounds can partially or completely cancel each other out, resulting in a quieter or thinner sound.

As an example: Two speakers playing the same sound, but one speaker experiences a slight delay compared to the other. Depending on the delay time and the specific frequencies involved, the sounds from the speakers may combine constructively (in-phase) or destructively (out of phase). This can lead to comb filtering, where certain frequencies are boosted while others are attenuated, creating an uneven tonal response.

The Interplay in Crossover Design

In crossover design, both delay and acoustic phase interact to influence the sound reaching the listener. Here’s how:

• Phase Alignment: Ideally, at the crossover frequency, the acoustic phases of the woofer and tweeter outputs should be aligned. This ensures their peaks and troughs coincide, resulting in a coherent and balanced sound.

• Phase Shifts in Filters: Crossover filters inherently introduce phase shifts at different frequencies. By strategically adjusting the delay applied to each driver, we can compensate for these phase shifts and achieve a more linear overall phase response across the crossover region.

The Collaborative Effort

Delay and acoustic phase are distinct concepts, but in crossover design, they work together to achieve a smooth and accurate transition between drivers. By understanding their individual roles and their interaction, loudspeaker designers can optimize crossover performance for a superior listening experience.

What is “Honk” Sound

The term “honk” in audio is often associated with an undesirable coloration that gives a nasal or hollow character to the sound. This phenomenon can arise from several combined sources:

• Throat resonances: Unintended resonances within the throat of a horn can introduce peaks in the frequency response, leading to a honky character.

• Time-domain anomalies: A combination of throat resonance and an abrupt termination of the horn profile can create reflections and energy storage effects, resulting in temporal smearing.

• Path length differences: A significant delay caused by a long acoustic path in the horn compared to other frequency components can lead to phase cancellation, creating irregularities at the crossover point.

• Propagation modes in the horn: Certain horn geometries, especially older and curved designs with non-optimized profiles, can support unwanted propagation modes (cutoff modes). These modes interfere with the main signal, introducing frequency and phase anomalies that contribute to a honky sound.

• Diaphragm breakup: Older compression driver diaphragms exhibited breakup modes at lower frequencies than modern designs, potentially contributing to a honky coloration.

History

At the beginning of the audio industry, amplifiers were unable to deliver significant power. Early tube amplifiers could only produce a few watts:

         

         

To compensate for this limitation, the audio industry relied on high-efficiency acoustic loading — at the expense of everything else. This focus on maximizing efficiency with a very long throat came with severe trade-offs in linearity, directivity control, resonances, viscothermal losses, higher-order modes (HOM), and increased distortion at high frequencies — together, these phenomena can be perceived as “Honk”.

This approach also led to significant compromises in overall sound quality and directivity control.

A prime example is the Western Electric 15A, introduced in the 1920s:

         

         

With measurement and distortion at 90dB SPL at 1m with a Lamar compression driver:

         

Over time, this early limitation wrongly became a defining trait of all horn-loaded systems, giving rise to a persistent and unfounded cliché. Despite decades of advancements in horn design, many still associate horns with this outdated flaw, even though modern designs have completely eliminated the causes of “honk.”

How Audio Solved It

The issues that caused the “honk” sound a century ago have been progressively eliminated thanks to technological advancements. Key improvements include:

• Amplifier advancements: With the transition from low-power tube amplifiers to Class AB and now Class D, power is no longer a limiting factor. We can now use the adapted horn loading, optimizing horn throat design while respecting wavefront propagation.

• Finite Element Analysis (FEA) and simulation: Modern modeling tools allow engineers to simulate wavefront behavior with precision, ensuring optimal throat shaping and loading without introducing unwanted artifacts.

• DSP and active filtering: Digital processing has definitively solved the delay issues between components, making phase alignment and crossover transitions seamless.

• Fluid horn profiles: These advanced geometries eliminate throat resonances, further enhancing clarity and accuracy in sound reproduction.

• Improved compression drivers: Innovations in diaphragm materials, surround design, and phase plugs have pushed time-domain issues far beyond the range of human hearing, effectively eliminating artifacts associated with older designs.

• Better understanding of wavefront behavior and directivity: Over the years, extensive research has deepened our knowledge of how wavefronts propagate within horns, helped by FEA. We now fully understand the importance of directivity matching between drivers to ensure a smooth frequency response tansition at crossover and avoid accidents at the crossover region.

The Role of Crossover Optimization and Directivity Matching

A common misconception is that midrange crossovers inherently degrade sound quality.

However, modern design techniques ensure that, when properly implemented, crossovers pose no issue. By precisely controlling:

• Delay
• Phase alignment
• linear SPL
• Crossover frequency chosen considering distortion and directivity matching
• Proper and stronger slope

Properly implemented systems achieve seamless transitions between drivers without introducing audible artifacts.

One crucial aspect often forgotten is directivity matching at the crossover point. If the directivity patterns of adjacent drivers do not align properly, this can lead to a perceived “empty midrange,” where energy is either lost off-axis or becomes accidented.

By carefully designing the crossover region to maintain a consistent radiation pattern, we ensure a smooth and natural transition across the frequency spectrum.

Today’s tools, such as VituixCAD and REW, allow for advanced crossover simulation, measurements and optimization of crossover design including directivity match, ensuring perfect integration between components. Thanks to these technologies, crossover points in the midrange are no longer a limitation but rather an integral part of achieving optimal performance.

Conclusion

The so-called “honk” sound was a byproduct of early horn-loaded systems, where efficiency was prioritized over all other design considerations due to amplifier power limitations. These compromises led to resonance issues, poor directivity control, and time-domain distortions that reinforced the negative perception of horns.

However, modern advancements in amplification, simulation, DSP, horn geometry, and compression driver technology have completely eliminated the root causes of “honk”. Today, properly designed horn-loaded systems benefit from optimized throat loading, controlled directivity, and seamless crossover transitions. Software like VituixCAD ensures precise phase alignment, time correction, and directivity matching in crossovers, making them transparent and free of artifacts.

In short, “honk” is a relic of the past, a problem solved long ago. Properly implemented horn designs now offer high efficiency, controlled dispersion, and accurate sound reproduction without compromise.

The outdated cliché of honky horns persists, but the reality is that modern constant directivity horn systems, when properly designed with loading capacity as we do, achieve unmatched linearity, phase coherence and neutrality, setting the benchmark for high-performance loudspeaker design.

Demystifying Directivity Match

In the world of loudspeaker design, achieving a seamless transition between different driver components is crucial for optimal sound quality.

This article delves into the intricacies of directivity matching between horns or waveguides, and woofers, a process that ensures a cohesive and natural listening experience.

The Importance of Directivity Match

When designing a loudspeaker that combines a woofer with a horn-loaded or waveguided high-frequency driver, one critical aspect is matching their directivity patterns around the crossover region.

Each direct radiation driver has its own transition frequency, the frequency at which the loudspeaker’s directivity changes from wide (omnidirectional) dispersion to narrower, more focused dispersion due to the physical size of the source. This transition frequency is roughly estimated by the formula f = c / (2πR), where R is the effective radiating radius.

Understanding Cone Radiation Directivity

There are two main stages of diaphragm – or cone driver – behavior as frequency increases: pistonic motion and non-pistonic motion.

At low frequencies, the diaphragm moves uniformly in pistonic motion, radiating sound broadly and evenly.

As frequency rises, the size of the radiating surface becomes comparable to the wavelength, causing phase differences (delays) between the diaphragm center (driven by the voice coil) and its edges. These phase shifts lead to a progressive narrowing of directivity.

This transition from pistonic to non-pistonic motion primarily results from geometric and wave propagation effects across the diaphragm surface, and it occurs even if the diaphragm material were perfectly rigid.

Material properties like stiffness and damping can also influence diaphragm behavior but have a lesser impact on directivity compared to the geometric phase effects.

This narrowing of directivity is the reason why the crossover to the high-frequency driver is usually placed around that frequency, so that both drivers have matching directivity for a smooth sound transition.

The size and shape of the baffle also affect this directivity transition.

This transition frequency f_transit can be approximated by:

f_transit ≈ c / (2 π R)

where c is the speed of wave propagation in the diaphragm material, and R its radius.

Why Directivity Match Matters

At the crossover frequency (close to the transition frequency), the directivity of both drivers should ideally match to ensure a smooth spatial response.
Without this match, response dips appear off-axis, degrading the coherence of the reproduced soundstage.

Even when listening on-axis only, the reverberated energy — shaped by off-axis radiation interacting with room acoustics — plays a significant role in the perceived sound.

This is because, at typical listening distances around the critical distance, the sound reaching the listener is approximately a 50/50 mix of direct sound from the speaker and reverberated sound reflected by the room.

If the woofer’s directivity narrows too much in the crossover region, it emits little energy off-axis in that frequency range. As a result, the room receives less energy in this midrange band, creating an energy dip in the perceived sound and a sensation of an “empty midrange.”

This interplay between directivity and room reflections makes directivity matching crucial for natural tonality, clarity, and spatial coherence.

Acoustic Center Distance

Another key factor is the physical distance between the acoustic centers of the woofer and the high-frequency driver.
Ideally, this spacing should be less than or equal to 66% of the wavelength at the crossover frequency — a topic we cover in more detail in our vertical lobing article.

Minimizing this distance helps maintain vertical consistency, reducing lobing artifacts and further reinforcing the perception of a seamless transition between drivers.

Empty Midrange Feeling

Some mid-woofer drivers, such as those from PURIFI, have excellent distortion performance. This often makes it tempting to push their usable range higher than usual.
However, as previously discussed, a woofer’s directivity narrows as frequency increases.

For example, an 8-inch woofer becomes too narrow in dispersion after around 1200–1300 Hz to blend properly with a wide-dispersion device like an AMT or a direct-radiating tweeter.
Using such a crossover point leads to a poor directivity match: at crossover, the tweeter still radiates energy widely off-axis, while the woofer no longer does.

The result is a significant mismatch in how sound is distributed in space.
This isn’t visible in the on-axis frequency response but becomes obvious in polar plots and, more importantly, audible in the room.

It can produce what many describe as an “empty midrange” — not because those frequencies are absent on-axis, but because the woofer no longer emits energy off-axis in that range.
As a result, the room does not reflect those frequencies back to the listener as it does for lower or higher bands, creating a dip in perceived energy and listener envelopment in the midrange.

In other words, it’s the interaction between the woofer’s narrowing directivity in the crossover region and the room’s reflective field that creates this perceptual gap.

The Perfect Match: A Myth?

The pursuit of a perfect directivity match at all frequencies, can be a misguided approach. Measurements taken in anechoic chambers (highly sound-absorbent environments) often reveal that achieving this perfect match is practically impossible. Here’s where the crossover filter design comes into play.

The crossover slope, along with meticulously adjusted time delays, plays a vital role in ensuring a smooth transition between the woofer’s coverage and the horn/waveguide’s coverage. This transition should be free of abrupt changes (on-axis or off-axis) to avoid unwanted coloration or distortions in the sound.

Moreover, a common misconception in modern loudspeaker design is prioritizing an exact 120-degree directivity match at crossover and up to 20 kHz on the depends of more important aspects like coverage adapted to listening distance.

This “one-120°-coverage-fits-all” approach leads to completely ignores psyckoacoustics principles and coverage adapted to distance as see in critical distance article.

Improved Directivity with Round-Over Returns

Our horns incorporate a design element called a “round-over return.” This feature enhances directivity control by mitigating the narrowing effect call midrange narrowing/beaming that occur in the midrange frequencies.

The round-over return is a smooth, curved transition that seamlessly follows the horn’s profile until it meets the side of the enclosure. This design minimizes disruptions to the wavefront, preventing unwanted narrowing of the sound dispersion pattern in the midrange.

Benefits of Round-Over Returns:

• Improved Directivity: By eliminating midrange narrowing, the round-over return ensures a more consistent and predictable directivity pattern across the entire frequency spectrum.

• Smoother Sound Transition: The smooth curvature of the return minimizes potential phase cancellations and contributes to a more natural and seamless transition between the horn and the enclosure.

• Enhanced Off-Axis Response: The improved directivity control translates to a more consistent tonal balance thanks to coherent power response (the fusion of direct and reverberated field as seen upper), for listeners positioned both on and off-axis from the speaker.

Directivity Matching Between Horns: A Different Approach

When dealing with multiple horns or waveguides in a loudspeaker design, the crossover approach differs slightly. Here, the ideal crossover point is not where each component loses its directivity, but rather where both maintain a constant directivity pattern. This constant directivity should be consistent not only at the crossover frequency but also one octave below and one octave above the crossover point.

Following these principles of directivity matching ensures a natural and cohesive sonic experience for the listener, free from unwanted artifacts and with a smooth transition between different driver components within a loudspeaker.

When sound travels from your speakers, it bounces off nearby surfaces. Reflections from the floor and ceiling, in particular, can significantly impact the overall sound you hear. These reflections arrive slightly later than the direct sound from the speaker, creating a phenomenon known as comb filtering.

Comb filtering essentially adds and subtracts certain frequencies at specific points in the listening area. This can lead to uneven tonal balance, with some frequencies being boosted and others being cancelled out.

How Directivity Affects the Bounce

The way a speaker distributes sound (directivity) plays a big role in how susceptible it is to floor and ceiling bounce.

Speakers with narrow vertical dispersion tend to excite less the rebound, minimizing the impact of reflections from above and below.

Total Early Reflection (TER) and the Room Equation

While speaker manufacturers typically provide a frequency response curve showing a speaker’s output at different frequencies, this is usually measured in an anechoic chamber – a special environment designed to absorb sound reflections. In a real room, reflections from the floor, ceiling, and walls significantly impact the sound you hear.

Total Early Reflection (TER) is a crucial concept that helps us understand this real-world sound experience. TER specifically measures the combined effect of the first reflections that arrive at the listening position after bouncing off nearby surfaces. These early reflections can significantly alter the tonal balance and overall clarity of the sound.

Evolutionary Adaptation and the Human Auditory System

Interestingly, our brains have likely adapted to compensate for the effects of room acoustics to some extent. For millennia, since the days of Homo sapiens living in caves, our auditory systems have been processing sound in environments with reflections.

This means our brains may be able to partially “correct” for some of the coloration caused by floor and ceiling bounce.

Crossover Design and Minimizing Interference

Another factor to consider is speaker crossover design. A crossover is a circuit that divides the audio signal into different frequency ranges and directs them to the appropriate speaker drivers (woofer, tweeter, etc.).

When the crossover frequencies are close to the resonant frequencies caused by floor bounce, it can be use, by looking power response, to diluate the bounce effect by taking account in crossover design.

Imagine two drivers in a speaker – one positioned higher and one positioned lower. If they are reproducing similar frequencies at the same time, but one is slightly delayed due to its distance from the floor (floor bounce), they can interfere with bounce effect differently.

Crossover design can plays a role in minimizing the impact of floor bounce. While the height difference between drivers can cause slight phase delays, a well-designed crossover can address this. By analyzing the power response, the crossover can be designed to “dilute” the bounce effect, reducing unwanted reflections but it shouldn’nt be done at the expense of putting mid-woofer/woofer as close at possible of tweeter section.

Taming the Bounce: Achieving Optimal Listening

By understanding the effects of floor and ceiling reflections, directivity, power response, and even our own evolutionary adaptations, we can achieve a more balanced and enjoyable listening experience in any room. Here are some tips:

• Speaker placement: Experiment with speaker positioning relative to the walls and your listening area. Even a few inches can make a difference.

• Room treatments: Consider acoustic panels or diffusers to absorb or scatter sound reflections, especially if your room has hard, reflective surfaces.

• Understanding crossover design: While not directly controllable by the listener, being aware of how crossover design can minimize interference due to floor bounce can be helpful when choosing speakers but it must not be done on the depend of the point below.

• Lower crossover frequency: As mentioned earlier, a lower crossover encourages the woofer to handle a wider range of frequencies at lower wavelengths. This promotes better directivity at the lower frequencies most susceptible to floor bounce, reducing the overall energy bouncing around the room.

• Narrower vertical dispersion: Speakers with wider vertical dispersion spread the sound out more, which can actually increase reflections off the floor and ceiling. Conversely, speakers with narrower vertical dispersion tend to focus the sound more towards the listening area, minimizing the interaction with reflective surfaces above and below. It’s one of the raison that the coverage should be choosen according to listening distance and acoustic.

Horn Loading and Efficiency

Horn loading is a technique used in loudspeakers to improve efficiency by shaping how sound is transferred from the driver to the surrounding air. This article explores the different aspects of horn loading, its frequency dependence, and its relationship with directivity and wavefront geometry.

We will expose technical considerations necessary for a full understanding of the phenomenon, then present a conclusion.

Acoustic Impedance

Acoustic impedance (Z) is defined as the ratio of sound pressure (Pa) to particle velocity (v):

Z = Pa/v

It characterizes how easily an acoustic wave propagates through a medium or across a boundary between two media. In practice, acoustic impedance measures the adaptation between two acoustic environments, such as a loudspeaker coupling into a room, or a compression driver coupling into a horn.

Acoustic impedance is not directly audible. Instead, it governs how much of the acoustic energy is transmitted versus reflected at a boundary. A well-matched acoustic impedance maximizes energy transfer and minimizes unwanted reflections.

In horn-loaded loudspeakers:

• At low frequencies, where the wavelength is larger than the horn dimensions, the horn does not load efficiently and the acoustic impedance mismatch leads to reduced efficiency.
• At mid frequencies, the horn improves the impedance match, thereby boosting efficiency.
• At high frequencies, the impedance tends to rise again due to smaller wavelengths and internal viscous losses, reducing the overall gain.

Additionally, directivity impacts impedance: as a source becomes more directional (naturally or by design), the radiated impedance increases. Horns use this effect intentionally to “concentrate” the energy, but it must be controlled to avoid creating too much mismatch at the horn mouth.

Finally, acoustic impedance at the horn throat typically increases with frequency, and a very high impedance combined with high particle velocity can lead to thermal compression and distortion at high SPL levels.

With a horn featuring a smooth roundover at the mouth to avoid midrange narrowing, the acoustic impedance at the horn’s mouth approaches that of free air—very low and nearly linear—while the horn geometry progressively transforms this impedance towards the throat, ensuring efficient coupling with the driver.

Acoustic impedance is a complex quantity, comprising both resistive (dissipative) and reactive (energy-storing) components.

The horn influences both parts, but the reactive load is especially important as it temporarily stores and releases acoustic energy, shaping the frequency response and directivity of the system.

Reactive Loading

Reactive loading refers to the non-dissipative component of acoustic impedance — the portion that stores, rather than dissipates, energy.

In an acoustic system such as a horn, certain elements — like the confined volume of air near the throat — behave somewhat like a spring or a mass, temporarily storing energy in the form of potential or kinetic energy without dissipating it.

This reactive impedance resists rapid changes in pressure or displacement and varies with frequency.

At low frequencies, the confined air acts as an acoustic compliance (spring), increasing the total acoustic impedance and improving energy transfer from the driver to the air.

At high frequencies, this effect decreases, as the wavelength becomes shorter and the confined air no longer behaves as a significant reactive load.

In short, reactive loading is the frequency-dependent acoustic impedance caused by the storage of elastic energy in the air near the throat (and other regions), which helps match the transducer to free air — especially at low frequencies.

Particle Velocity

Particle velocity (v) is the oscillating motion of air particles caused by a sound wave. It differs from the speed of sound (celerity), as it describes the back-and-forth movement without any net displacement.

In audio systems:

• High particle velocity typically occurs in constricted areas, such as bass reflex ports, narrow ducts, or horn throats.
• At constant sound pressure, higher particle velocity means lower impedance.
• In general, as the cross-section narrows, the particle velocity rises, even if the frequency or SPL remains constant.

Thus, particle velocity must be carefully monitored when designing small apertures or highly compressed structures to avoid excessive velocities that cause distortion and energy losses; controlling it properly helps minimize nonlinear distortion and maximize power handling.

These nonlinear effects extend beyond simple harmonic distortion — they also generate intermodulation distortion, which arises from the interaction of multiple frequencies. Intermodulation distortion particularly degrades clarity and precision, adversely affecting the perceived fidelity of the sound.

The particle velocity within the throat limits the maximum power the horn can handle. This is why compression horns often feature throats with an optimized diameter — to control particle velocity, reduce turbulence and flow losses due to viscous and thermal boundary layer effects at the throat walls, and prevent the flow from exceeding the critical Mach threshold.

However, modern phase plugs allow for much higher compression ratios by ensuring equal impedance across each acoustic path.
This design distributes particle velocity more evenly, reducing local velocity peaks and enabling greater power handling without increased distortion, or allowing a smaller throat size to extend directivity control to higher frequencies without sacrificing maximum power.

Critical Mach Number

The critical Mach number describes when the particle velocity becomes a significant fraction of the speed of sound (Mach 1). In loudspeaker design, this is particularly relevant in narrow passages or throats where particle velocity can increase substantially.

The Mach number is defined as:

M = v/c

Where:

• v is the particle velocity,
• c is the speed of sound in the medium (≈ 343 m/s in air).

At a Mach number of around 0.1 to 0.3, the acoustic behavior starts to become nonlinear. Exceeding this critical Mach number results in:

• Strong nonlinearities (distortion),
• Turbulent flow,
• Thermal compression (heating due to intense localized motion),
• Potential efficiency loss and audible degradation.

Keeping particle velocity well below the critical Mach number ensures low distortion and optimal efficiency in horn-loaded designs.

For ports, we have developed a flat velocity port that allows us to keep the Mach number low.

How These Concepts Interact with Frequency

The interaction between reactive loading, acoustic impedance, particle velocity, and the Mach number depends strongly on frequency.

• At lower frequencies, reactive loading dominates. The confined air near the horn throat acts as an acoustic compliance, temporarily storing energy and improving energy transfer from the driver to the air. Sound waves have longer wavelengths, which results in lower particle velocities, reducing the risk of reaching the critical Mach number. Horn-loaded systems generally handle these frequencies efficiently, with minimal distortion or turbulence, benefiting from the positive effect of reactive loading.

• At higher frequencies, wavelengths become shorter and particle velocity increases more rapidly. In narrow openings, such as the throat of a horn or the port of a bass reflex system, the risk of exceeding the critical Mach number rises. This can cause distortion, thermal compression, and reduced efficiency.

  In practice, these effects occur mainly at very high SPLs or with extremely narrow throats. Modern phase plugs and impedance-optimized designs help manage airflow, reducing peak particle velocities and mitigating nonlinearities, while still allowing efficient sound radiation.

Proper impedance matching remains essential in horn design to minimize reflections and ensure optimal energy transfer. At higher frequencies, impedance tends to increase at the throat due to viscous and thermal losses, which can partially offset the efficiency gains from the horn.

In summary, frequency, horn geometry, throat size, and intended SPL all contribute to the balance between reactive loading, particle velocity, Mach number, and impedance. Understanding these interactions is key to achieving optimal performance across the horn’s operating range.

High-Order Modes (HOMs) in Horns

High-Order Modes (HOMs) are unwanted sound waves that can occur within a horn due to its geometry.

They deviate from the ideal plane wave propagation, causing peaks and dips in the frequency response as well as localized internal resonances.

These resonances affect directivity and linearity, coloring the sound and compromising acoustic neutrality and transparency.

Minimizing HOM Excitation

A well-designed horn aims to:

• Maintain a flat impedance profile across the desired frequency range. This helps to suppress the excitation of HOMs.
• Have a smoothly expanding horn throat to encourage the propagation of the fundamental wave mode (desired sound wave) and discourage the excitation of higher-order modes.

Influence of Throat Geometry and Mass Corner on Horn Loading

The way a horn loads the driver is primarily dictated by the throat design and the expansion profile, but the mass corner of the diaphragm also plays an important role.

• Throat geometry and expansion: A longer, more constricted throat increases low-frequency loading by enhancing impedance matching at low frequencies. However, this comes at the cost of increased acoustic resistance at higher frequencies, which can reduce efficiency and bandwidth in the upper midrange and treble. Conversely, a rapid flare (wider throat expansion) improves high-frequency performance but sacrifices low-frequency loading because of poorer impedance matching.

• Mass corner effect: The mass corner defines the transition between compliance-controlled (spring-like) and mass-controlled (inertia-like) behavior of the diaphragm. Above the mass corner, the diaphragm operates in a mass-controlled region where energy transfer into the horn is more efficient. Below the mass corner, the diaphragm becomes increasingly compliance-controlled, making efficient horn loading more difficult.

Thus, horn loading performance results from a combination of throat geometry and diaphragm behavior relative to its mass corner. When experimenting with different throat characteristics, a horn may appear to shift its frequency response at a certain point. This isn’t solely due to the mass corner or the horn’s geometry—it’s the result of both.

In classic direct-radiating loudspeakers with horn-loaded cones, it’s possible to optimize the impedance match between the cone and the horn’s throat by carefully designing the throat profile, like with a compression driver, thus minimizing efficiency loss around the mass-controlled transition while maintaining good loading.

Impedance Matching and Low-Frequency Considerations

For a cone driver in a horn-loaded speaker, impedance matching between the diaphragm and the throat is crucial, especially at higher frequencies, as this helps maximize SPL and minimizes energy losses due to reflections.

However, as frequency decreases toward lower midrange and bass regions, impedance matching becomes less critical for the following reasons:

• Longer wavelengths allow the throat to behave more “linearly” at lower frequencies.

• Acoustic resistance of the throat becomes less significant at lower frequencies, as pressure variations are smoother and energy propagates better over longer wavelengths.

• The horn’s low-frequency loading effect becomes more dominant, and impedance matching has less impact.

In summary:

• At high frequencies, proper impedance matching between the diaphragm and the throat is crucial for efficient energy transfer, minimizing reflections, and maintaining consistent frequency response.

• At low frequencies, imperfect impedance matching has a reduced impact on efficiency. Horn design at these frequencies is more concerned with maximizing acoustic loading and maintaining extension, rather than achieving a perfect impedance match.

How a Horn Increases Efficiency at Low Frequencies

The loading of a horn depends on several factors, including:

• Horn Geometry: The geometry of the horn, particularly the throat design and the expansion profile, strongly affects the acoustic loading and impedance matching. Surface propagation and horn depth also play a role, but the throat shape and expansion law are the primary factors.

• Mouth Size and Directivity Control: The size of the horn mouth largely defines where directivity control ends, particularly in the horizontal plane. If the horn loses control in the vertical plane too early, a portion of the acoustic energy can be lost or dispersed unpredictably, leading to reduced efficiency.

• Frequency of the Sound: Frequency fundamentally influences how the horn interacts with air impedance and controls sound radiation. Lower frequencies require larger horns to maintain good loading and directivity.

Here’s a breakdown of the key points:

• Acoustic Loading: A horn acts as an acoustic transformer, influencing the acoustic impedance “seen” by the compression driver. This allows for a better match between the driver’s impedance and the horn’s impedance profile across the desired frequency range, improving efficiency and sound radiation characteristics.

• Low Frequency Efficiency: At low frequencies, the impedance mismatch between the driver diaphragm (high impedance) and the air (low impedance) hinders efficient energy transfer.

• Matching the Air Load for Efficiency: Air has a relatively low acoustic impedance compared to the diaphragm of a compression driver. This impedance mismatch can lead to inefficient energy transfer from the driver to the air. A well-designed horn can influence the impedance profile “seen” by the driver, particularly at low frequencies. This allows for a better match between the driver’s impedance and the radiating medium (air). This improved impedance match can lead to increased efficiency, allowing the driver to operate with potentially reduced diaphragm movement for the same sound output (dB).

• Reduced Diaphragm Movement: With improved impedance matching, the driver needs to move less to produce the same sound pressure level at low frequencies. This reduces distortion and improves the overall efficiency of the driver.

Important Note:

This principle primarily applies to low frequencies. At higher frequencies, the horn’s effect on impedance matching becomes less significant, and other factors like diaphragm size and material come into play.

The “loading effect” is frequency-dependent. It has a stronger influence at lower frequencies and gradually diminishes as frequency increases.

For more information on energy distribution in horns, see : Horn and energy

A point about Constant Directivity Horns:

Since energy isn’t “free,” a constant directivity horn redistributes some of it off-axis to maintain consistent coverage. As a result, the on-axis response often shows a dip or a broad bell-shaped curve.

Conclusion

Importance of Throat

Building on the concepts developed in this article, it becomes clear that a deeper horn — meaning one with a longer throat before the flare — significantly improves acoustic loading in the lower portion of its usable bandwidth.

At higher frequencies, where wavelengths are shorter, this reactive loading (i.e., frequency-dependent impedance due to stored acoustic energy, like air mass or compliance near the throat) diminishes, reducing the acoustic impedance and therefore the loading effect.

At low frequencies, horn efficiency is largely driven by the acoustic loading effect at the throat. This occurs because, at these frequencies, the acoustic wavelength is large compared to the throat dimensions, causing the confined air near the throat to behave as a reactive element — primarily as acoustic compliance and inertance — which increases the acoustic impedance seen by the driver.

This impedance rise at low frequencies enhances energy transfer by better matching the high impedance of the transducer diaphragm to the very low impedance of open air — a transformer effect provided by the horn.

A deeper and properly proportioned throat allows for a more gradual impedance transition, enabling more acoustic energy to be transmitted with less diaphragm excursion. This leads to higher sound pressure levels for the same excursion, reduced reflection losses, and lower particle velocity at the mouth — which limits distortion risks and prevents exceeding the critical Mach number.

This efficiency gain is especially noticeable in the lower range of the horn’s operating bandwidth, where wavelengths are long and direct radiation would be very inefficient without a guiding structure. Horns designed for low-frequency extension often feature a narrow, long, and well-profiled throat. This geometry promotes more stable loading, better efficiency, and reduced distortion.

However, a too long or too narrow throat can cause viscothermal losses, encourage higher-order modes (HOM), generate unwanted transmission line resonances, or increase acoustic resistance and distortion at high frequencies, ultimately degrading the horn’s overall performance. These phenomena, collectively known as “Honk”, primarily degrade efficiency and linearity in the upper frequency range. Therefore, this part of the horn must be carefully designed to balance effective acoustic transition with control of these secondary effects.

Loading and Directivity

Importantly, loading is fundamentally tied to the horn’s directivity control. Beyond a horn’s directivity boundary, additional loading cannot be delivered effectively. Horns exhibiting strong loading effects often show a pronounced cutoff near this boundary, which defines the lowest usable crossover frequency while also factoring in directivity matching and driver distortion considerations. The interaction between loading and constant directivity often produces the characteristic “bell response”.

Loading is frequency-dependent, decreasing with increasing frequency. This explains why the high-frequency “anchor point” around 14–15 kHz — used for our horn EQ — remains largely unaffected by loading, but still depends on the horn’s directivity behavior.

Another important factor is off-axis energy distribution: at a given frequency, energy radiated off-axis is no longer present on-axis. This is one reason why pursuing constant directivity up to 20 kHz is not necessary, especially considering audibility thresholds and psychoacoustics.

Non-Uniformity of Loading

It is also critical to understand that loading is not uniform. The combination of expansion geometry and surface area creates a pressure curve over frequency, which interacts with the energy distribution imposed by directivity. This complex interaction defines the range and effectiveness of acoustic loading in conjunction with the driver’s output.

Horn Response

When looking at a horn’s frequency response, a dip in high frequencies compared to mid frequencies might lead you to believe you’ve “lost” decibels (dB) and need to boost the highs with additional amplification.

However, this way of thinking is not accurate and we will see here why.

To gain a more comprehensive understanding of the concepts discussed here, particularly about horn loading (energy) and constant directivity, we recommend referring to our articles dedicated to these subjects.

Essentially, the bell response of a horn arises from the combined influence of its directivity pattern and acoustic loading effect. While constant directivity horns typically maintain a consistent directivity behavior up to around 7-8 kHz, the acoustic loading effect is inversely proportional to frequency. This means it has minimal impact on high frequencies.

Bell Response and Energy Balance

The interplay between driver characteristics, horn loading and horn directivity creates a phenomenon known as the “bell response”.

This describes a perceived roll-off in high frequencies. However, it’s important to understand that this doesn’t necessarily mean there’s less high-frequency energy overall.

The reasons of the bell response are:

Larger diaphragm compression drivers produce more low-midrange energy compared to smaller ones. So in comparaison the high frequency can look lower than a tinier diaphragm when in fact that is mainly the medium range that is upper.

The horn’s loading effect enhances this low-midrange presence, that is a very important aspect, as the loadding effect is strongly inversely proportional to the frequency, more we goes up in frequency less we have it. So for two horns that are constant at the same frequency, reducing coverage (see the point below) will principaly gives more SPL in low end.

Directivity distribution of the initial energy as we have seen upper, this initial energy will always remains the same, it’s the way to distribute it that change and affect the on-axis response.

This can make the high frequencies seem less prominent in comparison to medium, creating the bell response.

When we see these high frequency lower than medium in comparison we tend to thinks that we have “lost” dB in high frequency, we will see that in fact it doesn’t work like this in Horn Response and Hiss article,

In most cases we in fact have “gain” in the midrange area, it’s the high frequency level that doesn’t have moved.

Flattening Frequency Response with EQ

Typically, to achieve a flat on-axis frequency response, we choose a reference frequency above which we want a flat response. This is often set at 15 kHz.
Beyond this point, we allow the natural roll-off of the driver to occur, or use equalization (EQ) again if there’s a rise.

Negative or positive EQ can be used to achieve a flat response. The direction (positive or negative) isn’t crucial, the final result will be the same.
The primary goal is to avoid clipping (in the source, DSP, or amplifier) and maintain a proper gain structure to our desired maximum power output.

Minimum-phase EQ (IIR) is a valuable tool for correcting on-axis horn response because it addresses both the frequency response and the phase response simultaneously.

When a significant dip or peak occurs at a specific frequency, minimum-phase EQ (IIR) not only corrects the level at that frequency but also adjusts the phase response in a way that complements the level correction. This combined effect helps to achieve a more linear overall frequency and phase response.

Here are two EQ examples for an X-Shape X25 horn

BMS 5530 one:

18Sound 1095N one:

Our article about audibility can help to understand one of the reasons why we do nothing after 15 kHz in the 1095N case.

This region is also where the breakup occurs, that is the second main reason why we don’t try to increase volume here.

In each case 15 kHz is our anchor point, EQ are different but the main judge will be, as alway, the distortion after having EQ it flat below 15 kHz, as we have seen on our 1" compression driver test.

If we push constant directivity very high on the same horn, way after 7/8 kHz, the effective loss of energy in 12/17khz area will be in fact minimal, around 1 or 2dB maximum.
Its due to the fact that only directivity will impact it and not the loading effect.

L-PAD

To reduce hiss and protect the driver, an L-pad to reduce driver sensitivity is often recommended; it’s a simple resistor network placed just before the driver:

You can simulate appropriate L-pad values using VituixCad, considering the driver’s impedance and the horn on-axis response. For the X25 horn, this might involve a 1.5-ohm resistor in parallel and a 12-ohm resistor in series, depending on the desired dB reduction to match the mid-woofer level.

The L-pad resistor network does not degrade audio quality; it simply absorbs some amplifier energy which therefore does not reach the compression driver or tweeter.

S/N ratio and Hiss

Hiss is a low-level noise often noticeable in high-sensitivity components related to the system’s signal-to-noise (S/N) ratio.

A common concern when comparing horns, especially regarding EQ use, is increased hiss.

It might seem that extensive EQ adjustments, along with the gain changes needed to achieve a flat response,
would increase hiss, reduce S/N ratio, or consume more power.

However, this vision is partial. Here’s why:

• Power Amplifier: No change in S/N ratio or hiss.

  • Our reference frequency is 15 kHz. Constant Directivity Horns stop exhibiting constant directivity behavior around 7-8 kHz.

  • Therefore, directivity above this point has minimal impact on energy at 15 kHz, which is mostly dictated by the driver.

  • Acoustic loading is inversely proportional to frequency and has almost no influence at 15 kHz.

• DSP: Slight decrease in S/N ratio.

  • Extensive EQ adjustments may slightly increase noise as they consume part of the DSP’s dynamic range, but systems typically operate well below their maximum range (around 96-125 dB), so this effect remains minimal.

In conclusion, while EQ adjustments might influence how the DSP perceives the S/N ratio, the impact on hiss is still minimal.

Conclusion

For a given driver, the energy level at 15 kHz is mainly determined by the driver itself, regardless of horn type or coverage area.

Different constant directivity horns generally have similar hiss levels and S/N ratios when using the same driver.

The bell response is not a problem but relates to both directivity and loading effects:

• It shows the horn is constant directivity; a flatter response may indicate a narrower coverage horn.

• The loading effect in mid and low frequencies provides an energy “bonus” that reduces overall distortion and allows lower crossover frequencies.

• EQ adjustments may influence how the DSP perceives the S/N ratio, but impact on hiss is minimal.

• From the amplifier’s perspective, there’s no change in S/N ratio. Even pushing constant directivity beyond limits reduces it only by 1-2 dB.

• The L-pad allows for adjusting overall sensitivity and counteracts the amplifier’s inherent noise.

• Advanced users can use passive equalization (RC networks) to limit EQ application and preserve DSP dynamic range.

• Effects also depend on compression driver characteristics.

What is the listener envelopment?

The listener envelopment describes the temporal evolution of sound energy in a room after a sound is emitted.

It’s characterized by the density and distribution of early reflections on surfaces, notably the EDT (Early Decay Time), which measures the initial decay of sound level and directly influences the clarity of the sound. A shorter EDT generally corresponds to greater clarity.

In other words, the Listener envelopment determines how sound propagates and reflects in a space, impacting our perception of the spatialization or extent of a place.

It’s crucial to distinguish this from the overall dynamics, which is the difference between the loudest and quietest sound of an audio signal.
The listener envelopment describes the temporal behavior of the sound energy, while dynamics describe the level variations.

Listener envelopment measurements and studies are relatively new, and this article can be updated.

Factors influencing the listener envelopment

• Early reflections (EDT): Early reflections, which occur on the room’s surfaces, play a crucial role in the perception of spatialization.

  These reflections arrive shortly after the direct sound. EDT (Early Decay Time) refers to the time it takes for the sound level in the room to decrease significantly after the sound source has stopped emitting.

  A short EDT corresponds to a rapid reduction in sound energy, which contributes to better clarity, as the early reflections are absorbed or diffused quickly.
  A long EDT creates a more enveloping sensation, as the lingering reflections help enrich the perception of the space.

  More details : Clarity, EDT and ITDG

  The pattern and timing of these early reflections are critical for envelopment. Too few reflections can sound sparse, while too many can blur the sound.

  The Haas effect (or precedence effect) describes how our auditory system integrates these early reflections, often perceiving them as a single fused sound event.

• Room proportions: The dimensions of a room influence the formation of resonance modes (standing waves) and the distribution of reflections.

• Materials: The materials used for the walls, floor, and ceiling determine the amount of sound absorbed or reflected. Absorbent materials reduce reverberation, diffusing materials scatter sound waves in multiple directions. A balanced acoustic design often uses a combination of absorption and well placed diffusion. Too much absorption can make a room sound “dead,” while too little can make it sound overly reverberant.

• Directivity: The characteristics of the sound source, including its directivity, play a significant role in listener envelopment. This directivity must be adapted to the environment, ensuring it is constant, with coverage suited to the listening distance in order to maintain a balanced 50/50 ratio between the direct and reverberated fields taking account of our sensitivy. As we will see, with early reflections and diffusers, the horizontal axis becomes the most important in achieving this balance.

The critical distance

The critical distance refers to the distance from a sound source at which the level of direct sound equals the level of reverberated sound.

Beyond this point, reverberant sound dominates the sound field. The critical distance depends on both the characteristics of the sound source (such as its directivity) and the acoustics of the room.

While being at the critical distance influences the balance of direct and reflected sound, achieving a sense of good envelopment also requires careful management of early reflections and the distribution of sound throughout the space.

Optimization of the listener envelopment

To obtain an optimal listener envelopment, it is necessary to:

• Control early reflections: By using absorbent or diffusing materials strategically, it is possible to reduce unwanted early reflections (e.g., those that arrive too quickly or from unfavorable angles). This might involve using absorption at specific points on the walls or ceiling to tame strong reflections, while using diffusers to scatter sound and create a more spacious feel.

• Create a density of lateral reflections: A sufficient number of lateral reflections (reflections from the side walls) contributes significantly to a feeling of envelopment and better spatialization. These reflections should arrive slightly later than the direct sound and contribute to a sense of width and spaciousness.

• Eliminate specular reflections: Specular reflections, which are like mirror-like reflections, create echoes and comb filtering, degrading intelligibility. It is important to diffuse or absorb them. Convex or 2D diffusers are often used to diffuse specular reflections.

• Room proportions: The dimensions of the room influence the resonance modes and the distribution of reflections. In a corridor-type room, it will be very difficult to have a good envelope due to the lateral reflection and their management.

In some cases, it may be tempting to over-reduce the opening of the horns below what we recommend but this may create a gap in the envelope between low and high frequencies. This can result in a situation where the high frequencies are well-distributed, but the low frequencies are more focused, creating an uneven envelope and impacting the variation of intelligibility and frequency balance.

Early reflections are essential for creating a sense of envelopment in a room. These reflections contribute to the spatial perception of the sound, but their timing and pattern are crucial.

If reflections arrive too quickly or are too sparse, they can negatively impact the sense of space, leading to a feeling of emptiness or a lack of definition.

On the other hand, if there are too many reflections, they can blur the sound, reducing clarity and spatial precision.

The perception of envelopment is influenced by the interaction of these reflections with the direct sound, and the brain tends to integrate reflections that arrive shortly after the direct sound. The ideal balance of reflections helps create a rich and immersive experience without compromising clarity.

This explains why achieving a good listener envelopment is particularly challenging in small, narrow rooms, where reflections tend to occur too closely in time to create a sense of spaciousness. Modal issues are also more pronounced in smaller spaces, further complicating the creation of an optimal sound envelope.

Measurability

Several parameters can be measured to characterize the listener envelopment:

• IACC (Inter-aural Cross-Correlation Coefficient): a measure used in acoustics to evaluate the similarity of sound signals that reach our two ears. Lower IACC values generally correlate with a wider, more enveloping sound, as the signals reaching the two ears are less similar.

• Lateral Fraction (LF): a measure used in acoustics to quantify the proportion of sound energy that reaches a receiver after being reflected by the side walls of a room. Higher LF values suggest a greater contribution from lateral reflections, which are associated with a wider, more enveloping sound.

  However LF is typically measured in concert halls, its application in small rooms is less common.

These measurements make it possible to characterize the envelope, but they generally require the intervention of a professional specialized in the field.

Conclusion

The listener envelopment plays a fundamental role in listening quality. By understanding the mechanisms that govern it and using the appropriate measurement tools, it is possible to optimize the acoustics of a space and create an immersive and realistic listening experience.

Source:

Objective measures of listener envelopment, 1995: https://nrc-publications.canada.ca/eng/view/accepted/?id=be12bb70-20ce-4d9e-ab16-99b48af4ef6c

LF:

http://www.winmls.com/2004/help/lflateralfraction.htm

http://www.winmls.com/2004/help/lglatelateralstrength.htm

http://www.winmls.com/2004/help/lfclateralfractioncosine.htm

IACC:

https://iaem.at/ambisonics/symposium2009/proceedings/ambisym09-avnirafaely-iaccspatcorrsh.pdf

Audibility

We are less sensitive to anomalies or even SPL drops above 10 kHz. This is due to the natural decline in our hearing sensitivity at high frequencies.

Here is our sensitivity according to frequency and SPL:

The bottom red line represents the sensitivity threshold of the human ear.

We must also consider that we live in a constant and measurable background noise. If a sound or a distortion (such as a high-order harmonic generated at high SPL) falls below this noise floor, it will be less audible—or completely masked.

Frequency Range and Information Density

From 10 to 20 kHz spans only one octave. This octave contains much less useful auditory information than lower bands. It’s rarely used by musical instruments or the human voice. In addition, our sensitivity in this region can be 10 to 20 dB lower than in the vocal range, making it very difficult to notice any issues—especially in the upper part of this octave.

The Masking Effect

The masking effect is a phenomenon where the presence of one sound (the masker) reduces the audibility of another sound (the masked).
This is particularly important when discussing low-frequency content and harmonic distortion.

Key Points

• Low-frequency masking: When a low-frequency sound is boosted, it can mask higher-frequency content. This can lead to a perceived loss of “kick” and a boomy or muddy sound.
• Frequency relationship: Masking is most pronounced when both sounds are close in frequency.
• Intensity: A louder masker will have a stronger masking effect.
• Distortion masking: This explains why high-order harmonic distortion (farther from the fundamental) is often more audible than low-order harmonics.

Here is how masking works from a fundamental tone:

Pierre-Yohan Michaud combined these aspects, audibility and distortion, in his thesis “Distorsions des systèmes de reproduction musicale : Protocole de caractérisation perceptive” (Distortions in Music Reproduction Systems: A Protocol for Perceptual Characterization):

In this example, we can see that H3 is in the audible range, whereas H2 falls within the masking zone.

Practical Case: subwoofer masking the kick

A common real-world example of masking is when excessive low bass (e.g. below 70/80 Hz) rises too quickly. This will mask the upper bass — especially the “kick”/impact around 100–200 Hz.

To learn how to avoid this and integrate your subwoofer without degrading impact and clarity, see the Subwoofer and Masking Effect section.

Audibility of Compression Driver Breakup

The main difference between compression driver diaphragm materials lies in the breakup frequency and the associated temporal behavior, which can be more or less violent.

In practice, these effects wil be inaudible if or because:

• It’s placed high enough: Above 8–10 kHz, human hearing sensitivity decreases exponentially compared to its midrange sensitivity. Depending on age and individual hearing, sensitivity in this region is typically between −15 dB and −40 dB relative to midrange. This alone makes high-frequency breakup much less perceptible.

  

• The temporal behavior is below human threshold: Breakup temporal issues are usually around −15 to −20 dB on a good diaphragm. Combined with the already reduced human sensitivity in this region, this can sum to roughly −30 to −35 dB, at the highest point, perceived by the auditory system, further reducing audibility.

  

• Limited musical information: The affected high-frequency range contains very little actual musical content. Even if there are temporal artifacts, they are unlikely to be noticed by listeners if placed high enough and at a low enough level in terms of dB.

⚠️ Warning

Do not try to “correct” ear sensitivity. The brain is naturally adapted to the ear’s frequency response curve. Attempting to artificially “flatten” this sensitivity can result in unbalanced sound and may even damage your ears (hearing loss, tinnitus) due to overexposure in the high-frequency region.

A speaker must be flat at 30–60 cm, as explained here: how to implement my horn and my speaker

sources:

• AES - The Masking Effect: https://www.aes.org/e-lib/browse.cfm?elib=200
• Wikipedia - Auditory masking: https://en.wikipedia.org/wiki/Auditory_masking
• Wikipedia - Equal loudness contour: https://en.wikipedia.org/wiki/Equal-loudness_contour
• Pierre-Yohan Michaud thesis : https://theses.hal.science/tel-00806288v1/document
• Frequency response of the human ear: https://www.compadre.org/nexusph/course/Frequency_response_of_the_human_ear

Unveiling a Speaker’s Sonic Behavior: Power Response and Directivity

Loudspeaker design is a delicate balance of factors.

Understanding a speaker’s directivity (how sound radiates in different directions) and its interaction with power response (the speaker’s ability to reproduce sound consistently across the frequency spectrum) is crucial in loudspeaker design, especially when considering listening distance.

While constant directivity waveguides offer distinct advantages, the interplay between a speaker’s coverage pattern (how sound energy is distributed) and the listening room’s acoustics plays a vital role in achieving a balanced sound.

A point about Critical Distance

In sound reproduction, understanding the critical distance is crucial, as it defines the ideal listening distance for achieving a balance between the direct sound from the speakers (direct field) and the reflected sound from the room (diffuse field).

A common target is a 50/50 ratio of direct to reverberated sound, although preferences can vary.

Our dedicated article about critical distance goes deep in this concept, where room acoustics (measured by Sabine absorption) and speaker directivity factor are the two main parameters.

The Challenge Beyond Critical Distance

As the listener moves further away from the speaker, two key challenges arise beyond the critical distance:

• Inadapted Coverage to Listening Distance (Critical Distance): A loudspeaker with a coverage pattern that is inadapted to the listening distance (critical distance) will cause uneven sound reproduction, particularly in high frequencies. This can manifest in two ways:

  • Too Restricted Coverage: This leads to a perceived lack of detail and brightness (a muffled sound). This is because the sound reaching listeners lacks sufficient high-frequency energy due to the limited coverage pattern.

  • Too Wide Coverage: Conversely, a coverage pattern that is too wide relative to the critical distance can deliver an excessive amount of high-frequency energy to distant listeners. This can make the sound seem overly bright or aggressive, leading to listener fatigue.

• Excessive High-Frequency Energy due to Room Acoustics: Even with a well-designed loudspeaker, the reverberant field in the listening room can sometimes add an excessive amount of high-frequency energy. Rooms with reflective surfaces like hard floors and bare walls can exacerbate this issue. This can contribute to a perceived harshness or fatiguing sound, particularly for listeners positioned further away from the speaker.

Power Response

This metric reflects the speaker’s ability to reproduce sound across the frequency spectrum with consistent loudness.

Imagine it as a frequency-dependent Sound Pressure Level (SPL) output. Ideally, a flat power response signifies the speaker outputs all frequencies at the same intensity, resulting in a balanced sound.

Deviations from a flat response, such as peaks or dips, indicate variations in loudness across different frequencies.

Power response is typically measured in an anechoic chamber (a specially designed room that absorbs sound reflections) and visualized as a frequency response curve. This curve plots the sound pressure level (SPL) output of the speaker in decibels (dB) across the frequency range (Hz).

There’s no single formula to generate this curve as it’s a result of the speaker’s physical design and materials.

Directivity Index (DI)

This measurement focuses on how the speaker radiates sound in different directions.

Unlike power response, DI doesn’t consider overall loudness, but rather how efficiently the speaker directs sound energy towards the intended listening area.

A high DI suggests the speaker is more directional, focusing its energy forward, while a low DI indicates a more omnidirectional sound pattern.

Then, a flat DI curve indicates a constant directivity behavior, meaning the speaker emits constant off-axis energy relative to on-axis.

DI calculation is demonstrated in Appendix section.

Optimizing Loudspeaker Design for Balanced Listening

The key lies in carefully considering both power response and directivity characteristics:

• Coverage Pattern Design: A well-designed loudspeaker, regardless of whether it utilizes a constant directivity waveguide or another approach, should provide a constant coverage pattern that effectively disperses energy, particularly high frequencies but by respecting psyckoacoustics principles too, tailored to the intended listening distance, the critical distance. This helps maintain a balanced and detailed sound experience across the listening area.

• Accounting for Reverberant Field: Understanding the impact of the listening room’s acoustics on the reverberant field is crucial. In some cases, acoustic treatments or room correction techniques may be necessary to mitigate excessive high-frequency buildup and ensure a natural listening experience.

Conclusion

By carefully considering power response, directivity characteristics, and the influence of the listening room, loudspeaker designers can create speakers that deliver a natural and detailed listening experience across a wider range of distances.

This comprehensive approach is essential for achieving a balanced sound, regardless of the specific loudspeaker design.

Appendix: DI Formula

The formula for DI using the spherical integral is:

DI(θ) = 10 log ( (∫ P(θ, φ) dΩ ) / P(0, 0)^2 )

• DI(θ): Directivity Index at angle θ (degrees)
• P(θ, φ): Off-axis Sound Pressure Level at a specific angle (θ, φ) in spherical coordinates (θ for horizontal angle, φ for vertical angle)
• dΩ: Differential solid angle element (used in the integration process)
• P(0, 0): On-axis Sound Pressure Level (dB)
• ∫: Integral symbol representing summation over the entire sphere’s surface area

Understanding and calculating dΩ:

The differential solid angle element (dΩ) represents an infinitesimally small piece of the sphere’s surface area. It’s crucial because the integral in the DI formula sums the off-axis sound pressure levels (P(θ, φ)) across the entire sphere. However, areas closer to the poles have a smaller surface area compared to those near the equator. dΩ accounts for this variation:

Formula for dΩ in Spherical Coordinates:

dΩ = sin(φ) dθ dφ

• φ (phi): Vertical angle (ranging from 0° to 180°)
• θ (theta): Horizontal angle (ranging from 0° to 360°)

Explanation of dΩ Formula:

• sin(φ): This term ensures that off-axis sound pressure levels near the poles (where φ approaches 90°) are weighted less due to the smaller surface area in those regions. As φ increases towards the poles, the sine of φ gets smaller, effectively reducing the weight given to those SPL measurements.

• dθ and dφ: These represent infinitesimal changes in the horizontal and vertical angles, respectively. Multiplying them by sin(φ) calculates the area of a tiny rectangle formed by these infinitesimal changes on the sphere’s surface.

Integration and DI Calculation:

1. For each off-axis measurement point defined by specific θ and φ values, we:
   • Calculate the corresponding dΩ using the formula above.
   • Multiply the measured sound pressure level (P(θ, φ)) by this dΩ. This weights the SPL measurement based on the area it represents.
2. The integral (∫) symbol then sums these weighted sound pressure levels (P(θ, φ) * dΩ) across the entire sphere.

By incorporating dΩ, the integration process considers the varying sizes of surface area elements. This ensures an accurate calculation of the total sound power radiated by the speaker, which is then compared to the on-axis SPL to determine the directivity index (DI) for different off-axis angles.

The Physics of Perception:

Sound travels as waves, characterized by properties like frequency (pitch) and amplitude (loudness). Psychoacoustics delves deeper, examining how our ears and brains interpret these physical properties to create the auditory experience we know.

Key Concepts in Psychoacoustics:

• Loudness Perception: Our ears don’t perceive loudness linearly. A sound that’s twice the intensity of another won’t necessarily sound twice as loud. Psychoacoustics helps explain this phenomenon, known as the Fletcher-Munson curves, which depict how human hearing perceives loudness at different frequencies.

• Masking: Psychoacoustics explores how different frequencies interact and how masking affects our ability to distinguish sounds and why some are masked, see the full article here: The Masking Effect.

• Localization: We can identify the direction of a sound source with remarkable accuracy. Psychoacoustics examines how our brain uses minute timing and intensity differences between our ears to localize sound.

• Timbre: This quality allows us to distinguish between different instruments playing the same note. Psychoacoustics helps us understand how the complex interaction of overtones and harmonics within a sound wave contributes to timbre perception.

Applications of Psychoacoustics:

The principles of psychoacoustics have numerous practical applications:

• Audio Engineering: Sound engineers leverage psychoacoustics to optimize sound recordings and playback systems. They can manipulate elements like compression and equalization to create a more pleasing listening experience.

• Hearing Aids: By understanding how hearing loss affects sound perception, psychoacoustics helps in designing hearing aids that compensate for these deficiencies and improve speech intelligibility.

• Noise Reduction: Psychoacoustic principles are used to create effective noise-cancelling headphones and active noise control systems, which reduce unwanted sounds by generating cancelling sound waves.

Practicals Studies

Dr. Floyd E. Toole’s studies indicate that listeners tend to prefer a decay in the high frequencies and a smooth change in directivity index (DI), even though the DI should increase in very high frequencies (making the speaker more directive near 7/8 kHz).

To mitigate the conclusion about the significant decay in frequency response, it should be noted that the Revel speaker’s 120° radiation pattern used here is often too wide for many listening spaces and typical listening distances.

This wide dispersion contributes to the desired attenuation, but a more tailored coverage and a better energy balance will have reduce the severity of the frequency response decay.

Bellow this very high frequency decay the radiation must be constant and controlled as lower as possible, without major accidents or diffraction.

With a horizontal polar relative to 0°, it will look like this, with no abrupt change when we lose control at high frequencies:

We select a horn with an opening coverage adapted to the listening distance and room acoustics, while the woofer’s direct radiation pattern remains fixed.
Because of this, their directivity characteristics differ at certain frequencies.
To avoid abrupt changes in directivity, the crossover frequency is chosen where both the horn and woofer have similar radiation patterns: where the horn loses its wide directivity and the woofer starts to become more directional.
This ensures a smooth transition between the two drivers, as explained in the Directivity Match article.

The primary goal is to adapt coverage to listening distance and acoustics without causing an abrupt change in the Directivity Index.

Conclusion:

Psychoacoustics plays a crucial role in shaping our auditory world, but a one-size-fits-all ideal target curve does not exist, as it depends of your acoustics, listening distance and speaker directivity so each “curve” is unique as seen in last point in how to implement my horn and my speaker, do not try to match a generic target curve at listening position.

By understanding the intricate relationship between sound waves and human perception, we can not only appreciate the science behind hearing, but also leverage this knowledge to improve sound design, enhance listening experiences.

Introduction

Loudspeakers, despite their crucial role in sound reproduction, can introduce unwanted distortion.

One significant contributor is cone breakup, a phenomenon related to the moving material (diaphragm, cone…) resonance at high frequencies.

This article dives deeper into the science behind cone break-up, its impact on sound quality, and explores filtering techniques to mitigate this issue, focusing on woofer breakup, for compression drivers we recommend reading our masking effect and audibility article.

What is speaker break-up?

1. Basic operation

When a speaker emits sound, the voice coil, driven by the signal from the amplifier, moves. Since it is attached to the membrane (cone driver) or a diaphragm (compression driver), it pulls the radiating surface along in its movement.

There are three stages of membrane behavior as frequency increases: pistonic motion, non-pistonic motion, and breakup modes — the latter being a more severe form of non-pistonic behavior characterized by modal resonance patterns across the membrane materials.

At low frequencies, the membrane or cone driver moves uniformly in a pistonic motion.

2. Transition from pistonic to non-pistonic motion

As frequency rises, the radiating surface size becomes comparable to the wavelength, causing phase differences across the surface that lead to a progressive narrowing of directivity.
This geometric effect alone occurs even if the membrane behaves like a perfectly rigid piston.

Simultaneously, material properties induce internal wave propagation delays and localized resonances,
which affect the membrane’s motion and sound distortion but have a secondary influence on directivity compared to the geometric factor.

These phase shifts between the membrane center (driven by the voice coil) and its edges cause the motion to deviate from pure pistonic behavior,
marking the onset of non-pistonic motion. However, this stage does not yet involve breakup or fractionation.

3. Breakup modes and material implications

Breakup modes (or fractionation) arise at higher frequencies, when parts of the radiating surface resonate independently, forming complex modal patterns that depend on the material properties of the membrane.
This results in distortion and irregular radiation distinct from the earlier smooth non-pistonic behavior.

To delay the onset of fractionation, manufacturers can opt for more rigid membranes. However, an ultra-rigid membrane is not ideal, as it introduces internal vibrational modes, also known as modal resonances.
At certain frequencies, these modes cause localized resonances across the surface of the membrane, where different parts vibrate inconsistently, generating undesirable distortions.

Fractionation is inevitable because it is inherent to the shape and material of the membrane.
However, a more rigid membrane will fractionate at higher frequencies and with greater intensity, while also generating more internal vibrational modes, which can contribute to additional distortion.

4. Material strategies and special cases

This is why cone speaker designers often use composite materials and blends to construct membranes, the goal is to strike a balance between rigidity, damping, and weight.
Rigidity pushes fractionation to higher frequencies, while damping reduces the energy of internal resonances, thereby limiting distortion and resonance peaks caused by vibrational modes.

For compression drivers, the diaphragm is usually smaller, and its breakup typically occurs outside the ear’s sensitive range, so it’s less of a problem.

Causes of Cone Break-Up

Cone break-up occurs when the loudspeaker cone resonates at high frequencies, causing it to vibrate in unwanted ways beyond its intended pistonic motion. Several factors influence this resonance:

• Dimensions, Thickness, and Shape of the Cone:
  The size, thickness, and curvature of the cone significantly impact its resonant behavior. Thinner or flatter cones tend to break up earlier than rigid or curved ones.

• Cone Material:
  Different materials possess varying stiffness and damping properties. Stiffer materials like metals are more prone to break-up, while materials with inherent damping, like treated paper or composites, can help reduce it.

• Boundary Conditions of the Cone:
  How the cone is secured to the frame (suspension) also plays a role. A flexible suspension allows for a wider range of motion before break-up occurs, while a stiffer suspension might limit total excursion but could lead to earlier break-up at specific frequencies.

Impact of Cone Break-Up on Distortion

When the cone breaks up, it generates standing waves that distort the original audio signal.

These distortions manifest as harmonic distortion, perceived as a coloration or harshness in the sound, a H3 distortion at 1khz, so create by a 1khz signal alone, will create sound at 3khz (3 times fundamental).

When a violent break-up occurs at 1500Hz, we have a H3 rise-up at 500Hz (1500/3), so even if we cut at 1kHz we will have the distortion associated to the break-up in the signal and when we will play 500hz we will have an unwanted signal at 1500Hz.

Breakup will also bring Time-domain problems and – for compression drivers – out of plane wave radiation behavior, expecially visible with compression drivers in horns.

Cone Break-Up and Electrical Current

The speaker cone is a mechanical system. When it encounters its resonant frequency, it tends to vibrate in uncontrolled ways – this is cone break-up.

This uncontrolled motion is related to the electrical current flowing through the voice coil.

As the cone vibrates, it generates a back electromotive force (EMF) that opposes the current flow and creates current distortion in the voice coil.

Inductance and Impedance

An inductor opposes changes in current flow. When you increase the inductance in the circuit (like the inherent self-inductance of the voice coil or by adding an external inductor), the overall impedance of the circuit also increases.

Impedance acts like electrical resistance for AC signals like audio.

How Increased Inductance Helps

Here’s how increased inductance tackles cone break-up:

• Limits Current Flow at Resonance: At the cone’s resonant frequency, the back EMF from the uncontrolled vibration is strongest. The increased inductance makes it harder for the current to rise significantly at this frequency. This reduces the electrical energy delivered to the voice coil, thereby lessening the uncontrolled movement of the cone.

• Partial Damping Effect: Though not a traditional damping mechanism, the increased opposition to current changes caused by the inductance can have a damping effect. This helps to suppress the excessive vibration of the cone at resonance.

However, it’s important to consider these points:

• Limited Effect: Increased inductance alone might not entirely eliminate cone break-up, especially for severe break-up issues. It’s often a contributing factor in conjunction with other design elements like cone material and suspension.

• Frequency Dependence: The impedance increase due to inductance is most significant at higher frequencies. So, the effectiveness in mitigating break-up depends on the resonant frequency of the cone relative to the desired operating range of the woofer.

Filtering Techniques for Break-Up Reduction

Several filtering techniques can be employed to address cone break-up and reduce associated distortion.

As it’s based on impedance rise-up, an EQ in DSP will not have an impact.

The result depends on the woofer’s motor, but it mainly impacts the H3 in most cases. It depends on the design of the motor, the voice coil, and the inductance value. The lower and more linear it is, the less current distortion and distortion in the midrange occur (i.e., a plateau distortion not linked to excursion), which explains why a notch filter has no effect on the distortion of compression drivers, tweeters, and other speakers such as 18Sound AIC speakers.

It’s important to note that these filtering techniques are most effective when the break-up rise up in frequency (one or more big peaks) and/or when woofer is rising up in his final box. If the breakup is already damped, so more or less flat and the woofer has already a flat response in box, it will useless to try something about it.

Each with its advantages and limitations:

Notch Filters

These passive filters use a combination of inductors (L) and capacitors (C) to create a high impedance at the resonant frequency. This effectively reduces the current flow at that frequency, minimizing cone excitation.

However, precise tuning is crucial, and if certain components are placed in parallel with the circuit, this will bypass the impedance effect and make the notch effect on breakup distortion ineffective. So it will work well in conjunction with active filtering, less in passive filtering.

Here is the H3 of a Dayton RS52 with and without LC notch :

Air core inductors with active filtering

These first-order filters, in series, often implemented with a single inductor, allow lower frequencies to pass through while attenuating higher frequencies, including those near the break-up point. This approach offers a simpler design and also linearize the woofer, it’s the easier solution.

It will increase gradually the impedance and replace some EQ to linearize the woofer in the same time, it works very well if the woofer is already rising up in his final box.

The inductor must be an air core inductor and not an iron core inductor; otherwise, it will add H3 distortion in the low end.

Here is the H3 of a SbAcoustics WO24P with and without air inductor in serie :

Compensation Networks

More complex networks can be designed to address specific break-up modes. These may involve additional components and require detailed analysis of the cone’s behavior.

Self Inductance

While not a filter in the traditional sense, the inherent self-inductance of the voice coil can also contribute to a rise in impedance at higher frequencies.
This can have a similar effect to filtering, potentially mitigating break-up to some extent.

However, it’s often a secondary effect and may not be sufficient for significant break-up control.

Conclusion

Cone break-up is a significant factor in loudspeaker distortion, impacting sound quality.

By understanding its causes and employing targeted filtering techniques like notch filters or high-pass filters, speaker designers can achieve smoother, more accurate sound reproduction.

Introduction

When it comes to crafting the perfect speaker, meticulous attention is paid to every detail, from the materials used to the precise arrangement of the drivers.

One crucial factor, often overlooked, is the center-to-center distance between the mid-woofers and the tweeter section.

Placing them too close together can create a phenomenon known as vertical lobing, negatively impacting sound quality.

Understanding Vertical Lobing

Imagine sound waves as ripples emanating from a speaker in all directions. When two driver sections – like woofers – are positioned too close, their sound waves can interact, causing cancellation at specific frequencies.

This cancellation creates dips and peaks in the off-axis frequency response, resulting in an uneven and disjointed listening experience by degrading power response.

Especially because we listen at the so called critical distance where direct and reflected sound (from walls) are roughly balanced (50/50).

Think of a speaker with a single woofer. The sound it produces spreads uniformly in a vertical plane, like cutting a cake in half. Now, add another woofer positioned too close. At specific frequencies, the sound waves from each woofer will overlap and partially cancel each other out, especially above and below the speaker’s center axis. These cancellations create “lobes” – areas where the sound is weaker – causing the perception of an unbalanced soundscape, with the woofers and tweeter seemingly playing separately.

The Impact on Listening

Vertical lobing leads to a loss of sonic coherence.

At close or medium listening distances, you might perceive a disconnect between the low frequencies (woofers) and high frequencies (tweeter).

The overall soundstage may seem disjointed, lacking a unified sonic image and impacting the perceived power of the sound.

Here’s a polar map representation of vertical lobing effects:

While the ideal center-to-center distance is roughly 66% of the crossover wavelength, achieving perfection isn’t always necessary.

Additionally, our ears are more sensitive to horizontal reflections than vertical ones due to their positioning and our brain’s adaptation to floor reflections.

MTM Configuration: A Balancing Act

The MTM (Mid-Tweeter-Mid) configuration, where the tweeter sits between two mid-woofers, also faces similar challenges.

To minimize vertical lobing in this design, the woofers often require an even lower crossover frequency, meaning they handle a larger range of bass compared to speakers with wider-spaced woofers, careful design considerations are crucial to avoid vertical lobing pitfalls.

Another elegant solution is 2.5 voices filtering in MTM disposition, we adress it in the dedicated article: MTM, 2.5 or 3 voices ?.

Horizontal Lobing: A Bigger Problem

Placing woofers horizontally introduces another complication – horizontal lobing.

This creates similar cancellation effects but across the horizontal plane, affecting the stereo image and overall soundstage to a greater extent than vertical lobing.

One solution for minimizing horizontal lobing is the WTMW (woofer-tweeter-mid-woofer) arrangement, where a mid-range driver sits directly below the tweeter, creating a vertically aligned “TM” section.

Perfect Vertical Alignment

Vertical alignment between the high-frequency section (tweeter) and the mid-woofer section is crucial.

Misalignment can cause phase cancellation at different angles on the left and right sides of the speaker, leading to reduced power response and create sound inconsistencies.

The diffraction impact

The closer the sound-emitting elements are to each other, the fewer vertical lobes but the more pronounced the diffraction becomes.

If we use horns that allow a low crossover, lobing issues are no longer a significant problem. However, the diffraction impact between elements becomes even more noticeable, leading to a degradation of the vertical polar plot and even to the horizontal one when the elements are very close.

This behavior is complex, so we recommend reading our article dedicated to diffraction, especially the “Diffraction on woofer” section.

The Takeaway and How to Fix It?

Careful consideration of both center-to-center distance and vertical alignment is essential for achieving optimal sound quality. By maintaining a suitable separation and precise alignment, speaker designers can minimize lobing and ensure a smooth, coherent listening experience.

Remember, minimizing lobing involves a delicate balance. While lobing caused by excessive spacing is generally easier to address compared to other acoustic challenges, achieving optimal sound quality requires careful consideration of both center-to-center distance and other design factors. Placing drivers closer together is the solution, but a lower crossover frequency might also be needed.

Here are some techniques speaker designers use to address lobing:

• Maintaining a suitable center-to-center distance: This distance is roughly 66% of the crossover wavelength for optimal performance, but slight deviations can be acceptable depending on the overall design.

• Lower crossover frequencies (a design consideration): A lower crossover frequency help to mitigate lobing in some designs, it affects the overall response (we have to take care about distortion and directivity match at crossover) and is a factor weighed during the design process.

Time alignment is another important tool in a speaker designer’s arsenal. By electronically adjusting the timing of signals sent to each driver, they can achieve better phase coherence and reduce lobing effects. However, it’s a separate consideration from the physical placement of drivers.

By understanding these techniques and the trade-offs involved, speaker designers can create speakers that deliver a rich and well-balanced listening experience.

When it comes to compression driver horns, the energy distribution across frequencies is a crucial factor as a horn is an energy distribution device.

This article explores how the driver itself and the horn interact to shape this energy distribution.

The Driver’s Role

The energy a compression driver produces is determined by several factors:

• Diaphragm Size: Larger diaphragms naturally produce more low-frequency energy, but their breakup can impact very high frequencies .

• Motor Characteristics: The motor’s sensitivity and resonance frequency (Fs) as other characteristics influence the overall energy output and roll-off at low frequencies.

The overall balance and brain

We listen at a so-called critical distance where the direct field (sound coming directly from the speaker) and the reverberant field (sound that rebound on walls) is at 50/50 or 60/40.

If you perceive a sound as aggressive at high volumes but not at lower volumes or an imbalance between treble and the rest of the spectrum when you went further of you speaker , it’s likely due to an imbalance in the energy radiated and perceived by the ears across the frequency spectrum.

Our ears are particularly sensitive to the upper midrange and audible treble frequencies, and excessive energy in these regions can lead to fatigue and discomfort. More details in our audibility article.

To prevent damage to your ears, your brain instinctively limits the volume when the sound becomes too intense in this area. Balancing the energy between the midrange, low midrange, and high frequencies can help mitigate this issue. One effective strategy is to use a loudspeaker with constant directivity, to balance and adapt radiated energy across the spectrum according to your listening distance and acoustic.

This type of loudspeaker is often praised for its ability to deliver high sound levels without causing discomfort. This is because the well-balanced energy distribution allows your brain to “authorize” higher volumes without triggering the pain response. In contrast, direct-radiating loudspeakers, which typically disperse sound over a wider area (120 degrees or more), can create uneven sound fields that may be more prone to causing fatigue.

By using a loudspeaker with constant directivity and optimizing your room acoustics, you can enjoy a more balanced and immersive listening experience, even at higher volumes and gain more impact in the low end spectrum.

The Horn’s Influence

The horn plays a significant role in how energy is distributed:

• Loading: Horns act as a load on the driver, affecting its response at different frequencies. This loading effect is most prominent at lower frequencies and diminishes strongly as we move up the frequency range. More details here : acoustic loading

• Horizontal and vertical directivity: The horn’s directivity pattern, both vertical and horizontal, significantly influences on-axis energy. Decreasing horizontal coverage helps to retain more energy on-axis.

  Reducing vertical coverage will redirect some off-axis energy back to the on-axis region, however, it’s important to note that reducing vertical directivity improves sensitivity only within the bandwidth where vertical and horizontal coverage overlap. As the horn’s mouth height decreases, vertical control is lost earlier, while horizontal control is maintained. When vertical control is lost but the horn is still in use, overall loading is impacted because a portion of the energy escapes vertically.

  We lose more than just loading by constricting the vertical profile too much—the horn becomes too narrow, limiting its vertical control to a very small bandwidth located in the high frequencies, it also causes a loss of directivity control earlier than expected. In the end, by trying to reduce vertical dispersion, we actually lose constant directivity, as the loss of vertical control leads to excessive and uncontrolled widening.

  Additionally, if the throat is too tall, as seen in oversized ribbon or AMT drivers as directivity is initially dictated by the throat itself, only a small portion of the horn acts as a “pseudo” waveguide, providing limited control over dispersion.

  This effect is counter balanced with the loading effect see upper, when both horizontal and vertical control are lost, according to horn mouth size, the horn cannot bennefit of loading, sets an absolute limit to the potential loading effect.

• Constant Directivity: Horns designed for constant directivity (consistent sound dispersion across a specific angle) send energy off-axis that will be not more present on-axis, particularly at higher frequencies, as some part of the energy gets redirected off-axis to maintain the directivity pattern.
  For a good listening experience ,psychoacoustic give us a global rule to be constant until 7/8 khz then decrease slowly after.
  More details here : Constant directivity

The interplay between driver characteristics, horn loading and horn directivity creates a phenomenon known as the “bell response” that is explained in Horn Response article.

High Frequencies and Physics

Physics dictates that horn loading has minimal impact on very high frequencies, as it’s related to acoustic loading.

In this region, the driver’s motor characteristics become the primary determinant of energy output as, on best horn about loading, loading is inversely proportional to frequency and ends when horn’ control ends.

As we said upper and in the related article the effect of acoustic loading (so the “loading effect”) is strongly inversely proportional to the frequency.

Horn Low-End Roll-Off

However, the driver’s motor naturally start to produces less energy at lower frequencies from some point, depending on its characteristics and diaphragm size.

This reduction in motor output, combined with the decreasing horn loading effect at lower frequencies, contributes to the natural roll-off in low-end response.

Ultimately, as the horn’s width becomes insufficient to control sound waves, the directivity pattern widens significantly. This signifies the end of the horn’s effective loading capability, resulting in a drop in sound pressure level.

From this low point, whatever we will try to do to load more will not works.

Don’t Waste Energy: Directivity and Efficiency

Adapting the horn’s directivity pattern according to the listening distance isn’t just about improving the listening experience. It also allows us to respect the critical distance, the point where the direct sound from the driver and the reflected sound in the room reach a balance (around 50/50 or 60/40).

By directing energy constantly until 7/8khz with a coverage adapted to our critical distance, we ensure to keep efficiency and, at the same time, achieve clear and accurate sound reproduction. This approach respects the balance between direct and reflected sound within the critical distance.

Here’s where a concept called “midrange narrowing and beaming” comes in. This phenomenon, though primarily affecting off-axis response, can also slightly impact the on-axis response, representing a loss of usable energy and contributing to an imbalance in sound reproduction. You can find more details about this in the linked article: Midrange narrowing and beaming

A Point about Frequency Correction (EQ) and Phase Shift

As described here: How to implement my horn and my speaker, correct the frequency response with IIR (minimum phase filtering) EQ is the way to do:

• Minimum phase filtering also modifies the phase and it’s a very good point: Where there is a deep on a pick on frequency the phase is also impacted in the same way, an IIR EQ will not only correct the response in frequency but also phase response in the same time, and in a good way, we need this phase response impact for linearize it too.

• FIR filtering (linear phase filtering) must be only used for crossover, when we want to do crossover we want to cut the response but without touching the phase, it’s what FIR filtering does, so no EQ in FIR, only crossover.

Conclusion and impact on distortion

Understanding how energy distribution works in compression driver horns allows for informed choices when selecting drivers and horns for our applications, especially when it come to adapt our coverage to our critical distance.

We don’t listen horn without EQ it, even in passive filtering, the horn response should be more or less flat at 30/60cm right in front of him, so the raw on axis response is not a factor of choice.

It’s more interesting to EQ the response flat at 30cm and measure the distortion, in this case the distortion response at high volume will be the crucial factor about the driver as well as Time-domain measurements.

Considering horns with similar loading capacities and directivity pattern (complete polar map of both axis) that determines how sound is dispersed across different angles at different frequencies:
The on-axis frequency response will show very minimal variation with the same driver.

Loading can give use more SPL at mid-low frequencies, but the starting energy is fixed at the beginning by the compression driver and cannot be changed.

Sound Source Behavior: Near Field, Transition, and Far Field

Understanding how sound waves behave near their source is crucial in various audio applications.

Here, we’ll explore the characteristics of sound in three key regions, including how sound pressure level (SPL) changes with distance.

Near Field & Fresnel Zone

Near field and Fresnel Zone is not exactly the same concept:

• Fresnel Zone: This zone focuses on wavefront curvature. It defines an area where the curvature of the wavefront is important for accurate calculations of sound propagation.

• Near Field: This zone focuses on sound pressure variations. It’s the region where sound waves haven’t fully developed their characteristic shape.

  The near field, is the region close to the sound source where sound waves are flat or haven’t fully formed (chaotic), depending on source drivers and frequency.

In a single source they both end at the same place, at the transition distance, but not in the case of a composed source (Line Array, SBA).

Sources:

• “Sound System Engineering” by Carolyn Audio Engineering
• “Audio Engineering Handbook” by Gary Davis and Ralph Jones

The behavior of different sound sources in the near field can vary

• Cone and Dome Drivers: Due to their operating principle and emissive shape, cone and dome driver wavefronts in the near field are complex and exhibit pressure variations. This complexity arises because the sound wave hasn’t propagated enough to establish a stable wavefront structure and diffractions occurs whith surround. As a result, the sound pressure can vary significantly depending on the frequency of the sound wave.

• Compression Drivers: Compression drivers exhibit a more plane wave-like behavior in the near field, especially at lower frequencies. However, it’s important to note that this “flatness” is relative and depends on the specific distance and frequency. Even in the near field, the wavefront can exhibit some curvature or phase variations, especially at the edges. As the sound wave propagates through the horn throat, it starts to interact with the horn’s geometry, further influencing the wavefront shape.

• Line Arrays (composed source): Line arrays, with their elongated design, can present a relatively flat wavefront becoming cylindrical-like with the distance in the Fresnel Zone, they can operate in the Fresnel zone over a very long distance in relation to and depending on their large size if the wavefront doesn’t encounter obstacles and the line array posisioned far from any obstacle or surface.

SPL Decrease in the Fresnel Zone

It can vary depending on the specific shape and frequency so no precise rules can be given, however, line arrays, due to their cylindrical-like wave propagation in Near Field, may exhibit a decrease in sound pressure level closer to 3 dB per doubling of distance compared to the 6 dB rule of the far field.

Transition Distance

The transition distance marks the point where Fresnel zone with their spherical wave transform into the far field’s characteristic flat wavefronts. This distance depends on several factors, including:

• Source Size: Larger sources generally have a larger near field compared to smaller sources at the same frequency.

• Sound Frequency: Lower frequencies tend to have a larger near field compared to higher frequencies for a given source size.

It’s important to note that in case of single source, the near field end when Fresnel zone basically end, but not for combined source like SBA or Line Array where Fresnel zone ends way further.

For a cone, dome and compression drivers :

In Line Array case :

Formula can be found in Appendix.

Far Field (Fraunhofer Zone)

The far field, also known as the Fraunhofer zone, is the region where sound waves are considered to have minimal curvature. This characteristic allows for straightforward calculations and predictions of sound propagation through a space.

Behavior of Different Sound Sources in the Far Field

While the wavefronts in the far field are more predictable for all sources compared to the near field, there are still some subtle differences in how different sound sources radiate sound:

• Cone and Dome Drivers: In the far field, cone and dome driver sound pressure follows the inverse square law for the most part. However, for large drivers, at the edges of the radiating area, there might be a slight roll-off in high frequencies due to diffraction effects. The interaction of the driver’s wavefront with the enclosure edges can also contribute to bending it towards a more rounded shape, further influencing the far-field behavior.

• Compression Drivers with Horns: Once the sound wave exits the horn in the far field, it generally follows the inverse square law. However, the horn’s directivity pattern (how it focuses sound in specific directions) determines how the sound pressure is distributed in the far field, the midrange narrowing if present and horn mouth will also impact wavefront edge.

• Line arrays: Line arrays, due to their design, tend to maintain a more coherent wavefront over a larger area in the far field compared to point source speakers like cone and dome drivers. This translates to a more consistent decrease in sound pressure with distance according to the inverse square law within the coverage area of the line array.

SPL Decrease in the Far Field

In the far field, sound pressure level (SPL) generally decreases by approximately 6 dB for each doubling of the distance from the source. This phenomenon is known as the inverse square law. It allows for simpler predictions of sound level at different distances in the far field. This decrease occurs because the wave propagation is spherical, and the expanding wavefront covers a much larger surface area with increasing distance.

Walls effect

In Far field and in a room , the shape of a wavefront typically changes, transforming into a plane-wave like behavior due to three factors.

Firstly, like a wave in a tube, the wavefront in a room can’t expanding infinitely on its sides, walls act as barriers, forcing the spherical wave to interact with them.
Secondly, wavefronts tend to travel perpendicular to the surfaces they encounter.
Thirdly, the further the wavelength propagate in the room, the more the circle section looks flatter in the room point of view.

This interaction with the walls essentially reshapes the wavefront, transforming its curvature into a more planar form as it propagates further within the room.

Here is the extension from a single point source in blue and the 90° interaction with walls in red dots:

note: This is a over simplified schema for underestanding purpose, reflections (on objects and walls) and frequency wavelength will affect it.

Composed Sources

In audio, a composed source refers to sound originating from multiple, distinct primary locations that combine to create a single perceived auditory event. These individual locations act as single primary point sources, each radiating sound waves. The combined effect of these waves creates the final characteristic of the composed sound after a certain distance.

- Multiple Primary Point Sources: Unlike a single-point source where sound originates from one location, a composed source involves several sound-emitting points.

- Combined Sound Waves: The sound waves from each individual point source interact and add together to form the final perceived sound.

- Examples: Instruments like pianos, violins, and drums are classic examples. Even a human voice can be considered composed as different vocal tract sections contribute to the overall sound.

Composed Sources in Audio

• Line Array: A line array functions more like a composed source. It consists of multiple speaker elements arranged in a line. Each element acts as a primary sound source, and their combined radiation pattern creates a specific directivity for the sound. This allows line arrays to project sound over longer distances and control its vertical spread.

• SBA (Single Bass Array): While named “array,” an SBA often behaves acoustically like a single-point source at low frequencies. It achieves this by strategically placing four or more subwoofers (typically 18" or 21" woofers) on the front wall at approximately 20% of the distance from the room boundaries (walls, ceiling, and floor). This configuration creates a rectangular virtual source that radiates low frequencies in a plane-wave radiation, more uniformly than a single subwoofer.

  For sound propagation purposes, an SBA can be considered as a single source, especially at low frequencies where the wavelengths are large compared to the subwoofer spacing.

Plane Wave Radiation when single source combines:

The near field for an 18" subwoofer is around 3 cm at 30hz. Within this zone, the sound behaves chaotically. Beyond the near field (around 3cm), the wavefront transitions into a spherical pattern.

Even though a line array and SBA behave like a composed source, each individual speaker element within the line array will still have its own near field region.  This is because the near field depends on the size of the individual element and the wavelength of the sound it produces.

As the spherical waves propagate further, they combines in Far Field in a way that creates a plane wave radiation pattern, creating a Fresnel zone outside and after the near field, but not as an instantaneous process. 

• In the case of an SBA, the strategic placement of subwoofers creates a larger virtual source compared to a single subwoofer. This larger virtual source, combined with the influence of walls in a room (as seen in “Walls effect”), contribute to a more persistent planar wavefront behavior at low frequencies within the listening area.

  Here with a absorbing materials at rear wall for absorb incoming wavefront from front wall:

  

• Line arrays, due to their length, will also exhibit a planar wavefront within a certain distance (defined by the Fresnel zone and line array length). However, this planar behavior weakens as the distance from the line array increases, and the wavefront transitions back to a more spherical pattern.

  

Additionally, it’s important to remember that even these planar wavefronts are not perfect. If a plane wave encounters an object like a sofa, it will diffract, or bend, breaking the plane wavefront and leading to a more complex wave pattern.

In the case au SBA and in more than we have said upper, asymetrical room will not allow a true SBA plave wave front behavior.

DBA

A Distributed Bass Array (DBA) leverages an opposed second SBA to nullify pressure waves generated by the first main SBA.

This cancellation, achieved through phase reversal and delay, effectively reduces low-frequency reflections within the room, leading to improve modal regime and modes.

Here is a simplified representation of wave interference. The blue wavefront represents the original wave, while the red wavefront represents a wave introduced to cancel it:

This approach targets low frequencies and doesn’t participate to overall pressure level, the DBA cancellation system works up to 80/100hz in optimal acoustic conditions (obstacles).

The system consumes some SPL pressure so at very low frequency it may be interesting to stop the cancellation DBA effect and use all the subwoofers in phase with delay to maintain SPL, depending on room gain and acoustics.

A suffisent absorbing material on a significant deep (at least 80cm) on rear wall will aslo bring a fair enought reduction of this incoming wavefront as seen with SBA.

Wavefront Behavior and Diffraction

The wavefront travels at the speed of sound, which is constant in a given medium.

The edges of the wavefront are always perpendicular (90°) to the profile of the source.

This schema just show the theory:

However, sudden changes in the source’s profile, like the end of a horn or the baffle itself, can disrupt this ideal behavior and cause diffraction.

Diffraction is the phenomenon of sound bending around obstacles or edges. This effect becomes significant when the wavelength (λ) is larger than the obstacle.

When the wavelength is smaller than the obstacle, sound behaves more like a ray of light. It is blocked by the object, creating an acoustic shadow zone behind it. As frequency increases (shorter wavelengths), the natural off-axis radiation diminishes due to beaming effects (when the wavefront leaves the surface and energy concentrates along the forward axis), making the sound more directional and more sensitive to small obstacles, such as a protruding screw. The sound forms a forward-directed beam, leaving the surface, reducing energy behind the object.

In loudspeaker design, it can occur when sound waves encounter the end of a horn, the edges of the cabinet, or other abrupt changes in the source profile.

This bending of the wavefront can distort the sound and affect the on and off axis frequency response of the loudspeaker, introducing unwanted effects like:

Midrange narrowing: Describe here, A very large dip in the frequency response on and off axis in the midrange frequencies.

Beaming: The concentration of sound in a specific direction, often at the expense of sound radiating in other directions.

To minimize these issues, loudspeaker designers strive for smooth transitions in the source profile to avoid creating sharp edges or mouth that can cause significant diffraction.

Beaming Effect

Beaming occurs when the sound radiated by a driver or horn becomes increasingly concentrated along its forward axis as frequency rises. At low frequencies, the wavelength is large compared to the radiating surface, so the sound spreads broadly in all directions. At higher frequencies, when the wavelength becomes comparable to or smaller than the radiating surface, the wavefront tends to detach from the baffle or horn mouth, forming a forward-directed beam.

With a horn, a sudden or abrupt change in profile will exacerbate this effect, causing a more pronounced forward concentration and potentially introducing unevenness or reflections in the wavefront.

This effect reduces the natural off-axis radiation, making the sound more directional. Both direct radiating woofers and horns exhibit beaming at higher frequencies, influencing perceived balance, spatial coverage, and sensitivity to obstacles in the sound path.

Radiation Space and “room gain”

Radiation space is a solid angle that characterizes the measurement context:

• 4π: whole sphere, measurement without a wall (on a mat for example)
• 2π: hemisphere, so one wall considered infinite
• 1π: quarter sphere, so two walls considered infinite
• 1/2π: 1/8 of a sphere, so 3 walls considered infinite

It will impact “low loading” of the speaker :

Additional Information

• The speed of sound in air is approximately 340 meters per second (m/s).
• The wavelength of sound (so called Lambda: speed of sound/Frequency) is inversely proportional to its frequency.

Appendix: Transition Distance Formula

For a circular radiating surface:

Zf = (2 * D^2) / λ

Where:

• Zf is the distance to the beginning of the Fraunhofer zone (meters)
• D is the diameter of the radiating surface (meters)
• λ (Lambda) is the wavelength of the sound (meters)

For a rectangular radiating surface:

Zf = (2 * a^2 * b^2) / (λ a + λ* b)

Where:

• Zf is the distance to the beginning of the Fraunhofer zone (meters)
• a is the length of the radiating surface (meters)
• b is the width of the radiating surface (meters)
• λ (lambda) is the wavelength of the sound (meters)

Calculating Lambda:

λ = c/F

Where:

• F is the frequency of the sound (Hz)
• c is the speed of sound (approximately 340 m/s in air)

The Sound

Sound, a ubiquitous pressure wave, carries information and shapes our auditory experience.

However, its journey from source to ear is not always a straight line.

Two fundamental concepts, diffraction and standing waves, play a crucial role in understanding how sound interacts with its environment and ultimately affects sound reproduction.

Diffraction

When sound waves encounter an obstacle or a narrow opening, a phenomenon called diffraction occurs. Here, the wavefront, the edge of the wave carrying the disturbance, doesn’t simply stop. Instead, it bends around the obstacle, constantly striving to maintain a 90-degree angle with the encountered profile. This characteristic allows sound to travel around corners, through gaps, and even diffracted through small openings, shaping its overall propagation pattern.

The concept of maintaining a 90-degree angle is crucial as seen in Wavefront Propagation article. As the wavefront bends, different sections travel slightly different distances. However, the speed of sound remains constant throughout the entire wavefront. This interplay between the bending wavefront and the constant speed of sound is what governs the overall behavior of diffracted waves.

Examples of Diffraction

• Non-continuous geometry: Sound travels as pressure variations in a medium like air. Inside a horn or on a baffle, the geometry can significantly impact how sound propagates. If the shape has abrupt changes or isn’t a “fluid profile,” diffraction will occur.

• Obstacles in the path: If an object sits in the path of the sound wave, diffraction causes the wave to bend around it. While some sound is blocked, some will diffract, creating a partial shadow effect. Depending on the size and position of the obstacle, the sound might diffract significantly, reducing its effectiveness. (e.g., woofer below a tweeter section)

• Phase shield: A phase shield is a small obstacle placed a few millimeters in front of an audio source like a dome tweeter for mainly create diffraction based directivity in high frequency.
  While it acts as a barrier, a phase shield uses diffraction to create a high frequency sound direction when a phase plug on the other hand, achieves optimal directivity with a plane wave behavior, avoiding diffraction for clearer, more accurate sound.

Baffle Step and Edge Diffraction

When a horn or sound source mounts onto a flat surface (baffle), a sudden change in geometry disrupts the wavefront. This discontinuity creates two key effects:

• Baffle Step and Directivity: As sound waves from the source reach the baffle’s edge, they diffract outwards (edge diffraction). This diffraction interacts with the sound waves traveling directly from the source. Depending on the baffle size relative to the wavelength, these interactions can cause:

• Baffle Step: A dip in sound pressure at the edge due to destructive interference between the direct and diffracted waves. The size of the baffle influences the severity of this dip. Larger baffles can mitigate baffle step at lower frequencies.

• Directivity: Edge diffraction can also affect the overall directivity (focusing) of the sound, especially at higher frequencies with shorter wavelengths.

Note: While baffle step introduces a dip in sound pressure, the overall surface area of the baffle can still contribute to a gain in radiated sound energy compared to a point source. Baffle Step article explores this phenomenon in more detail.

Diffraction on woofer

Even with a smooth profile, the physical presence of the woofer, positioned vertically, will influence the vertical response and, to a lesser extent, the horizontal response.

Here’s why, as illustrated by the pressure level from 1 to 10 kHz when the horn or waveguide radiates sound:

We can observe the impact of diffraction on the woofer’s shape.

The closer the woofer is to the horn, the fewer vertical lobes but the more pronounced the diffraction.

From the woofer’s perspective, the wavefront continues inside the horn, creating a kind of virtual or phantom source, we can observe it here from 200 to 2000 Hz:

This also explains why the horn tends to be the overall virtual point source of emission for the entire speaker, while in a regular speaker, it’s between the tweeter (in direct radiation) and the mid-woofer.

These diffractions significantly affect the vertical polar response and even the horizontal one when components are very close. This diffraction, present in all speaker designs, becomes more problematic when a waveguide is added to the mid-woofer and the vertical center-to-center spacing is less than 17-20 cm.

Let’s take the worst case

Here are two polar plots of a tweeter waveguide, one with the horn alone and another with a mid-woofer also using a waveguide at a center to center distance of 15 cm, but with the mid-woofer not emitting sound.

• Horizontally:

• Vertically:

As we can see, the diffraction effect impacts all wavefronts, including the mid-woofer’s.

Therefore, when the vertical center-to-center spacing between two components is less than 17-20 cm, whatever the crossover frequency, we recommend avoiding adding a waveguide to the mid-woofer.

An MTM arrangement will also exacerbate the problem.

Why it becomes less impacting when vertical center to center increase ?

By increasing the distance, you slowly move the impacted frequency range downwards so the impacted wavelength becomes larger, the impacted energy level also decreases slightly. But this frequency range will remain wide.

To increase the distance without introducing lobe problems, you will need to lower the crossover frequency so to use a larger horn so a bigger mid-woofer too.

Increasing vertical spacing allows longer wavelengths to pass through, reducing the obstacle’s (woofer surround or woofer shape) impact. Consequently, the obstacle appears less significant from the perspective of these longer wavelengths.

Technically: By increasing vertical spacing, the obstacle becomes less effective at obstructing longer wavelengths. This reduces the obstacle’s apparent size or “visibility” to these wavelengths.

We can argue that if we increase the distance and lower the crossover frequency, the woofer, as well as the horn, will be bigger. Consequently, the woofer’s surround will also be larger. Even if the impacted wavelength is larger, the woofer’s surround will still be a visible obstacle due to its increased size.

However, the wavelength will increase faster than the woofer surround size, ultimately reducing the woofer’s surround diffraction impact by increasing the vertical distance with the high frequency component. Of course, it will requires larger components and a lower crossover frequency.

Standing Waves

In contrast to diffraction, standing waves occur when a wave reflects off a boundary and interferes with itself. The reflected wave can either add up (constructive interference) or cancel out (destructive interference) with the incoming wave, creating specific points of vibration and stillness. Standing waves are less relevant within the horn itself, but they can come into at the exit

Exit of the Horn

At the horn’s exit, the expanding geometry might not perfectly support a single, propagating wave. If the horn isn’t properly designed, this can lead to the formation of standing waves near the exit. These standing waves can cause an uneven distribution of sound pressure, resulting in:

• Midrange Narrowing: Certain frequencies might experience destructive interference, leading to a dip in the sound pressure at those frequencies. This reduces the overall strength of the midrange sound.

• Midrange Beaming: Conversely, constructive interference can create focused beams of sound at specific frequencies, emphasizing them disproportionately.

Note: Mid-range Narrowing and Beaming article goes deep in these two concepts.

Understanding Wave Behavior: Diffraction vs. Standing Waves

It’s important to clarify that diffraction doesn’t actually break the wavefront into separate pieces. Instead, the wavefront itself bends and spreads as it encounters obstacles or openings. Imagine a perfect wavefront like a straight line of dominoes standing upright. When the dominoes encounter a curved wall, they topple over in a curved pattern, mimicking how the wavefront adapts to the new geometry.

In contrast, standing waves arise from the interaction between an original wave and its reflection. The reflected wave can superimpose on the original, creating regions where the peaks (crests) and troughs (valleys) reinforce each other (constructive interference) or cancel each other out (destructive interference). These regions of reinforcement and cancellation create a stationary pattern of vibration, hence the term “standing wave.” The wavefront itself, however, remains intact.

Coloration and Wave Interactions

Diffraction and standing waves, while interesting phenomena, can introduce unwanted colorations to the sound. These wave interactions can emphasize or weaken certain frequencies, leading to an uneven and distorted representation of the original sound.

For instance, diffraction around obstacles or improper horn design can bend the wavefront around obstacles, sometimes even partially destroying it, leading to frequency-dependent dips and uneven high-frequency response.

Similarly, standing waves can introduce peaks and nulls in the listening area, boosting or canceling specific frequencies.

These effects can manifest as a thin or bright sound lacking body, or an overly harsh and emphasized high-frequency range.

By understanding these wave interactions, we can design audio systems that minimize coloration for a more accurate sound reproduction.