Horn Loading

Horn Loading and Efficiency: Frequency Dependence

Horn loading is a technique used in loudspeakers to improve the efficiency and directivity of sound radiation. A horn acts as an acoustic waveguide, channeling the sound waves from the driver (speaker) in a specific direction. This focusing effect can significantly increase the sound pressure level compared to a simple driver without a horn.

We will describe technical terms here but loading works like this:

• Impact Loading: The closer and smaller the air surface near a horn’s throat, the greater the impact loading.

• Directivity Control: Loading cannot be “sent” beyond the horn’s directivity control end; this would be ineffective. Horns exhibiting good loading effects often have a strong cutoff approaching the horn’s control end, due to this effect, allowing for a lower crossover frequency that can be defined by Group Delay, in addition to directivity matching and driver distortion.
  This interplay between directivity and loading can also result in a “bell response” due to the interplay of constant directivity and loading.

• Loading and Frequency: Loading effect decreases with increasing frequency. Consequently, the “anchor point” (14/15kHz) SPL, used for our horn EQ, remains unaffected by loading but will be influenced by directivity, as discussed in the next point.

• Off-Axis Energy: At a given frequency, energy present off-axis is no more present on-axis. This is one of the reasons why pursuing constant directivity up to 20kHz is not necessary, especially when considering audibility and psychoacoustics.

• Loading Uniformity: Loading is not uniform at all. The characteristics mentioned above define a frequency range of loading effects, with a given dB pressure level, forming a curve that will interact with driver one. Surface area size, expansion, and directivity significantly influence these effects.

• Example of Loading Effect: Lengthening the horn throat can significantly alter loading. However, these manipulations must be approached cautiously as they impact wavefront propagation and, consequently, directivity. This is why FEA simulations are essential for accurate predictions.

Acoustic impedance

Acoustic impedance plays a crucial role in horn loading and its impact on efficiency. Ideally, a well-designed horn will present a gradual change in impedance across the desired frequency range, ensuring a good match between the driver’s impedance and the horn’s impedance (“acoustic impedance matching”). This minimizes energy reflection and maximizes the transfer of sound energy from the driver to the horn.

However, the effectiveness of horn loading and its impact on efficiency are frequency-dependent:

• At low frequencies: The wavelength of sound is larger than the horn throat dimensions, limiting its ability to efficiently control the sound wave propagation. The horn loading effect on efficiency may be minimal or even negative at very low frequencies.

• At mid frequencies: The horn starts to have a more significant influence on the sound wave propagation, potentially improving efficiency by focusing the sound energy. A well-designed horn can achieve a good impedance match in this range, maximizing the energy transfer.

• At high frequencies: As the wavelength of sound becomes smaller compared to the horn dimensions, the horn can more effectively control the sound wave propagation. However, viscous friction within the horn, contributing to acoustic resistance, becomes more pronounced at higher frequencies. This increased resistance can lead to some energy loss, gradually reducing the efficiency gains from horn loading as the frequency increases.

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 pattern and can cause irregularities in the directivity pattern (how the sound radiates in different directions) and degrade the sound quality.

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.

How a Horn Increases Efficiency at Low Frequencies

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

• Directivity of the horn, as it impact his surface propagation and deep

• Size and shape of the horn throat and horn in general

• Frequency of the sound

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.

Think of it like this:

• Imagine pushing a heavy object (high impedance) on soft sand (low impedance). It takes a lot of effort (large diaphragm movement) to move the object a small distance.

• Now, imagine placing a board (horn) under the object. The board influences the effective impedance of the sand, creating a better match for the object. Now, pushing the object requires less effort (potentially smaller diaphragm movement) to achieve the same movement distance for lower frequencies.

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.

More informations about global energy in horn: Horn and energy

A point about Constant Directivity Horns:

As energy is not “free”, a constant directivity horn cannot be straight on axis as the energy is dispashed off axis to be constant, that we need, so the on axis response will show a bell response curve.

Appendix

Acoustic Impedance (Z)

In the realm of acoustics, acoustic impedance (Z) is a critical concept. It represents the overall opposition a material offers to the propagation of sound waves. It’s a complex quantity, similar to electrical impedance in AC circuits. However, instead of combining resistance and reactance for current flow, acoustic impedance combines:

• Acoustic Resistance (R): This describes the energy loss due to viscous friction within the medium.

• Acoustic Reactance (X): This represents the storage and release of sound energy due to the material’s inertia and elasticity.

Unlike resistance, reactance doesn’t directly dissipate energy but influences how the sound wave propagates. The relationship between impedance and frequency is not strictly linear. It depends on the interplay between resistance and reactance at different frequencies. Understanding acoustic impedance is crucial for various applications in acoustics, such as loudspeaker design and noise control.

Acoustic Resistance (R)

Acoustic resistance (R) is a specific component of acoustic impedance that represents the energy loss that occurs as sound waves travel through a material. This loss is due to viscous friction, similar to air resistance slowing down a moving object. As sound waves propagate, the particles within the medium experience friction, causing some of the sound energy to be converted into heat.

The higher the acoustic resistance of a material, the greater the energy loss it inflicts on sound waves. This translates to a decrease in the sound wave’s intensity and amplitude as it travels through the medium. Materials with high acoustic resistance are often used for soundproofing applications as they effectively dissipate sound energy.

Understanding acoustic resistance is vital when selecting materials for various acoustic applications. For example, in soundproofing materials, we seek materials with high acoustic resistance to effectively absorb and dissipate sound energy.

Acoustic Reactance (X)

Acoustic reactance (X), another component of acoustic impedance, doesn’t directly dissipate energy like resistance. Instead, it represents the storage and release of sound energy within the medium due to its inertia (mass) and elasticity (stiffness). Reactance influences how the sound wave propagates, affecting the relationship between pressure and particle velocity in the wave.

There are two main types of acoustic reactance:

• Mass Reactance (Inertance): At lower frequencies, the mass of the medium plays a more significant role. Similar to inertia in mechanics, the mass can hinder the movement of sound particles, requiring more pressure to maintain wave propagation. This mass reactance contributes to a rising impedance with decreasing frequency.

• Stiffness Reactance: At higher frequencies, the elasticity of the medium comes into play. The stiffness can oppose rapid pressure changes in the sound wave, similar to a spring resisting compression or expansion. This stiffness reactance can lead to a potential decrease in impedance with increasing frequency.