Wavefront Propagation

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:

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:

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

Special cases

SPL Decrease in the Near Field

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:

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 :

fresnel

In Line Array case :

fresnel

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:

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:

wave front propagation

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.

- 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

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. 

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.

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:

Double Bass Array
By carefully controlling the phase and amplitude of the red wave, we can achieve destructive interference, preventing the blue wave from bouncing around and creating room modes.

Importantly, this approach targets low frequencies and doesn’t participate to overall pressure level, morehove 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.

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:

wave front propagation

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. 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.

Radiation Space and “room gain”

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

pi radiation space

It will impact “low loading” of the speaker :

pi radiation space speaker

Additional Information

Appendix: Transition Distance Formula

For a circular radiating surface:

Zf = (2 * D^2) / λ

Where:

For a rectangular radiating surface:

Zf = (2 * a^2 * b^2) / (λ a + λ* b)

Where:

Calculating Lambda:

λ = c/F

Where: