Wavefront Propagation
Near Field or Fresnel Zone
The near field is the region where the source behaves as a plane wave, meaning the wavefronts are flat and parallel.
This region is located near the source, typically a few millimeters or centimeters, in fact only line array allow by their size to be listen in near field area.
Transition Distance
The transition distance is the distance at which the wave transitions from the near field to the far field. It depends on the size of the source and the frequency of the sound.
Formula:
L = D² * F / (2 * c)
Where:
- L is the transition distance (meters)
- D is the diameter of the source (meters)
- F is the frequency of the sound (Hz)
- c is the speed of sound (approximately 340 m/s in air)
Far Field or Fraunhofer Zone
The Fraunhofer zone is the region where the wavefront of a sound wave is approximately spherical. The distance to the beginning of the Fraunhofer zone depends on the frequency of the sound and the surface area of the radiating source.
In other words, it is the point at which the wave transitions from a plane wave to a spherical wave.
Formulas :
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)
Near Field vs. Far Field
In the Fresnel zone (Near Field), the propagation of waves is cylindrical. As the distance increases, so does the surface area. This results in a 3dB attenuation (1/distance).
In the Fraunhofer zone (Far Field), the wave propagation is spherical. When the distance doubles, the surface area quadruples. This results in a 6dB attenuation (1/distance^2).
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. 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:
- 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 colled Lambda: speed of sound/Fr) is inversely proportional to its frequency.