by Michael Williams,
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More on Microphones
by Michael Williams,
(www.williamsmmad.com) △ < ∧ > |
3 - SOUND WAVE PROPAGATION
The sound wave, travelling at about 340m/s, will be transmitted through the air as small variations of pressure superimposed on the general atmospheric pressure around us. Physically this will produce a small localized vibratory displacement of air particles as the sound wave progresses. The upper part of Figure 2 shows a very much exaggerated representation of the air particle movement, whilst the lower part shows a graphical representation of the sound wave pressure variation. The darker areas in the upper part of the diagram represent an increase in pressure due to a higher density of air particles with respect to atmospheric pressure - the lighter areas represent a decrease in pressure due to a lower particle density.
Figure 2 - The Travelling Sound Wave
The variation in pressure caused by the sound wave is actually very much smaller than the atmospheric pressure around us. If we consider atmospheric pressure to be approximately 105 Pa (or 1 bar), then the quietest sound that we can hear is about 2.10-5 Pa (or 2.10-4æbar) and the loudest sound that we can tolerate without pain, is about 20Pa or 200æbar. The microphone must detect these small variations of sound wave pressure as a similar movement of the microphone diaphragm. The force exerted on the microphone diaphragm by this variation in sound pressure is essentially a function of the difference in pressure between each side of the diaphragm.
It is however impossible to introduce a microphone into the free field propagation of a sound wave without in some way disturbing the sound wave - the microphone can be considered as an acoustic obstacle to the propagation of the sound wave. The sound wave pressure acting on the diaphragm of a microphone will in general be different from the free field pressure which existed prior to the introduction of the microphone. This effect is due to diffraction. Sound diffraction results in distortion of the wave front of the incident wave due to the fact that part of the incident energy is re-radiated or scattered by the obstacle, thus interfering with the incident wave field. We can identify three components parts of this diffraction phenomena:The magnitude of the effect of diffraction will depend on the size and shape of the microphone and is inversely proportional to the wavelength of the incident sound. At the extreme high frequency end of the spectrum as shown in Figure 3 we can see a somewhat simplified representation of the effect of diffraction for a sound wave at an incident angle of 0ø and at a frequency where the microphone diameter is about 8 times the wavelength of the incident sound. This diagram shows the increase in pressure produced by reflection from the front surface of the microphone, the shadow zone created behind the obstacle created by the microphone, and the spherical wave re-radiation at each of the corners of the microphone capsule and housing.
- Increase in pressure due to reflection from the front surface of the microphone
- Shadowing behind the obstacle created by the microphone housing
- Secondary radiation by the edges of the microphone capsule and microphone housing
Figure 3 - Sound Wave Propagation in the High Frequency Range
around an Acoustic Obstacle
At very low frequencies, this effect is so small as to be almost negligible on the signal generation function of a pressure microphone. However this is not the case with a pressure-gradient microphone where the pressure-gradient acoustic coupling function, generated by diffraction (as described by H.A.Olson[3]), is identical to the theoretical pressure-gradient function produced by the traditional path-length-difference analysis (as shown in Chapter 4.2 in Figure 10)). The pressure increase on the front surface of the microphone can have an appreciable effect on the frequency response curve of the microphone. However the influence of this pressure increase on signal generation will depend on the type of microphone transducer.
Curve A in Figure 4 shows the pressure increase at the center of the diaphragm for a 20mm diameter microphone in a cylindrical housing. An electrodynamic moving coil microphone with a basic piston movement will however be subjected to the average increase in pressure represented by Curve B in Figure 4 (bearing in mind that a moving coil microphone will normally have a much larger diaphragm - therefore the peak in response will be at a lower frequency). Whereas the influence of the pressure increase on an electrostatic condenser transducer with a stretched membrane diaphragm will vary across the entire surface of the diaphragm according to the specific pressure on an area of the diaphragm, and the contribution of that area on the variation of condenser capacity - in general the effect will be somewhat less than the average pressure increase.
The influence of diffraction on the output signal generated by the microphone will also depend on the angle of incidence of the sound wave to the microphone diaphragm and housing - at about 90° to the axis of the microphone the effect of diffraction on the diaphragm is negligible.
Figure 4 - Pressure Increase on a 20mm Diaphragm due to Reflection of Sound Wave
[3] "Elements of Acoustical Engineering - Chapter 9.3: Velocity Microphones" by H.F.Olson, published by D.Van Nostrand Company in 1940/42/43
