I must start out by confessing that I've never used or built a parabolic mi=
crophone. In fact I've never even seen one. But all of this discussion ha=
s piqued my interest.
In order to achieve the theoretical gain, the actual recording circumstance=
s must result in the waves from various directions arriving at the focus wi=
th phase errors conforming precisely to the expectation of theory. Put ano=
ther way, everything must work exactly right, or the gain will be less than=
predicted by theory. This can be seen in Wahlstrom's figures 12, 13, and =
14. The measured gain is always below the theoretical gain with the except=
ion of one data point in figure 14.
If follows that Errors of the following types may occur in practice:
Focal length error
Non conformance to exact paraboloid
Aiming error
Violation of the plane-wave assumption
Focal length error: If the microphone is not located precisely at the focal=
point, then it will be progressively further away from the point where the=
high-frequency maximum is, and the high-frequency output will be less than=
the theoretical optimum. This is shown quite clearly in Wahlstrom's figur=
es 9, 10, and 11. One practical consideration is that the designer might l=
ike to use a tripod arrangement to support the microphone capsule from the =
rim of the dish, but for the case where =E1 =3D l this results in a non-rig=
id support system
Non-conformance to an exact paraboloid results in waves from one direction =
arriving with positive or negative phase shifts relative to other direction=
s of incidence. Variations of 1/2 wavelength, which is only about 8.6 mm a=
t 20 kHz, will result in complete cancellation. Not only can there be erro=
rs due to manufacturing tolerance, but for flexible paraboloids it is extre=
mely unrealistic to expect that they will snap back to exactly their origin=
al shape. Assuming that the errors are not systematic, the result is merel=
y a failure for the gain to continue to increase at higher frequencies.
A side implication is that a spherical reflector may work nearly as well in=
practice, and be easier to fabricate.
Aiming error when measuring (or using) the microphone will result in a roll=
ed-off frequency response. Because the polar pattern of a parabolic microp=
hone becomes progressively narrower with increasing frequency,
A violation of the plane wave assumption will occur if the source of the so=
und is not located at infinity. Again, in order to achieve the theoretical=
gain from the paraboloid reflector it is necessary that the planarity of t=
he wavefront not be in error by more than about 1/4 wavelength. Note that =
this effect increases with the size of the dish. A very large paraboloid i=
s not appropriate for recording near sources. Assuming that the dish is 0.=
5 meters in diameter, and that the distance is 10 m.
So for a dish of diameter 0.5 meters, 5 meters from the source, the "height=
" of the wavefront entering the dish is about 1.2 cm. This will result in =
cancellation for a source at approximately 14 kHz.
In looking at Wahlstrom's analysis in his appendices, I see that the figure=
s do not precisely portray the shape of the gain curve. Using Wahlstrom's =
analysis and the result in his Equation 14, I have calculated the theoretic=
al gain curve for a parabolic microphone of dimensions the same as that of =
the Telinga microphone. The horizontal axis thus takes on the dimensions o=
f Hz. The principle thing that can be seen that is not visible in the figu=
res in Wahlstrom's paper is that the oscillating part of the sound field af=
fects the response up to high frequencies. The implication of this is that=
the sound is dispersed in time, and indeed this would be expected given th=
at there is both a direct sound and focused sound component to the micropho=
ne signal.
If there is interest on the part of the group, I could expand upon this in =
more detail, and put the results into the files section of the Nature Recor=
dist group pages.
Eric
[Non-text portions of this message have been removed]
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