Note on the Effect of Reflection by the Microphone in Sound Measurements

The reflection of sound by the diaphragm of the microphone ordinarily used in the measurement of the instantaneous pressure in sound waves causes the indicated pressure to vary from equality with the actual pressure in the undisturbed wave at low frequencies, to twice this pressure at high frequencies. Due to the mathematically irregular shape of the conventional microphone and its mounting the effect cannot be calculated although it can be experimentally determined by comparison with the Rayleigh disk. It is proposed to evaluate the correction for reflection by employing a standard spherical mounting of which the diaphragm occupies a small area about the pole; the increase in pressure for this mounting can be calculated theoretically, and the correction for other mountings canl then be obtained by experimental comparison. The ratio of pressure in the pole of the spherical mounting to that in the undisturbed wave, for a plane wave of the type Exp i(t-x/V) is expressed in terms of Hankel's H
n+1/2
²
functions, for which tables exist up to the highest orders required for the computations in practical cases. Numerical computations are carried out in full, giving the vector pressure ratio at the pole facing the source for spheres of various diameters and at various frequencies throughout the acoustic range.