W. Kainz, ANALYTICAL SOLUTION OF A CONDENSER MICROPHONE MODEL AS AN EXAMPLE OF THE MATHEMATICAL TREATMENT OF COUPLED ACOUSTIC SYSTEMS, The Journal of the Acoustical Society of America, 100(4), 1996, pp. 2156-2165
In this work an analytical model for a condenser microphone with a pat
tern of holes in the electrode is solved approximately by applying an
operator method of quantum mechanics. Essential is the replacement of
the operators corresponding to the Green's functions of the cylinder i
n the fundamental integral equations of the system by products of iden
tity operators times an appropriately chosen constant. The second appr
oximation is the averaging of the holes and by replacing the effect of
the holes in the electrode by a product of the identity operator time
s the part of the area of the small holes in the electrode compared to
the whole area of the electrode. The last approximation is the replac
ement of the displacement of the fluid in the small holes by their mea
n value and the assumption of small holes compared to the total area o
f the electrode. By a summation method over zeros of Bessel functions
it is possible to do infinite summations exactly and to provide an ana
lytical solution of the average displacement of the membrane as a func
tion of the frequency of the incoming plane wave. The approximations a
re justified by the good agreement with experiment. (C) 1996 Acoustica
l Society of America.