APPLICATION OF HILBERT-SPACE TECHNIQUES AND GREENS-FUNCTION METHODS TO A REALISTIC CONDENSER MICROPHONE MODEL

A realistic model for a condenser microphone is theoretically investig ated. The model consists of a rigid cylinder closed on the bottom by a membrane and on the top by a rigid plate. The cylinder is divided int o two chambers by an electrode with a number of small holes. This coup led acoustic system is mathematically treated by an operator formalism . Each part of the system (outer space, membrane, electrode, two chamb ers) corresponds a linear operator in a Hilbert space. The interfaces (membrane, electrode with holes) correspond to state vectors in this H ilbert space. Applying Green's integral formula leads to a system of e quations in this space, corresponding conventionally to integral equat ions with Green's functions as kernels. By approximating the operators of the two chambers by multiples of the identity operator (i.e., conv entionally replacing the singular Green's function by multiples of the Dirac delta function) it is possible to solve the problem analyticall y, taking into account exactly the pattern of the holes in the electro de, thus avoiding an approximation made in the preceding paper. The ag reement with experiment is very satisfactory. (C) 1996 Acoustical Soci ety of America.