Free-Field Corrections for Condenser Microphones

A comprehensive theoretical investigation of the free-field response of Briiel and Kjaer standard condenser microphones type 4144 and 4145 for a plane, periodic wave system normally incident upon the microphone diaphragm is presented. The solutions to (a) the sound field in the external free-field region, (b) the internal sound field inside a recess and (c) the vibration of the diaphragm are connected by appropriate boundary conditions leading to a system of simultaneous matrix equations. Sound pressure and particle velocity are here represented by column infinite matrices whose elements consist of expansion coefficients arising from expansion by orthogonal functions. Semi-empirical expressions for diaphragm impedances and tensions are developed and numerical calculations are carried out on an IBM 370/165 digital computer. The numerical results comprise numerical solution convergency criteria, excess pressure and diaphragm displacement distributions versus frequency, frequency response curves versus diaphragm impedances and tensions, free-field corrections dependence on diaphragm impedance, depth and radius of recess and type of gas surrounding the microphone. The numerical results are compared to experimental findings by other authors and a very good agreement is found stressing the utility of the theoretical analysis for calibration and control purposes.