Theory of the Effect of a Thin Air Film on the Vibrations of a Stretched Circular Membrane

Abstract

In the design of condenser microphones it is standard practice to insert holes or furrows into the electrode face. This modification helps to prevent radial air flow through the electrode-membrane interstice which can result in large dissipative and reactive effects, provided the separation is small. The theory governing air reactions from an unmodified electrode is presented. An attempt was made to start with general fundamental equations. Only those simplifications which appeared to have a negligible effect on the accuracy of the results were made; for example, body forces and nonlinear terms have been neglected. Air inertia, rotational and irrotational velocity components, and viscous terms have been retained in the theory. Curves showing the effects of air reactions on the amplitude, phase, and impedance of a stretched titanium membrane are shown. The air stiffness, which continuously increased for increasing frequencies in the range 5 to 20 0000 cps, caused the amplitude of the membrane to diminish by more than 20 db. In general, air which is trapped behind the membrane will cause the response of the microphone to rise as the frequency is lowered.