Membranes, Plates, and Microphones

Abstract

AbstractThe restoring forces on membranes are due to the applied tension, while the restoring forces for plates are due to the flexural rigidity of the plate’s material. The transition to two dimensions introduces some features that did not show up in our analysis of one-dimensional vibrating systems. Instead of applying boundary conditions at one or two points, those constraints will have to be applied along a line or a curve. In this way, incorporation of the boundary condition is linked inexorably to the choice of coordinate systems used to describe the resultant normal mode shape functions. For two-dimensional vibrators, two indices are required to specify the frequency of a normal mode,fm,n, with the number of modes in a given frequency interval increasing in proportion to the center frequency of the interval, even though that interval remains a fixed frequency span. It is also possible that modes with different mode numbers might correspond to the same frequency of vibration, a situation that is designated as “modal degeneracy.” A membrane’s response to sound pressures provides the basis for broadband condenser microphone technology that produces signals related to the electrical properties of that capacitor and the charge stored on its plates.