Sound Radiation from a Plane Radiator Having a Prescribed Pressure Distribution

Abstract

A theoretical investigation has been made of the sound radiation from a (flexible) plane radiator having a prescribed pressure distribution. For such a radiator vibrating in an infinite rigid plane, the problem is of the mixed-boundary-value type and is not solved easily in general. However, the sound field resulting from a freely vibrating, flexible plane radiator may be calculated from an integral quite similar to that given by Rayleigh for a plane radiator having a prescribed velocity distribution. For the particular case of the circular disk with a uniform pressure distribution, solutions have been obtained for the sound-pressure and velocity distributions and for the radiation impedance. These results are compared with the corresponding results for the flexible disk vibrating in an infinite plane, which are obtained directly from an existing solution for sound diffraction by a circular aperture. An interesting four-way comparison also is made between this set of results and the corresponding set for the rigid circular disk. Application of the results to the analysis of the electrostatic loudspeaker employing a thin plastic diaphragm is discussed.