Title: Radiation Loading of Prolate Spheroidal Surfaces
Abstract: Prolate spheroidal coordinates and associated prolate spheroidal wave functions are used to study the acoustic radiation from arbitrarily vibrating prolate spheroidal surfaces. The theory was originally developed to study the farfield sound propagation from submerged ellipsoids of revolution with high fineness ratios (L/R). Boundary conditions are adjusted to the general wave solutions to obtain an expression for the sound pressure. The results show that a single prolate spheroidal vibration mode excites an infinite number of pressure modes. A local radiation impedance is defined and discussed. This impedance shows the effect of the strong locally variable nearfield and that the spheroid generates (L/2R) more acoustic power per unit area at the equator than at the poles. The application of the theory is demonstrated through numerical calculations of the farfield radiation from a particular submerged body of revolution in which experimental data was available. The agreement between the predicted and measured sound-pressure levels is good.