Scattering of Acoustic Waves by a Penetrable Prolate Spheroid. I. Liquid Prolate Spheroid

This is the first of a series of reports on the scattering of waves by a penetrable prolate spheroid. In this letter, the exact solution of the scattering of acoustic waves by a liquid prolate spheroid is obtained. Results are given in terms of the spheroidal functions. It is found that each expansion coefficient of the scattered or transmitted wave is coupled to all coefficients of the series expansion for the incident wave, except when the spheroid degenerates to a sphere. Detailed numerical computations for the radiation patterns of the scattered wave are carried out for a sphecific example. It is found that, in general, the radiation patterns for the scattered waves are more directional and possess more side lobes as the prolate spheroid becomes more elongated.