SCATTERING OF ACOUSTIC WAVES BY A PENETRABLE PROLATE SPHEROID, I. LIQUID PROLATE SPHEROID

The report is the first of a series on the scattering of waves by a penetrable prolate spheroid. In this article, 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 specific 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. (Author)