Low-frequency acoustic scattering by gas-filled prolate spheroids in liquids

Abstract

This paper presents an analytic method for studying scattering of acoustic waves by gas-filled prolate spheroids at low frequencies. The method is based on the Kirchhoff integral theorem and Strasberg’s finding that the surface acoustic field and the velocity normal to the surface are mathematically equivalent to electrostatic potential and charge density on a perfect conductor having the same shape [M. Strasberg, J. Acoust. Soc. Am. 25, 536–537 (1953)]. The boundary-value problem is solved with aid from a thermodynamic relation. An analytic formula for the sound scattering function is derived, and is compared to the results obtained using the deformed cylinder method and that obtained by the T-matrix numerical method. It is shown that the results compare favorably with that from the T-matrix method, but differ from that obtained by the deformed cylinder approach, with respect to the dependence of the peak scattering value on the aspect ratio of prolate spheroids. However, away from the resonance region, the results from the deformed cylinder method seem to approach to the present results. The results show that both the present method and the T-matrix approach yield nearly the same resonance frequency and the quality Q factor, while the deformed cylinder method predicts lower values in the resonance scattering regime. However, there exist some differences between the present results and that from the T-matrix method as the aspect ratio increases. Possible criteria for the present approach to be valid are also discussed.