Sound scattering by cylinders of finite length. III. Deformed cylinders

Abstract

A general solution is derived for the scattering of sound by cylinders of finite length with a deformed axis and composition profile and (cross‐sectional) radius that vary along the axis. The orientation of the axis, plane‐wave source direction, and point receiver position can also vary as long as the directions of incident and scattered fields are nearly perpendicular to the tangent of the axis (this restriction can be relaxed under some conditions). This approximate solution is a generalization of previous work [T. K. Stanton, J. Acoust. Soc. Am. 8 3, 55–63 (1988); and 8 3, 64–67 (1988)] where the scattering by straight finite cylinders of uniform fluid and elastic material, respectively, was described. In those articles, the volume flow per unit length of the scattered field of the cylinders was held constant along the length of the axis that restricted the axis to be straight and composition profile and (cross‐sectional) radius to remain constant along the length of the axis. In this article, the volume flow per unit length is allowed to vary, thus allowing the above‐mentioned quantities also to vary. As a result, an integral equation is derived that, in general, needs to be evaluated numerically. Examples are given in this article of the scattering of sound at all frequencies from a prolate spheroid with a high aspect ratio (i.e., high ratio of major axis to minor axis) and a uniformly bent finite cylinder of constant cross‐sectional radius. There is excellent agreement between the (deformed cylinder) calculations involving the prolate spheroid and the exact spheroidal wave‐function solution. Furthermore, numerical integration of the deformed cylinder formula required far less computer time than calculating the exact solution. Calculations involving the bent cylinder are compared to backscatter data from preserved euphausiids and suggest that the radius of curvature of the animals plays a major role in the acoustic scattercharacteristics of the marine organisms. For example, at 200 kHz, the backscattering cross section of a 23‐mm‐long euphausiid will decrease by 6 dB if the animal bends by as little as 1.4 mm at the ends.