Composite ray-mode approximations for backscattered sound from gas-filled cylinders and swimbladders

Abstract

The normal mode solution for sound backscattered by a finite fluid (gas)-filled cylinder in water is replaced by a Kirchhoff approximation for ka>0.15 and the normal mode solution for ka<0.15 where a is cylinder radius and k is the wave number. The composite solution was tested for density and sound-speed ratios g and h in the ranges of 0.0012<g<0.05 and h=0.23. The simplification and approximations have been tested over the range of 0.0005<ka<20. Expressions that include straight and bent cylinders are given. A derivation of the amplitude and phase factor for finite cylinder lengths is given. The amplitude factor is proportional to the length of the cylinder for lengths much less than the Fresnel zone diameter. At larger lengths, the amplitude factor oscillates above and below 1 as the increasing length passes through the Fresnel zones. The phase is −π/4 for very small lengths and oscillates above and below 0 as the increasing cylinder length passes through Fresnel zones. In experimental (laboratory) measurements of sound scattering, the lengths of objects relative to the diameter of the first Fresnel zone must be considered. Fourier transformations of the scattering amplitudes give the time-domain scattered pressures. The time-domain pressure is a negative impulsive function. Bending of the cylinder decreases the amplitude of the backscattered sound pressure. We expect the main applications of the techniques to be in the computation of sound scattering from fish swimbladders. Expressions for numerical computations are given. The expressions are accurate, easier to code than the complete mode solutions, and about two orders of magnitude faster to compute.