Sound Scattering by Fluid Cylinders

Abstract

The scattering of plane waves of sound from an infinitely long circular cylinder has been investigated both theoretically and experimentally. Wave motion in the cylinder cannot be neglected because the properties of the fluid in the cylinder are comparable to the properties of the external fluid. A rigorous series solution for the scattered radiation has been obtained, taking into account the possibility of compressibility, density, and attenuation differences between the two fluids. At high frequencies the series solution is difficult to apply because of the many terms that must be included. Consequently, approximate closed-form solutions have been developed which are useful for high frequencies and which agree essentially with the rigorous series solution in the limit of low frequencies. The approximate solutions follow from an integral equation formulation which has application in other coordinate systems and which is similar to the results of some recent work of Montroll and Hart. Measurements have been performed on cylinders containing mixtures of tertiary butyl alcohol and water immersed in water for wavelengths approximately 18 the diameter. The approximate theory predicts the angular positions of the minima of the scattered radiation within experimental error and the magnitude of the maxima of the scattered radiation within a few decibels.