Spherical Waves Coupled to a One-Dimensional Wave Guide

Abstract

Expressions are derived for the disturbance in a one-dimensional wave guide resulting from an expanding spherical wave which is loosely coupled to the wave guide at all points along its length. The example treated is a slender solid rod immersed in a fluid, and curves are presented showing axial stress, strain, and particle velocity due to an expanding step function rise in pressure. When rod velocity is higher than fluid velocity the first signal observed follows the refraction path, and the onset of a secondary signal coincides with the passage of the pressure front in the fluid. When the two velocities are equal, only one signal is observed, and its amplitude increases with distance from the source. When rod velocity is smaller, the first signal coincides with the passage of the pressure front, and a weak secondary signal appears to travel from the point nearest the source at rod velocity. These results are an extension of the approximate theory presented by White [J. Acoust. Soc. Am. 25, 906 (1953)].