Sound Propagation in Granular Media

Abstract

The sound velocity and attenuation in a granular medium such as air- or water-saturated sand are discussed theoretically and conclusions are compared with experiments. A simplified theory based on the gross properties of the porous medium is shown to predict a square-root frequency dependent attenuation coefficient and a nondispersive velocity dependent only on the porosity of the sand and the sound velocity in the fluid (provided the frequency is high enough). Calculated values for the attenuation coefficient agree fairly well with reported measurements in air-sand mixtures. Predicted sound velocities are consistent with geophysical data. Comparisons are also made with results of theories based on viscous-wave scattering by the particles. The scattering theory of Epstein and others, though not intended to be applied to such a close-packed medium as sand, is shown to yield an expression for the attenuation coefficient which is very nearly the same as that given by the gross theory.