Experimental test of the diffusion approximation for multiply scattered sound

Abstract

We have critically tested the application of the diffusion approximation to describe the propagation of ultrasonic waves through a random, strongly scattering medium. The transmission of short ultrasonic pulses has been measured through a concentrated suspension of glass beads immersed in water. The transmitted sound field is found to exhibit temporal fluctuations with a period determined by the width of the incident pulse. Provided that appropriate boundary conditions are used to account for the reflectivity of the interfaces, the time dependence of the ensemble-averaged transmitted intensity is shown to be well described by the diffusion equation. This enables us to determine both the diffusion coefficient for the sound waves as well as the inelastic absorption rate. The consistency of these results is established by varying the experimental geometry; while the transmitted pulse shape changes markedly, the values for the diffusion coefficient and absorption rate obtained through a description using the diffusion approximation remain unchanged. We have also measured the absolute transmitted intensity of the sound as the sample thickness is varied; this provides an accurate measure of the transport mean free path and thus also the energy transport velocity. These results convincingly demonstrate the validity of using the diffusion approximation to describe the propagation of sound waves through strongly scattering media.