DOI: 10.1103/PhysRevE.52.3106


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 ofthe 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.



The description of the propagation of classical waves through strongly scattering media is a problem of considerable importance to many areas of physics; it is also a problem of great difficulty and a full understanding has as yet remained elusive, despite considerable research effort. However, much progress has been achieved in recent years through the study of the propagation of electromagnetic waves through strongly scattering materials. To a considerable extent, this progress has been based on the success of the diffusion approximation in describing the propagation. Within this picture, the phase information of the scattering processes is neglected and the propagation of the average energy density is approximated as a diffusive process.


The diffusion coefficient is $D = v_{e}l^{*}/3$, where the transport mean free path $l^{*}$ is the mean distance traveled before the direction of propagation is randomized and v, is the velocity at which the energy is transported. The solution of the diffusion equation determines the distribution of multiple scattering paths; each of these paths is then assigned a phase based on its total length. This approach has been particularly successful with electromagnetic waves, in- cluding light and microwaves; it correctly accounts for a wide variety of fascinating phenomena, from the enhancement of the backscattered radiation [2,3] to the correlations of the transmitted intensity with variations in the incident frequency [4], the angle of the sample [5], or the temporal position of the scatterers [6,7].