Determination of particle size distributions from acoustic wave propagation measurements

The wave equations for the interior and exterior of the particles are ensemble averaged and combined with an analysis of Allegra and Hawley (J. Acoust. Soc. Am. 51, 1545 (1972)) for the interaction of a single particle with the incident wave to determine the phase speed and attenuation at low volume fractions. The theory is shown to compare very well with the measured attenuation. The inverse problem, i.e. the problem of determining particle size distribution given the attenuation as a function of frequency, is examined using regularization techniques that have been successful for bubbly liquids. It is shown that, unlike the bubbly liquids, the inverse problem can be solved satisfactorily only in some specific cases that depend on the nature of particles and the size and frequency range