Acoustic Bulk Parameters of Random Volume Distributions of Small Scatterers

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Abstract
General approximations for the “bulk parameters” of a uniformly random homogeneous distribution of relatively arbitrary scatterers are applied to obtain explicit results for the range where the significant dimensions of the scatterers are small compared to wavelength. We consider “slight scatterers” of arbitrary shape, symmetrical scatterers (plane slab, circular cylinder, and sphere) of arbitrary density and compressibility, elliptic cylinders, and ellipsoids (either aligned or averaged over orientations). For all cases, we give explicit results for the density and compressibility (or for the index of refraction and acoustic impedance) in terms of the isolated scatterer parameters. The range of applicability of the results should correspond essentially to that of “Clausius-Mossotti” type results for analogous electromagnetic problems.

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