Wavelength-Dependent Bulk Parameters for Coherent Sound in Correlated Distributions of Small-Spaced Scatterers
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF MATHEMATICS
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Earlier results for coherent propagation of sound in correlated random distributions of two-parameter particles of radius a with minimum separation b or 2a small compared to wavelength lambda 2 pik are generalized to obtain the refractive and absorptive terms and the corresponding bulk parameters to order ka squared. The present development includes higher order terms of the earlier multiple scattering by monopoles and dipoles, as well as scattering and multipole-coupling effects through quadrupole terms. The correlation aspects are determined by the statistical mechanics radial distribution function fR for impenetrable particles of diameter b. The new terms of slab scatterers and spheres involve the integral of f R first moment, or of R f ln R for cylinders. The new packing factor is evaluated exactly for slabs as simple algebraic function of the volume fraction omega, and it is shown that the bulk index of refraction reduces to that of one particle in the limit omega 1. Similar results are obtained for spheres in terms of the Percus- Yevick approximation and the unrealizable limit omega 1.
- Statistics and Probability