Acoustic bulk parameters in distributions of pair-correlated scatterers

Abstract

We develop simple approximations for the bulk acoustic parameters associated with coherent waves in pair-correlated random distributions of scatterers small compared to wavelength, and indicate their relations to earlier forms. Our initial functional equation for the bulk index of refraction applies for dense gas and liquid-state statistics in terms of integral analogs of lattice sums involving appropriate pair-correlation functions. For small-spaced scatterers (average separation of closest neighbors small compared to wavelength) we obtain explicit closed forms for the radiation loss effects by reducing the integrals to simple correlation-packing functions based on the scaled-particle equations of state for impenetrable particles. For uncorrelated sparse distributions, the present results reduce to those obtained by elementary procedures for small perturbations in the properties of the imbedding medium. For random lattice-gas statistics (a model for uncorrelated distributions which takes into account the space-occupying property of the obstacles), the results reduce, in general, to those obtained before for scatterers excited by the coherent wave and radiating into the imbedding medium.