Earlier results for coherent propagation of sound in correlated random distributions of two-parameter particles of radius a (with minimum separation b≥2a small compared to wavelength λ=2π/k) are generalized to obtain the refractive and absorptive terms and the corresponding bulk parameters to order (ka)2. 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 f(R) for impenetrable particles of diameter b. The new terms for 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 a simple algebraic function of the volume fraction w, and it is shown that the bulk index of refraction reduces to that of one particle in the limit w=1. Similar results are obtained for spheres in terms of the Percus–Yevick approximation and the unrealizable limit w=1.