Multiple scattering of acoustic waves with application to the index of refraction of fourth sound

A multiple-scattering model which previously explained the conducting properties of fluid-saturated porous fused glass beads is applied to the acoustic index of refraction n of an ideal fluid in a rigid porous frame. The model consists of ellipsoidal grains coated with an effective medium consisting of fluid and other fluid-coated grains; this nesting is continued ad infinitum in order to insure connectedness of the pore space to very low values of porosity. For the relevant cases considered here, the result is n^2=P^-, where P is the porosity and depends on the aspect ratio of the grains. By assuming that the scatterers used in fourth-sound experiments can be characterized by long filaments or needles, randomly oriented (=23), we have achieved excellent agreement with experimental values of n^2; the data also seem to agree with an earlier theory valid for low concentration of aligned needles (n^2=2-P), when extrapolated to high concentrations of scatterers (50%). The present theory contains neither approximation. We also resolve a controversy over the relationship between n and the hydrodynamic drag parameter ; the correct result is n^2= (1-) ^-1.