Equivalence between fourth sound in liquid He II at low temperatures and the Biot slow wave in consolidated porous media

Abstract

The theory of acoustic propagation in porous fluid‐filled media developed by Biot is applied to the case where superfluid ⁴He is in the pores (TV(slow wave/fourth sound)=V(fluid)/n. The index of refraction of fourth sound is related to the ’’structure factor’’α, of the Biot theory by n=α^1/2, and so use of the superfluid provides a direct means of measuring α in a given sample. Predictions for the velocities of the fast wave, the shear wave, and the slow wave/fourth sound are made for fused gass bead samples in which Plona has previously reported seeing these three waves under the condition of water saturation.