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

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 (T1.1 K where there is a negligible amount of normal fluid). For a consolidated (fused) matrix Biot’s slow compressional wave is shown to be identical to the phenomenon known as fourth sound; V(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=α1/2, 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.