Acoustical Properties of Superfluid Helium in Confined Geometry

TL;DR

This paper derives equations for sound propagation in superfluid helium within porous media, calculates wave velocities at various frequencies, and explores the coupling between temperature and pressure oscillations.

Contribution

It provides a comprehensive theoretical framework for understanding sound modes in superfluid helium in confined geometries, including specific velocity calculations and mode coupling analysis.

Findings

Derived general equations for sound propagation in superfluid-filled porous media.

Calculated velocities of longitudinal and transverse waves at different frequencies.

Identified coupling between temperature and pressure oscillations in the modes.

Abstract

The problem studied in this paper is to obtain the equations describing sound propagation in a consolidated porous medium filled with superfluid, determine the elastic coefficients, appearing in the equations, in terms of physically measurable quantities, and calculate the propagation velocities of transverse and longitudinal waves at high and low oscillating frequencies. In general, the obtained equations describe all volume modes that can propagate in a porous medium saturated with superfluid for any values of the porosity and frequencies. The derived equations are applied to the most important particular case when the normal component of superfluid helium is locked inside a highly porous media (aerogel, Im-helium sample) by viscous forces. For this case the velocities of two longitudinal sound modes and transverse mode are calculated from the derived equations. There are established the coupling between temperature and pressure oscillations in these fast and slow modes.