Wave Transmission and Reflection Phenomena in Liquid Helium II

Abstract

A method is formulated for treating acoustical transmission and boundary value problems in liquid helium II. According to present concepts, He II is a mixture of two fluids obeying a special system of complex hydrodynamics. In particular, this is known to result in two virtually independent modes of sound propagation. Therefore, a re-formulation of the intrinsic (or characteristic) acoustical impedance concept is required for which a matrix representation is applicable. By similarly associating a matrix form of impedance with plane-reflecting surfaces, boundary conditions may be imposed. The classical requirements (continuity of pressure and particle velocity at the boundary) are generalized to apply individually to each fluid component in He II. Expressions are obtained for the reflective properties of various types of surfaces. In particular, materials which present unlike boundary conditions to the two fluid components are shown capable of partially converting one mode of sound to the other upon reflection. For example, surfaces of highly porous substances exert unequal viscous forces and should therefore act as such converters (with possible application for extending present frequency ranges of second sound). These properties of reflectors are expressed in terms of reflectivity arrays. The array gives direct reflective factors for both types of sound, plus coupling factors between types. Examples are given for several special cases, and a form of reciprocity is shown to exist for the coupling process. The boundary condition is derived for still another type of coupling, due to heat transfer, which occurs at a liquid-vapor interface; a modified form is applicable to the resonance type (Yale) experiment.