Third Sound in Layered Films: H↓ -He4andHe3-He4

The (linearized) hydrodynamics of a layered film configuration is considered for propagating modes of third sound. The theory is applied to (normal) ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and H↓-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixture film systems. When both films are superfluid, two propagating modes at each wave vector $k$ will be observed. Thus, the detection of superfluid onset in the H↓ film should be direct and unambiguous. When the upper film is normal, an easily measurable shift in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ third sound velocity, directly related to the physical characteristics of the normal film, will be observed.