Superfluid fifth sound

A superfluid clamped so that the normal fluid is at rest can, under pressure-released boundary conditions, support a new propagating thermal mode whose phase velocity vanishes both at 0°K and $T_{\lambda }$. Some problems which complicate the observation of this mode as well as applications to ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ II research are discussed. It is expected that this thermal mode can propagate even when the temperature is so low that the wavelength is shorter than the phonon-phonon mean free path.