Hydrodynamics of superfluid helium below 0.6 0K. III. Propagation of temperature waves

The Propagation of second-sound waves in superfluid helium is considered for temperatures below 0.6 °K. A dispersion relation for the waves is obtained. This relation is valid for frequencies much less than the small-angle phonon-phonon collision rate. In the low-frequency limit the usual second-sound mode with velocity $\frac{c_0}{\sqrt{3}}$ is found c₀ is the phonon velocity). At higher frequencies the velocity of this mode increases towards c₀ and other modes of lower velocity appear. The nature of these waves is discussed. Finally, several experiments that might give information about the waves are considered.