Second Sound Propagation below 1°K
Dirk de Klerk, R. P. Hudson, John R. Pellam · Physical Review · 1954
The pulse method has been employed to measure the velocity of second sound in liquid helium, ${u}_{2}$, in the temperature range 0.015\ifmmode^\circ\else\textdegree\fi{}-1.0\ifmmode^\circ\else\textdegree\fi{}K. The liquid helium was in thermal contact with a sample of chromic potassium alum and cooling was achieved by adiabatic demagnetization.In the region of 0.8\ifmmode^\circ\else\textdegree\fi{}K, ${u}_{2}$ rises quite abruptly, reaching the Landau velocity of $\frac{{u}_{1}}{\sqrt{3}}$ by 0.5\ifmmode^\circ\else\textdegree\fi{}K. Thereafter it continues to increase, but much less rapidly, with decreasing temperature. A further sharp rise was observed for low-energy pulses at about 0.05\ifmmode^\circ\else\textdegree\fi{}K, suggesting an approach to the velocity of sound ${u}_{1}$ at absolute zero.In the phonon region below 0.5\ifmmode^\circ\else\textdegree\fi{}K, the thermodynamic quantity $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}$ shows very nearly the fourth-power (actually 4.18) dependence on temperature predicted by Landau. Values for the roton contribution to the normal fluid concentration $\frac{{({\ensuremath{\rho}}_{n})}_{\mathrm{rot}}}{\ensuremath{\rho}}$ agree very well with Landau's predictions, with a small adjustment of the constants in the theory.For the smallest pulses used, the distortion (or dispersion) is very small when the pulse temperature is smaller than the ambient value and large when the reverse is true. For larger pulses the spreading decreases very slowly as the temperature rises through the phonon region, then rapidly with the onset of excitation of rotons. Above 0.05\ifmmode^\circ\else\textdegree\fi{}K, the velocity associated with the leading edge of the received pulse appears to be independent of pulse energy and the degree of distortion.