Temperature and Frequency Dependence of Ultrasonic Absorption in Liquid Helium below 1°K

From measurements of the temperature dependence of the amplitude of ultrasonic pulses propagated over a fixed path in liquid helium, the attenuation coefficient has been determined at the six frequencies 1.00, 2.02, 3.91, 6.08, 10.2, and 11.7 Mc/sec, at temperatures extending down to 0.2°K. Below 0.6°K, the observed variation of the absorption coefficient $\alpha$ (${\mathrm{cm}}^{-1\mathrm{}}$) with frequency $f$ (Mc/sec) and temperature $T$ (°K) can be represented by the empirical equation $\alpha =0.11\mathrm{}$ $f^{\frac{3}{2}}$ $T^3$. This behavior differs from that predicted by several existing theories that are based upon the three-phonon or four-phonon interaction between longitudinal acoustic quanta and thermal phonons. Over the temperature interval 0.6-0.8°K, the measured attenuation is somewhat greater than would be expected from an extrapolation of the results below 0.6°K into this temperature region. A comparison of the data with some calculations by Khalatnikov suggests that the additional absorption arises from thermal conduction in the normal fluid. An equation that is analogous to the classical Kirchhoff expression adequately accounts for this contribution to the total absorption, even at temperatures for which the lifetime of the thermal phonons exceeds the period of the sound wave.