Velocity of sound, density, and Grüneisen constant in liquid He4

By measuring the pressure dependence of the velocity of sound, we have determined both the pressure dependence of the density and the Grüneisen constant u of liquid He4. Measurements were made below 0.1 K and in the vicinity of 0.5 K. Our determinations of the pressure dependence of the density agree quite well with that determined by Boghosian and Meyer, who used a capacitance bridge. Since the latter results rely on the validity of the Clausius-Mossotti relation and a pressure-independent electric polarizability, the present work can be interpreted as supporting both of these assumptions. We found that u(ρ0)≡(ρc)dcdρ=2.84 under the vapor pressure at 0.1 K. Using this value of u to calculate the attenuation of sound according to a three-phonon mechanism, we obtain an attenuation of less than half the measured value. Thus, the present theory of sound attenuation must be incomplete.