Hydrodynamics of Superfluid Helium below 0.6°K. II. Velocity and Attenuation of Ultrasonic Waves

Abstract

The attenuation and velocity of an ultrasonic wave in superfluid helium-4 have been calculated for temperatures below 0.6°K. The calculation is based on the kinetic equations given by Khalatnikov. The phonon Boltzmann equation is solved numerically without making simplifying approximations about the form of the collision integral. The theory predicts that the velocity of sound increases with frequency for very low frequencies, passes through a maximum, decreases to a minimum, and finally increases towards a constant value at high frequencies. A simple explanation for this peculiar behavior is given. The theory is in good agreement with the experimental results of Abrahams et al., and Waters et al.