Abstract
A theory is developed to describe the attenuation of high-frequency phonons in liquid helium at low temperatures, assuming a model excitation spectrum due to Jackle and Kehr (1971). At very low temperatures the attenuation is negligible when the dispersion is normal, but significant when dispersion is anomalous. The recent measurements of Narayanamurti et al. (1973) are interpreted as the decay of a broad-band phonon system.