Anharmonic correction to the sound velocity of amorphous and disordered solids above 4 K resulting from low-energy modes

It is shown that the linear decrease with increasing temperature of the fractional variation of the velocity of sound, or velocity shift, δv/${\mathit{v}}_0$ observed at intermediate low temperatures in glasses and disordered solids (Bellessa effect) can be reproduced by assuming anharmonic coupling between the sound waves and thermally excited low-energy vibrations. The values of the effective Grüneisen parameters required to fit the published velocity-shift data of polystyrene, PMMA, Se, NiP, and a sodium silicate glass are found to be physically reasonable.