High-Frequency Sound Attenuation and Dispersion in the Critical Region

A general theory is presented for sound attenuation and dispersion near the critical point in the region of frequencies which are much greater than the characteristic frequency of order-parameter dynamics, but are much smaller than the frequency of sound with the wavelength equal to the range of correlation of local order-parameter fluctuations. The method used is the most general version of the mode-mode coupling theory plus the static and dynamic scaling hypotheses and some general properties of time-correlation functions. If we ignore the small critical exponent α associated with the heat-capacity singularity, we find that the attenuation behaves as fε⁰ and the dispersion (relative sound-velocity change with frequency) as f⁰ε⁰, where f is the dimensionless frequency and ε the dimensionless temperature distance from the critical point.