The attenuation of ultrasonic waves in a perfect dielectric crystal has been calculated by the method of thermodynamic Green's functions. The calculation is valid for all values of ωt (ω sound wave frequency, τt average thermal phonon lifetime) but is limited to the case kθD>kTω, where T is the absolute temperature and θD is the Debye temperature.
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Humphrey J. Maris (1965) studied this question.
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