If we assume that scattering of phonons leads to breakup of the coherent properties of sound, then the attenuation of sound in a solid can be computed using the above formulas. Calculate the attenuation lengthof microwave sound with frequency 10 MHz in a solid with speed of sound 2 × 10⁵ cm/s and a defect density of 10¹² impurities per cm³, if the size of the impurities is roughly 20 μm, and the impurities have density variation Δρ/ρ = 0.1. The attenuation length l is defined by the relation

where N_coh(0) is the initial number of phonons in the coherent wave, and N_coh(x) is the number of unscattered phonons remaining after the wave has traveled a distance x.

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Ncoh(x) = Ncoh(0)e-x/1, (5.3.19)