Abstract
For transverse waves propagated along an even-fold axis, the phonon-phonon coupling parameters are zero for collinear interactions. This necessitates a consideration of the angular dependence of the coupling parameter. The angle at which these parameters peak affects the minimum energy deficit possible on interactions. A calculation including both the angular dependence of the coupling parameters and the uncertainty of phonon energy due to thermal-phonon lifetimes is done for the case of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ along the $a$ axis. The calculated attenuation fits the experimentally observed attenuation.
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