We study the attenuation of phonons at low temperature by neutral donor impurity atoms in germanium. Keyes as well as Griffin and Carruthers have calcualted the attenuation due to elastic-phonon scattering by trapped electrons. They applied their results to thermal phonons and obtained good agreement with thermal-conductivity measurements. However, recent experiments in acoustic-phonon attenuation indicate a much larger attenuation than that predicted by their calculation. It is shown here that the observed attenuation can be explained by other processes that dominate at low or acoustic frequencies, namely, inelastic scattering and thermally assisted absorption. Attenuation of phonons by resonance absorption is also considered using the thermodynamic Green's-function technique. © 1966 The American Physical Society.