  We study the spectral width as a function of the external momentum for the
dynamical structure factor of a disordered harmonic solid, considered as a toy
model for supercooled liquids and glasses. Both in the context of single-link
coherent potential approximation and of a single-defect approximation, two
different regimes are clearly identified: if the density of states at zero
energy is zero, the Rayleigh $p^4$ law is recovered for small momentum. On the
contrary, if the disorder induces a non vanishing density of states at zero
energy, a linear behaviour is obtained. The dynamical structure factor is
numerically calculated in lattices as large as $96^3$, and satisfactorily
agrees with the analytical computations.
