  A theory for the vibrational dynamics in disordered solids [W. Schirmacher,
Europhys. Lett. {\bf 73}, 892 (2006)], based on the random spatial variation of
the shear modulus, has been applied to determine the wavevector ($k$)
dependence of the Brillouin peak position ($\Omega_k)$ and width ($\Gamma_k$),
as well as the density of vibrational states ($g(\omega)$), in disordered
systems. As a result, we give a firm theoretical ground to the ubiquitous $k^2$
dependence of $\Gamma_k$ observed in glasses. Moreover, we derive a
quantitative relation between the excess of the density of states (the boson
peak) and $\Gamma_k$, two quantities that were not considered related before.
The successful comparison of this relation with the outcome of experiments and
numerical simulations gives further support to the theory.
