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.
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