  In scattering experiments, the dynamical structure factor (DSF) characterizes
inter-particle correlations and their time evolution. We analytically evaluated
the DSF of disordered solids with disorder in the spring constant, by averaging
over quenched disorder in the values of lattice bond strength, along the
acoustic branch. The width of the resulting acoustic excitation peak is treated
as the effective damping constant $\Gamma(q)$, which we found to grow linearly
with exchanged momentum $q$. This is verified by numerically calculating a
model system consisting of harmonic linear chains with disorder in spring
constant. We also found that the quenched averaging of the vibrational density
of states produces a characteristic peak at a frequency related to the average
acoustic resonance. Such a peak (the excess over Debye law) may be related to
the "boson peak" frequently discussed in disordered solids, in our case
explicitly arising from the quenched disorder in the distribution of spring
constants.
