  The normal modes of a continuum solid endowed with a random distribution of
line defects that behave like elastic strings are described. These strings
interact with elastic waves in the bulk, generating wave dispersion and
attenuation. As in amorphous materials, the attenuation as a function of
frequency $\omega$ behaves as $\omega^4$ for low frequencies, and, as frequency
increases, crosses over to $\omega^2$ and then to linear in $\omega$.
Dispersion is negative in the frequency range where attenuation is quartic and
quadratic in frequency. Explicit formulae are provided that relate these
properties to the density of string states. { Continuum mechanics can thus be
applied both to crystalline materials and their amorphous counterparts at
similar length scales.} The possibility of linking this model with the
microstructure of amorphous materials is discussed.
