  We study the attenuation of long-wavelength shear sound waves propagating
through model jammed packings of frictionless soft spheres interacting with
repulsive springs. The elastic attenuation coefficient, $\alpha(\omega)$, of
transverse phonons of low frequency, $\omega$, exhibits power law scaling as
the packing fraction $\phi$ is lowered towards $\phi_c$, the critical packing
fraction below which rigidity is lost. The elastic attenuation coefficient is
inversely proportional to the scattering mean free path and follows Rayleigh
law with $\alpha(\omega)\sim \omega^4 (\phi - \phi_c)^{-5/2}$ for $\omega$ much
less than $\omega^* \sim (\phi - \phi_c)^{1/2}$, the characteristic frequency
scale above which the energy diffusivity and density of states plateau. This
scaling of the attenuation coefficient, consistent with numerics, is obtained
by assuming that a jammed packing can be viewed as a mosaic composed of domains
whose characteristic size $\ell^ * \sim (\phi-\phi_c) ^{-1/2}$ diverges at the
transition.
