Attenuation of long-wavelength sound in quenched disordered media

TL;DR

This paper analytically derives and numerically validates how weak quenched disorder affects acoustic wave attenuation and dispersion in disordered media, revealing Rayleigh-type attenuation and sound speed reduction.

Contribution

It provides a theoretical framework for disorder-induced acoustic attenuation and dispersion renormalization, validated by molecular dynamics simulations.

Findings

Rayleigh-type attenuation $ ightarrow \, ext{proportional to } q^{d+1}$

Disorder in elasticity reduces sound speed

Density disorder causes attenuation without dispersion renormalization

Abstract

We derive analytically, and validate numerically, the dispersion renormalization and attenuation of acoustic waves propagating through quenched disordered media in the long-wavelength limit. We consider weak spatial fluctuations in elastic moduli and/or mass density and compute the disorder-induced self-energies within the leading (Born) approximation. For sufficiently weak disorder, the results depend only on the variances of the fluctuations and are therefore insensitive to the detailed form of the underlying random distribution. For spatially uncorrelated elasticity disorder we obtain Rayleigh-type attenuation, $\Gamma(q)\propto q^{d+1}$ , together with a reduction of the sound speed. In contrast, density disorder produces Rayleigh-type attenuation but does not renormalize the acoustic dispersion to leading order. Molecular dynamics simulations and normal-mode analyses of disordered one- and two-dimensional lattices quantitatively confirm the theoretical predictions.