  Sound waves are attenuated as they propagate in amorphous materials. We
investigate the mechanism driving sound attenuation in the Rayleigh scattering
regime by resolving the dynamics of an excited phonon in time and space via
numerical simulations. We find sound attenuation is spatiotemporal
heterogeneous. It starts in localised regions, which identify soft regions
within the material and correlate with low-frequency vibrational modes. As time
progresses, the regions where sound is primarily attenuated invade the system
via an apparent diffusive process.
