Role of rattlers in bottom loss and sound wave propagation

It is known from both laboratory and numerical experiments that weakly or poorly consolidated granular media have some fraction of the grains that do not contribute to the overall mechanical strength of the granular system. Such loose grains are sometimes called rattlers, and their presence affects both acoustic wave speeds and attenuation. Sound wave speeds tend to be reduced while the wave attenuation tends to be increased. An analytical model of such systems will be presented and comparisons to available data will be shown.