Acoustic properties of a layered medium with randomly distributed layer thicknesses

We study here the acoustic properties of a layered medium with randomly distributed layer thicknesses. The propagation of transverse elastic waves with polarization in the direction parallel to the laminations is investigated. The bulk modes and the transmission coefficients in a finite sample are calculated by the use of the transfer-matrix method. It is found that the density of states of these modes is drastically affected by the extent of disorder of such a system. Owing to the randomness, most of the waves are localized in the direction perpendicular to the laminations, but there still exist some waves with special frequencies which are completely extended. In some special cases we can analytically determine the frequencies of these extended waves. On the basis of this calculation a possible application of such structures is suggested.