Wave propagation in a finely laminated periodic elastoacoustic medium

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Abstract
The exact solution for plane wave propagation through periodically alternating solid and fluid layers has been derived for all frequencies and all wave numbers. In the low-frequency limit an explicit dispersion relation is found relating the wave slowness parallel to the layering to that perpendicular to the layering. At any angle of propagation, except perpendicular, there are two waves: a fast wave and a slow wave. The tangential motion across a solid fluid interface for the fast wave is in phase, and for the slow wave, out of phase. An equivalent medium is found which has the same equation of motion with an anisotropic density tensor as a periodically layered fluid, but which has a constitutive relation relating pressure and dilation which is nonlocal in space and time. This equivalent medium exhibits the same wave propagation properties as the layered solid, fluid medium in the long wavelength limit and is called an elastoacoustic medium.

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