The propagation of acoustic waves through a periodically stratified medium is examined theoretically and experimentally with the purpose of determining how the velocity of the composite material depends on the periodicity structure, the material properties, and frequency. A numerical simulation of a recently published experiment shows that the propagator method gives results in close agreement with the experimental observations. Using eigenvalue analysis, an expression for the sound velocity and scattering loss is calculated for all frequencies. The results show that, for frequencies lower than a certain critical (or limiting) frequency, the propagation is dispersive and no loss occurs. Above this frequency the waves are evanescent and suffer scattering loss at each interface. An expression for the limiting frequency is derived which takes into account the contrast in impedance between the two media.

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