Frequency-Dependent Acoustics of Composites with Interfaces

We study the scattering of an incident wave by a composite medium with periodic microstructure in a slab geometry. We compute the expansion on the wave field in powers of the parameter = d/λ, where d is the characteristic scale of the microstructure and λ is the wavelength. For ε = 0 this corresponds to homogenization theory. Here, we focus on the correction terms for ε > 0 and compute the frequency-dependent impedance and the energy reflection coefficient as functions of , the material properties and the volume fraction. This is used to describe the shape and amplitude of a transmitted or reflected pulse signal.