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 ε = dλ, 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 ε, the material properties, and the volume fraction. This is used to describe the shape and amplitude of a transmitted or reflected pulse signal.