  We investigate the acoustic properties of meta-materials that are inspired by
sound-absorbing structures. We show that it is possible to construct
meta-materials with frequency-dependent effective properties, with large and/or
negative permittivities. Mathematically, we investigate solutions
$u^\varepsilon: \Omega_\varepsilon \rightarrow \mathbb{R}$ to a Helmholtz
equation in the limit $\varepsilon\rightarrow 0$ with the help of two-scale
convergence. The domain $\Omega_\varepsilon$ is obtained by removing from an
open set $\Omega\subset \mathbb{R}^n$ in a periodic fashion a large number
(order $\varepsilon^{-n}$) of small resonators (order $\varepsilon$). The
special properties of the meta-material are obtained through sub-scale
structures in the perforations.
