We analyze the Helmholtz equation in a complex domain. A sound absorbing structure at a part of the boundary is modelled by a periodic geometry with periodicity ε>0. A resonator volume of thickness ε is connected with thin channels (opening ε3) with the main part of the macroscopic domain. For this problem with three different scales we analyze solutions in the limit ε→0 and find that the effective system can describe sound absorption.
@article{arxiv.2006.02701,
title = {Sound absorption by perforated walls along boundaries},
author = {Patrizia Donato and Agnes Lamacz and Ben Schweizer},
journal= {arXiv preprint arXiv:2006.02701},
year = {2020}
}