Design of sub-wavelength acoustic absorbing panels using accumulation of resonances due to slow sound

We report sub-wavelength resonant panels for low-frequency sound absorption by using the accumulation of cavity resonances due to the slow sound phenomenon. The panels are built by bricks of sub-wavelength thickness with periodically distributed horizontal slits, in the walls of which identical Helmholtz resonators are attached (HRs). Due to the presence of the HRs, the propagation in the slit is highly dispersive with low group velocity that goes to zero due to the gap produced by the resonance of the HRs. In the slow-sound regime, the resonant frequency of cavity modes in the slit are shifted down and they are accumulated before the HRs frequency. Near the accumulation point, simultaneously symmetric and antisymmetric modes can be nearly critically coupled and produce nearly perfect absorption. However, due to the distribution of the resonant modes perfect absorption is not possible in this kind of structures. Therefore, we further analyze the case of different HRs in the slit, in which the structure of resonances is modified and symmetric and antisymmetric resonances can be simultaneously critical coupled. In this conditions we report perfect absorption for a transparent panel of 1/26 wavelength thickness.