The use of slow waves to design simple sound absorbing materials

Abstract

We demonstrate that the phenomenon of slow sound propagation associated with its inherent dissipation (dispersion + attenuation) can be efficiently used to design sound absorbing metamaterials. The dispersion relation of the wave propagating in narrow waveguides on one side of which quarter-wavelength resonators are plugged with a square lattice, whose periodicity is smaller than the wavelength, is analyzed. The thermal and viscous losses are accounted for in the modeling. We show that this structure slows down the sound below the bandgap associated with the resonance of quarter-wavelength resonators and dissipates energy. After deriving the effective parameters of both such a narrow waveguide and a periodic arrangement of them, we show that the combination of slow sound together with the dissipation can be efficiently used to design a sound absorbing metamaterial which totally absorbs sound for wavelength much larger than four times the thickness structure. This last claim is supported by experimental results.