Complex frequency analysis and source of losses in rectangular sonic black holes

The amount and practical source of losses required by rectangular sonic black holes in air to effectively absorb low-frequency sound are analyzed numerically and experimentally. In the sole presence of viscothermal losses, only high-order (high frequency) Fabry-Perrot resonances are likely to be critically coupled in realistic rectangular sonic black holes. This results in sharp absorption peaks that do not reach unity at low frequencies, because the quality factors of the associated resonances are high. To avoid these drawbacks, slits of rectangular sonic black holes are partially filled with porous materials so that a profile of porous filled slits is superimposed on the sonic black hole profile itself. The improvement in the absorption coefficient is significant, particularly at frequencies below the viscous/inertial transition frequency of the porous material. This transition frequency is assumed to be the limit of possible perfect absorption of the bulk porous material layer. The numerical results are supported by experimental results, which also show that the vibrations of the plates forming the acoustic black hole must be considered with caution.

Automated summary

This study numerically and experimentally analyzes the amount and practical source of losses required for rectangular sonic black holes in air to effectively absorb low-frequency sound. The results show that in the presence of solely viscothermal losses, only high-order Fabry-Perrot resonances are likely to be critically coupled in realistic rectangular sonic black holes, resulting in absorption peaks that do not reach unity at low frequencies. To solve this issue, slits of rectangular sonic black holes are partially filled with porous materials, which significantly improves the absorption coefficient, especially at frequencies below the viscous/inertial transition frequency of the porous material.