Principles of progressive slow-sound and critical coupling condition in broadband sonic black hole absorber

Recent advances in sonic black hole (SBH) provide new opportunities for controlling sound waves and designing wave manipulation devices. SBH is a device that consists of partitions with gradually decreasing inner radii inserted into an acoustic duct. Several studies have reported that SBH can achieve a broadband sound absorption coefficient close to 1, avoiding the issue of alternating high and low absorption coefficients observed in traditional sound absorbers. However, the fundamental mechanisms and principles behind this behavior are not yet fully understood. This study aims to investigate the detailed sound absorption mechanisms of SBH, including the progressive slow-sound effect and the critical coupling condition that leads to broadband sound absorption. To achieve this goal, an analytical model based on the effective medium approach is developed to investigate the layer-by-layer retardation in sound propagation. The sound absorption coefficient is then determined based on the surface impedance calculation. The effective medium analysis reveals that SBH enables a unique condition to progressively decelerate wave propagation across its layers. As a result, the critical coupling condition becomes more easily established with smoothly increasing SBH partitions and more discretised layers, as elucidated by the complex frequency analysis results. The physical insights gained from this study reveal the distinctive features of SBH compared to classical sound absorbers, paving the way for its engineering applications.