Propagation and absorption of sound in a waveguide with side-wall impedance gradient

Over the past two decades, acoustic retarding structures, analogised to sonic ‘black holes’ (SBH), have garnered significant attention for their potential to achieve perfect sound absorption. Typical designs feature annular rings with progressively smaller radii designed to bring sound waves to rest at zero radius. Yet these structures still reflect significant sound, a flaw widely attributed to the engineering impossibility of achieving a true zero radius with infinite acoustic admittance. In this study, we examine the analytical solution for a typical SBH configuration and conclude that sound waves cannot be trapped or otherwise ‘stopped’ by slowing down to zero phase speed. We attribute this impossibility instead to the breakdown of the approximate side-wall boundary condition used in the original theory. When an accurate boundary condition for the configuration is used, the phase speed is found to increase to infinity leading to incompressible-flow behaviour; this result contrasts with what the term of ‘black hole’ may reasonably imply. Recent SBH literature frequently employs distributed damping, which effectively absorbs waves over a considerable bandwidth. Given these findings, it is necessary to benchmark the original SBH structure and its damped variants against traditional acoustic wedges with identical geometrical profiles. Using two-dimensional axisymmetric finite element analysis and a pink incident noise, we conclude that an ordinary wedge filled with optimised bulk porous material matches the performance of the SBH configuration and some of its variants.