LAUSR

Abstract In acoustic black holes (ABH) at low frequencies, catastrophe sound energy flux behaviour occurs spontaneously if the tip size of the ABHs reaches a critical value. This report demonstrates that this catastrophe behaviour can be quantified by analysing the relative phase transitions using Landau’s phase-transition theory. Two catastrophe behaviours corresponding to two stable phases (states) were observed using analytical calculations and a numerical analysis. The sound energy flux was proportional to 3 power laws and square relationships with the tip diameters, respectively. The 3 power law relationships were proved using low-frequency experimental observations. For engineering applications, ABH structures with small tip diameters can isolate more than 11 dB of low-frequency sound waves below 1600 Hz. We associated this cataclysmic phase transition with the geometric structure of the ABHs.