Spontaneous catastrophe behaviour in acoustic black holes at low frequencies

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.