Degenerate bound states in the continuum in square and triangular open acoustic resonators

We consider square and equilateral triangular open acoustic resonators with the ${C}_{4v}$ ${C}_{3v}$ symmetries, respectively. There is a unique property of accidental number fourfold degeneracy eigenstates that gives rise to twofold-degenerate Friedrich-Wintgen (FW) bound states in continuum (BICs). Compared usual FW BICs, degenerate BICs maintain high $Q$ factor wide range size resonators. That removes fabrication difficulties proper choice resonator. The presence extremely sensitive switch output flows by small perturbations $100%$ efficiency.