  Bound states in the continuum (BICs) provide a viable way of achieving high-Q
resonances in both photonics and acoustics. In this work, we proposed a general
method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a
coupled acoustic waveguide-resonator system. We demonstrated that FW BICs can
be achieved with arbitrary two degenerate resonances in a closed resonator
regardless of whether they have the same or opposite parity. Moreover, their
eigenmode profiles can be arbitrarily engineered by adjusting the position of
attached waveguide. That suggests an effective way of continuous switching the
nature of BIC from FW BIC to symmetry-protected BIC or accidental BICs. Also,
such BICs are sustained in the coupled waveguide-resonator system with shapes
such as rectangle, ellipse, and rhomboid. These interesting phenomena are well
explained by the two-level effective non Hermitian Hamiltonian, where two
strongly coupled degenerate modes play a major role in forming such FW BICs.
Besides, we found that such an open system also supports accidental BICs in
geometry space instead of momentum space via tuning the position of attached
waveguide, which are attributed to the quenched coupling between the waveguide
and eigenmodes of the closed cavity. Finally, we fabricated a series of 3D
coupled-resonator-waveguide and experimentally verified the existence of FW
BICs and accidental BICs by measuring the transmission spectra. Our results
complement the current BIC library in acoustics and provide new routes for
designing novel acoustic devices, such as in acoustic absorbers, filters and
sensors.
