  We prove a quantum version of the Sabine law from acoustics describing the
location of resonances in transmission problems. This work extends the author's
previous work to a broader class of systems. Our main applications are to
scattering by transparent obstacles, scattering by highly frequency dependent
delta potentials, and boundary stabilized wave equations. We give a sharp
characterization of the resonance free regions in terms of dynamical
quantities. In particular, we relate the imaginary part of resonances or
generalized eigenvalues to the chord lengths and reflectivity coefficients for
the ray dynamics, thus proving a quantum version of the Sabine law.
