Acoustic reflection and transmission at an interface

For two inviscid media, continuity of normal displacement and normal stress determines the reflected and transmitted longitudinal amplitudes.

Equal normal velocities and the membrane tension-mass balance determine complex pressure amplitudes. With identical fluids on both sides the reflected and transmitted squared amplitudes sum to one, expressing conserved mean energy flux.

Equating the absolute reflected and transmitted displacement amplitudes, then using acoustic Snell's law, gives an algebraic condition on incidence angle and the two moduli-over-speed impedances.