Acoustic boundary conditions

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I am studying acoustic wave reflection. The boundary conditions of acoustics are continuity of pressure and normal particle velocity. Can anyone tell me if these boundary conditions are completely independent? (Since the pressure and particle velocity are in phase, I would believe they are not independent.) By the way, how could pressure be in phase with particle velocity, and not with particle displacement? I belive that Snell's law of refraction follows from the continuity of pressure over the boundary and the wavenumbers in the two media, which are determined by the respective sound speeds. Does the boundary condition for particle velocity also relates to Snell's law? I also want to derive the reflection- and transmission coefficient for oblique incidence for general waveforms (not necessarily harmonic waves), and wonder whether it is possible. I have not found such a derivation in any textbook. Thanks.
 

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