From this explanation, I learn that sound is refracted according to Snell's Law upon passing a border between materials of different sound speed.

I also learn that upon passing the border, a mode conversion takes place: The incoming longitudinal wave is partly converted into a shear wave, and also continues as a longitudinal wave. These two waves travel at different velocities in the other medium, and are, again according to Snell's Law, refracted at different angles.

The above article tells me:

As the angle of an incident longitudinal wave with respect to a surface increases, an increasing portion of the sound energy is converted to a shear wave in the second material, and if the angle is high enough, all of the energy in the second material will be in the form of shear waves.

What I'd like to know is: How exactly - depending on the incident angle, maybe? - is the energy of the incoming sound wave split between the two outgoing sound waves? How much of the energy is retained in the longitudinal wave, and how much energy is passed to the shear wave? Is there a formula that I could use to calculate how much energy exactly is the increasing portion mentioned above?


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