For a given size of explosion, how to calculate how large the shockwave gets before becoming a sound wave?

Question

and how many decibels it is at that boundary?

What's the formula

Does anything special happen at the supersonic-sonic boundary (reduced damage capability maybe?)

Answer 1

You've got it backwards. If a sound wave gets too high in amplitude it becomes a shock wave. For a single frequency (plus its inevitable nonlinear harmonics), the shock transition will occur about when the sound under-pressure reaches (ambient) minus 1 atmosphere (zero absolute pressure). This means the over-pressure is about 1 atmosphere (there's a nonlinear correction). I don't know what that is in Decibels.

Mathematically speaking , a shock results if pressure rises too quickly for the dynamic fluid equation to be solvable for a continuous solution with positive pressure everywhere. Negative pressure is physically meaningless. The only meaningful solution, then, becomes *discontinuous* (in the fluid approximation). The discontinuity is the shock front. A shock wave can be of any amplitude; it has more to do with the abruptness of the pressure rise - like from an explosion.

Answer 2

I believe that 176 dB is the point where the pressure is +/- one atmosphere.