Also, I might be wrong, but sound propagation through a medium happens despite its compressibility, not because of it.
Imagine a column of water and a column of air. For sound to travel through each column, vibrations at one end need to somehow be transmitted to the other end. If the medium is very compressible, vibrations don’t have much of a chance to travel. If it is incompressible, like a length of steel or a column of water, then what happens at this end is almost perfectly transmitted to the other end.
That’s why, for example, sound travels so much faster through water.
The Newtown Laplace equation puts the speed of sound at sqrt(Ks / rho), where Ks is the bulk modulus, or how stiff the medium is, and rho is its density.
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