Just as an unrefresher, about 1000 atmospheres of pressure reduces the volume of water by about 5%. You mean, "not significantly compressible." And, it hurts my brain to think about it, but could a pressure wave (shock waves, sound) propagate through water if it was absolutely incompressible?
I was going to post that but I didn't want to pour salt on the wound after seeing his reaction to my earlier correction.
Why does it hurt your brain to think about it? Were you worried we'd bring propagation of electrons or electric fields that could carry the information of sound waves through the medium?
Although maybe they could, that wouldn't count as propagating sound waves which are very different.
Actually the question you posed is an impossible one because as far as we know there is no such thing as an incompressible medium which can be proven by sound waves themselves:
The more incompressible, or put another way, the more rigid the structure the faster the sound wave propagates. An incompressible medium would cause the wave to travel instantaneously which is not possible as that would cause instantaneous information propagation, an impossibility
as far as we know(why do I say that sometimes?*

).
This might bring up the question of singularities such as black holes. What if the medium they are made of has been compressed to the maximum limit making them incompressible any further? Is that then an example of the existence of a substance I just said earlier is impossible? Maybe. The truth is we don't know
what black holes are made of. Sure we can give it a name, assign a label to it and call it a day. But our math breaks down and physics doesn't have an answer for what goes on there. So far. As far as I know. That could change. *So that's why I say that sometimes. It's really as far as I know. Today. Tomorrow is a different day.
