|MadSci Network: Physics|
There are a few important differences between water and air. Air is a gas, and is therefore what we call a compressible fluid. This just means that if you squeeze on a packet of gas its volume will shrink (imagine being able to squeeze on a balloon). Water is a liquid, and is an incompressible fluid, ie. if you squeeze on water, its volume doesn't change. Well, it doesn't change much--it actually changes a tiny bit, but the shrinkage is almost impossible to measure.
On the other hand, there are a lot of similarities. Sound travels at a given speed in water and in air. The speeds in water and air are different--the speed of sound in water is 4-5 times faster than in air. There's a nice, short table of sound speeds in different media in Chapter 18 of "Fundamentals of Physics," by Halliday, Walker, and Resnick. There are probably similar tables in other introductory physics texts.
The effects of travelling faster than the speed of sound would be fairly similar in either water or in air. You would send out a shock wave, that would be perceived as a sonic boom. It would be much harder to do this in water than in air, however. First, there's the fact that the speed of sound is much higher in water, and is faster than just about anything other than a rocket in air can travel. Even worse, the density of water is much greater than that of air, and so drag forces are enormously stronger in water.
I believe that the sound speed of water is much more sensitive to temperature and impurities (salt in sea water, for example) than it is to pressure. Sound speed is determined by two things: how dense a material is, and how its density responds to changes in pressure. These change most sensitively with temperature, and chemical makeup. The faster the molecules in a gas or liquid can move, the faster pressure changes (like sound waves) can be transmitted along. The molecular speeds are higher in fluids with lighter molecules or that are hotter, and so those have higher sound speeds.
Any changes that you see in the speed of sound with depth in the ocean, for example, would probably be due to changes in either salinity or temperature with depth. Both of those do happen, which in some cases results in very abrupt changes in sound speed with depth. I believe that military submarines can take advantage of that. Sonar waves from above will tend to reflect off of the interface where the sound speed changes abruptly, and so the subs can hide just below the interface.
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