This is an interesting question. Think about it. Why does thing have a sound? When you shatter glass, why does it make that "krrassssh" noise? When you bite into a cracker, what makes it crunch?" It's all the same thing.
All solids are atoms arranged in an orderly manner, held together with various types of bonds. Bonds represent states of low energy which universally, is preferred. (Why this is so is why physicists are still employed.)
Anyway, when you tear paper, what you are doing is creating a localized area of high stress and transferring energy from your arms into the bonds. They get to the point where the energy level is so high that atoms tear away from each other. The energy you pumped in now exists as two unbonded atoms. Any excess is thrown away. It has to go somewhere (energy is conserved in the universe, more or less, except a tidbit that can turn into mass), so it goes into the air. Air molecules soak it up and hand it off from molecule to molecule. Eventually, a molecule close to your ear moves, bumping into your eardrum, which you register as sound.
Now imagine this process happening at once to billions of atoms in the paper, and billions of air molecules. Add it all up and you have a ripping noise. The sound is strictly a matter of the frequency of the air molecules' vibrations. With wet paper, the water has already broken a lot of the bonds (but in a different way, (a way that doesn't toss excess energy into the air as sound). There are probably many other factors at place, all of which involve physics in a non-ideal universe, and that has me stumped, since my work mostly revolves around an assumption of ideality. Hope you had fun reading all this; I'm pretty sure what I said was at least 90% accurate, even though, again, it is a non-ideal scenario that I'm not an expert in.
Also, what John B said. He seems to know more about this in general than I do.
I'm a scientist.