 Let's take a moment to discuss why so many different kinds of systems actually have the same mathematical description, so why one physical model works on so many different kinds of waves in so many different kinds of media. And the answer is, for all of them, the medium is trying to return to some basic state. For a guitar string, it's trying to be straight. For the surface of the earth, it's trying to be a nice still piece of rock. For the air in the room, it's trying to be an even pressure all the way through. And so when I induce a wave by stretching the guitar string or the rock or by compressing some of the air in the room, then the wave might be traveling. But if I look at one little piece of that medium, it's always being pushed back to where it started from. The air is always being pushed back to having a nice even pressure, the guitar strings being pulled straight, and the rocks being pulled straight. And so if we look at that little piece, it's got a force acting on it pushing it back. And it doesn't matter what the shape of that force is. And that's the trick, you see. If I have a different curve for the force for each of those different situations, if I have just a small amplitude, if I have a little perturbation, then I'm zooming in on that curve. And if you zoom in on any curve enough, it looks straight. And so every different medium basically has the same kind of mathematics. It's just a linear force versus displacement. And that means that we get very similar models describing all the different kinds of waves.