Wave Inversion

Let's talk about wave inversion, wave inversion is something that happens when a wave moving through 1 medium hits a boundary between that medium and another, the two speeds the wave have to be different. Remember that wave speed depends only on medium and that means it can change when I go from one medium to another. Now when the wave is incident on this boundary, what will happen in general is part of the wave will be transmitted into the new medium and another part of the wave will be reflected back into the old medium. Now you maybe familiar with this, I hope you're familiar with this by looking at like a sliding glass window. Part of the reflection that you see is actually inside the house and part of what you see is outside the house. This is the same idea but we're going to do it just with mechanical waves for right now. Alright so what happens is sometimes the reflected wave will be flipped up-side-down by the boundary sometimes, this does not always happen but it sometimes does.

The transmitted wave will never be flipped up-side-down, alright so let's see if we can figure out what conditions we need to achieve in order to get inversion alright. Rigid boundaries always invert, so I've got a wave coming in like this to a rigid boundary and then the reflected wave coming back is inverted all up-side-down disturbance is going the other way. This is a consequence of Newton's third law, as the wave comes up and hits the rigid boundary it's pulling on the rigid boundary. Newton's third law means the rigid boundary is going to pull back and that downward force is as great as it needs to be to make it so that this rigid boundary doesn't move. And it's that downward force that generates the inverted reflected wave. Alright now let's see what happens in more general situations when it's not a rigid boundary. So suppose that I've got a medium coming in where I've got a slow wave speed. And that means that this guy is thick, well what's going to happen is this guy is going to pull on the lighter medium and it's easy for it to do that. So the Newton's third law doesn't put enough force to flip this guy over. It makes him smaller but it doesn't flip him over, so in this case there's no inversion.

Down here if I've got a light medium pulling on a heavy medium it's going to pull real hard to initiate that transmitted wave. And that Newton's third law again will in this case flip the guy up-side-down. So that means that in general, we get no inversion when the new speed is greater than the old speed and we always get inversion when the new speed is less than the old speed and that's wave inversion.