 We've talked about the properties of waves, including some properties, that are unique to waves. Chief amongst those, the ability to be in more than one state at once. You have one oscillation of a medium, and another oscillation of a medium, and they can both be there at the same time, and they just add constructively or de-constructively to any point in the medium. Also, waves within a medium, their speed is only really affected by the medium. If you have a particular shape of wave, in a particular medium, it must do something. It can't be faster or slower than that, because the only reason it's moving is because of the interactions of the different parts of the medium with each other. What we haven't talked about is what happens when a wave is moving in a medium, and the medium changes, either fast or slow. What happens at the boundaries of media? So if you take a still pool of water in a bathtub, or something with a clearly defined boundary, and you start making a disturbance in the center, then it's going to send out ripples, and the ripples will go out, and you'll see this happen, and they'll get smaller as they go out, because the energy has to be spread out across the entire circle, so the amplitude goes down, but it's still heading out. And what happens when it hits the edge? Well, you've seen this, and if you haven't seen this, you can go and see this any time. What happens is that those ripples reflect, and so the wave reflects, and it bounces off basically as a lovely mirror image, just like normal optical reflection, and comes back. And so these waves will be going out, or in this direction they'll be going forwards, and these waves are coming back and spreading out. And what you get is these beautiful interference patterns as the ripples go on top of each other. Now if you watch that really carefully, which is probably easier with just a one-dimensional wave, like a string up against a wall, or something heavy, so you have a string attached to a wall, and you're sending a wave at it, then what you'll find is the wave reflects fine, and it in fact goes upside down when it does the reflection. So it'll come up to this wall and reflect, and come back pretty much exactly as it came except upside down. And if you have a less dramatic kind of transition, for example, you might be going from a light rope to a heavy rope, then what's going to happen then? Well, if you put in a wave, then when it gets that boundary, something interesting will happen. And the first thing is you get a reflection. So that wave is going to reflect just as though it had bounced off something hard. But the extra interesting thing that will happen is that you'll also have some of the wave continue to go on the way it was before. And so in this large, heavy piece of material, you'll actually get a small wave going forwards as well. And so what you get is you get reflection, yes, but you also get transmission. And this is something, of course, that a wave can do that a particle can't. You can have it go through and come back at the same time. Now, of course, the energy in this part of the wave, plus the energy in this part of the wave, can't be greater than the initial energy, but you can still have both transmission and reflection provided you get the right amounts of each. Now, if you go the other way from a wave in a heavier material like this, that transfers into a light material, then you'll get transmission and reflection again. But the only difference is that in this case, the reflection doesn't go upside down. And the property that affects whether or not a wave is going to reflect a boundary doesn't depend on any other property of the material really, other than the speed of the wave and the way the speed of the wave will change. So in this region, the speed of the wave is fast. And when it goes into a slow speed area, it tends to reflect and invert. And here we're going from a slow speed to a high speed area.