 We already spoke about the fact that waves tend to travel at a particular speed in a particular medium. And then if the speed changes, because there's something about the medium changes, then you can get reflection from that boundary. But you can also get other effects as well. Suppose you have a wave in medium where the wave is traveling slow, and we get to a point where the medium changes, and so the wave is going to go faster. Now obviously, if we sit at one point in the old wave, it would have been going up and down at a particular frequency. And that point, even where the medium changes, is still going to be going up and down at the same frequency. And so the frequency of the wave in the second part of the medium is not going to change. But if the speed is changing, and the frequency is not changing, then the wavelength has to change. That's fairly easy to think of. If you've got these crests coming through at a certain rate per second, so maybe you'd have 10 of those every second, in this area they're going slow, then they're only going to go a certain distance. But if over here they're going much faster, then the same time, in the same period, they're going to go further. And so the wavelength is going to get bigger. And so remember the speed is equal to the frequency times the wavelength. And so if the speed goes up and the frequency stays the same, then the wavelength has to go up proportionately. And conversely, if it comes into an area where the speed is much, much slower again, then the wavelength has to get much, much smaller. And the speed can change for many reasons. In a string, if it's tighter or it's lighter, then the wave goes faster. In air, if the air is denser, then the sound goes faster. Or in solids, sound goes even faster again. In water, the deeper the water, then the faster the wave. And water is a good example to use to talk about waves that are spreading out in more than one dimension. Here we have a wave that's just traveling along a string. It's only got one dimension to travel along, left or right. In water, of course, you can go out in all directions. So one way to make a particularly large water wave is to have an earthquake. In an earthquake, if you have a chunk of, say, the sea floor move dramatically, then that can displace enormous quantities of water. And that enormous quantity of water, of course, involves a huge amount of energy. And what's going to happen is that that ripple is going to travel. And so what you get is ripples traveling out across the water. Now in deep water, waves caused by the wind typically have a wavelength of something like 100 meters. But the wavelength for a wave caused by one of these really deep and large earthquakes can be much, much larger than that. In fact, it can be hundreds of kilometers. And the speed at which that travels can be hundreds of meters per second. That's because it's got a frequency, which is a large fraction of an hour. Maybe we can look at the frequency. It's just the speed divided by the wavelength. And so that is something like 200 meters per second divided by 200 kilometers, which means it's about one one-thousandth of a cycle per second, which means it takes about a thousand seconds for one cycle of this wave to go past. And because that enormous amount of energy is spread out over such a large area, the height of that wave can be something like just a meter, like a normal wave out in deep water. And so you could be a ship on this sea and barely notice this wave because it would lift you up and down slowly only one meter over about a thousand seconds. But when this wave gets near shore, terrible things happen. Because the shore gets much, much shallower up to actually being running out of shore just going to land, the wave gets slower and slower. And as it gets slower and slower, all that energy across that entire 200 kilometers worth of wavelength gets squished up into a very small amount of space. And so you have these enormously high waves. You can have a hundred meter high wave coming in still very fast. And that wave smashes and that's a tsunami. And so it's really important to know where tsunamis go. And the direction that tsunamis and other waves go is strongly affected by a property of waves called refraction.