 So we can transport energy by either moving objects or by sending waves within an object. Now, in some ways, waves and objects or waves and particles can behave very similarly. And in some ways they're very different. So let's look at some of the similarities and differences between waves and particles. Okay, so they can both carry energy. And in fact they can both also carry momentum. You can send momentum with a wave or you can send momentum with particles. However, in particles you're sending the actual matter and in waves you're not. So the medium stays where it is. So particles can go in straight lines. Can waves go in straight lines? Well waves in a string certainly go in a line because they just travel along the line. If I have a water wave coming into a beach it can be very straight. Those wave fronts can be very straight as they come in. So they can go straight and they can go in lines. But if I put ripples in water then they do tend to spread out. Is there some way of making a wave in say water that goes in a nice narrow straight line? An answer is actually yes. If you have very high frequency waves then you can make them go very much like little pulses of particles. They will still be blurring and spreading out at the very edges but the scale of that spreading out is typically on the order of the wavelength. And the wavelength can be very small for certain kinds of waves. And when we go outside that regime we see a very stark difference between particles and waves. So particles exist in a particular place. And they also have a particular velocity. Whereas waves are spread out. A water wave can be anywhere on the entire surface of the water and indeed all over the surface of the water. And it can be going not just in one direction but a different direction and different parts of the wave can be going at different speeds. As an extension of that if you have one wave, one oscillation of the medium and one small displacement coming in contact with another travelling wave when they come in contact with each other the two displacements just add up. And so if you have a displacement up then they add up constructively and you have a bigger wave but if they're displacing in opposite directions then they cancel out and you get no displacement at that point. And that's called superposition. So if they add up like that so in other words they're coming in and maybe this one might be going one way and the other one might be going the other way when they're just like that then you can see that this point's going up and this point's going up at the same time. And that means they're going to add up to be a bigger thing and so those two things have what's called constructive interference where they add together. On the other hand if you have one like this then the other one is going the other way at that moment in time then when you add those two together there's nothing, no displacement. And that's called destructive interference. So let's look at two simple waves interfering. You can see that as they're moving they're spread out but when they pass through each other there's constructive and destructive interference and then when they're passed through they're just themselves again. Because the waves are going up and down at different points when they pass through each other they don't have complete destructive interference or complete constructive interference. It happens differently at different points in space. And in fact if you look at the energy the momentum carried in that wave it doesn't change while they're passing through each other and so it has a certain amount of energy beforehand a certain amount of energy all the way through and then that is conserved to the end as well. One thing that particles can do that waves can't do is travel at different speeds. The only reason a wave travels at all is because of the interactions between different parts of the medium. So the speed of a wave is a property of the medium. So for example supposing I was trying to communicate by throwing rubber balls with messages written on them I could throw those at any speed I liked but if I was trying to communicate by sound then I'm limited by the speed of sound. If I shout louder all I'm doing is changing the amplitude of the sound wave I'm not actually changing how fast it travels and the fact that the speed of a wave in a medium is basically only dependent on the medium actually provides a limit to how fast you can make a boat because boats tend to make a wave as they move and then they tend to sit in that wave as they travel. So the boat drives harder and if it doesn't make the wave go faster it just makes it have a higher amplitude and so that really limits how fast it can go and that's called the hull speed of a boat.