 So a guitar string is fixed at the bridge and then again at the other end when it runs over the nut At least I'm told that's the nut and I have no reason to distrust my friends So have a guitar string that's fixed there and fixed there then these points must be equivalent to these nodes So there could be two nodes that were next to each other like that Or they could be two nodes that are some distance away And what that means is that the standing wave has to look like one of these Maybe it look like that or alternatively it could look like the next one that has a node in the middle Where these things are just going up and down all the obvious ones with higher numbers of nodes Now this one here is called the fundamental and the higher-order ones are called the harmonics and Sometimes the fundamental is called the first harmonic and then this one would be the second harmonic and therefore that would be the third And that would be the fourth but some people label them differently They say no the fundamental is special and then this would be the first harmonic and then this one would be the second Harmonica and so forth So it doesn't matter what we call them. We know what they are Now these things sound different. Why do they sound different? They sound different because in order to make this wave here In order to have that wavelength and because the speed of the wave in that string is set by the string How tight it is and how heavy it is that means it's got a very particular frequency and remember different sounds come with different Frequencies so this string is going to drive the air at a particular frequency, and that's going to make a sound of a particular frequency And so what frequency is it going to be? Well What's the wavelength? Remembering that the wave here a full wave Goes like that and then comes back and then it repeats again And so that would be the full wavelength this distance here would be the full wavelength So that would be the wavelength and so this part here is of course just half the wavelength So the length of that string is going to be half the wavelength in This case the length of the string is precisely one wavelength In this case we have one wavelength there and then another half And then we have two full wavelengths and So on so you'll see for each of the higher harmonics the wavelength is getting shorter and shorter and shorter so here The wavelength is twice the distance between our bridge and our nut Here it's exactly the distance between our bridge and our nut and then it's two-thirds and then it's a half and so on So as we said the speed of a wave and we normally call the speed C The speed of a wave in a guitar string is basically only dependent on how tight the string is and how heavy the string is So as we change the wavelength we're going to change the frequency because the speed remember is related to the frequency and The wavelength such as the frequency times the wavelength in other words It's how far you travel per cycle divided by how fast you do it, which is one period and the frequency is one on the period So if we rearrange that to find the frequency Let's just see on lambda. So as you make the wavelength smaller and smaller you make the frequency higher and higher