 So, let's discuss the kind of why standing waves that are possible, we write down standing wave on a string to be standing wave on a string, so there are situations please write down situation one is both end of this string are fixed, example data string, this is length any kinds of standing wave can be there on this guitar string, only one type as in how many wavelengths are possible, only one wavelength is possible, there can be this wavelength, there can be that wavelength, there can be this wavelength, so how many wavelengths, infinite practically infinite, so maximum possible wavelength is infinite, maximum possible wavelength, we will talk about it, but listen here, when you are increasing number of lobes, what is increasing, frequency or wavelength, frequency is increasing, so maximum possible frequency is infinite is minimum possible frequency is 0, no, right, minimum possible frequency 0 means wave is not there, so I am asking you wave is there, what is the minimum possible frequency of that wave, is that a very, I mean is it a close to 0 or it has some fixed value, some fixed value, right, so you cannot have, I mean the minimum possible wavelength does it depend on the length, yes it does, you guys are not getting it, Ajah please draw the situation, please draw a situation for minimum possible frequency and maximum possible wavelength, try it, minimum frequency is minimum frequency is same as maximum wavelength, standing wave I am talking about, standing wave, is this the minimum possible frequency, this is the minimum possible frequency, in any structure the minimum possible frequency is called the fundamental frequency, please write down, this is the fundamental frequency, this is like common name, the IOPSE name is first harmonic, no take it literally, there are two names fundamental frequency and first harmonic, but you can say fundamental mode or first harmonic, fundamental frequency or fundamental mode of vibration, there are many names, so again fundamental is the least possible frequency of the standing wave that is possible, okay, so if tell me, if mass per length is mu of the string and tension in the string is t, the length of the string is l, find out the fundamental frequency, how much, the formula for the frequency is velocity divided by wavelength, for any wave velocity divided by wavelength is the frequency, find out, all of it, velocity how much, under root t by mu and the length is equal to how much, l is lambda by 2, so lambda is 2l, so lambda is 2l, so the frequency is 1 by 2l times t by mu, this is the fundamental frequency, okay, this is also called the first harmonic frequency, please draw the next possible frequency, next possible, between 0 and this, there is no frequency possible, between 0 and this there is no frequency, so next possible frequency is what, after this what is the next higher frequency, find out, derive this, I am not going to tell you that, I am not going to derive it for you, you do it yourself, it will be like this or not, it will be like that, this has higher frequency or not, there is one natural node that get created over here, now length is equal to lambda, l is lambda, the velocity is root of t by mu only, velocity depends on the medium only, nothing else, so the frequency is 2 by 2l, why I am writing like this, so that I can arrive at the common formula, what should be the name of this, second harmonic, I am facing name is very simple, so this is second harmonic, what about common name, it is called first overtone, you cannot guess it, point is called second harmonic by the way, the second frequency is 2 times the first frequency, there are situations in which after first harmonic, directly third harmonic is there, second harmonic does not exist, any doubts, so why is it called first overtone, I see, logic, so first overtone, this is fundamental, fundamental is basic, on top of it, overtone, first thing overtone, what about that, you can remember like that, second, sorry third, third possible frequency, please draw the structure, first draw the structure, this has one i, it has two i's, it will have three i's, total five nodes or four nodes, four, it will like this, frequency will be 3 by 2, 2, lambda by 2, lambda by 2, 3 lambda by 2 is equal to l, so lambda is 2 l by 3, so the frequency will be 3 by 2 l, root or t by mu, so what should be the name, third harmonic, this will be third harmonic, why it is called third harmonic by the way, why it is called third harmonic, three times the first harmonic, that is why third harmonic, okay, and this is called second overtone also, in this sequence, can you tell me the nth harmonic, n by n minus 1, n by 2 l, what will be its common name, this frequency, n minus 1th overtone, okay, so these are the situations when the both ends of the strings are, both ends of the string is, both ends of the string are fixed, end outs, okay, so now, second situation, one end is fixed, the other end free to move, example, so real what else, day to day life example, tie, tie or when you put clothes for drying purpose, okay, but there are many such things, but anyways, our main agenda is to understand what is happening here, so this is the string, if it is being sent from this side, okay, you are taking this side and wave is getting sent from there, but this end is free to move up and down, so please write down the free end will always be anti-node, the free end, so wave is sent from this side, it get reflected from here, the free end will always be anti-node, okay, so can you tell me the fundamental frequency of this, what is given is length, mu or ket of tension, these things are given, tell me the frequency, fundamental frequency of this situation, which one, so the fundamental frequency will be this or not, a string low, one is fixed, that and you do like this, that can create it, by frequency of this situation, now this is how much, in terms of lambda, this is how much distance, lambda by 4, so lambda by 4 should be equal to tell from here, so the fundamental frequency is 1 by 4 L velocity by wavelength, this right, this is called little fundamental, fundamental this is also called, what is this also called, first harmonic, tell me the second possible frequency, second possible, second possible mode of vibration, this end has to be anti-node that has to be node, first situation, second situation is what, little bit like this, like this only, right, so find out the frequency for this, in terms of lambda what is the distance from here to here, even divided into 1, 2, 3 equal parts, each part is lambda by 4, so lambda by 4 is L, D lambda by 4 is L from here, L is equal to 4 L by 3, so the frequency will be what, 3 by 4 L root over D by mu, what is its name, no this is third harmonic, harmonic and this is first overtone, understood why it is third, 3 times the fundamental, 3 times the first harmonic, so even harmonic does not exist in this case, next frequency will be 5 by 4 L, so next situation will be something like this, there will be 2 I's like that, so you can divide into 5 equal parts, 1, 2, 3, 4, 5 lambda by 4 is equal to L, so please write down even harmonics does not exist in case when, in this case, even harmonic does not exist, understood, so can you write a generic formula for this, 2 N minus 1 by 4 L, 2 N minus 1 by 4 L, which harmonic it is, Nth harmonic, no, it is 2 N minus 1th harmonic, got it, N starts from 1, it is not Nth harmonic, it is 2 N minus 1th harmonic, what if both ends are free to move, that situation is not practical, so we will not discuss that.