In this lecture we will cover the fundamental frequency, the harmonics and the overtone. Many occasions there is a confusion between the harmonic and overtone. We should first calculate the fundamental frequency and fundamental frequency is the lowest frequency. So you have fundamental frequency, then first overtone, then second overtone, then third overtone and so on. But harmonic is not like that. Only fundamental frequency and first harmonic are equal. But thereafter you have fundamental frequency, first overtone, second overtone. You don't have straight away fundamental frequency, first harmonic, second harmonic in all cases. It can happen in some cases as we will see. So I am repeating, fundamental frequency and overtones you should find out and harmonic you should find out using a formula. Let us take these cases and let me draw a line to separate them. This is open pipe, this is closed pipe. What is the lowest frequency possible here for the sound waves? You can have this arrangement for the standing sound waves. This has how many lambda by 4, twice lambda by 4. So, l is equal to lambda by 2 or lambda is equal to twice l. Frequency is equal to v upon lambda v upon twice l. This is the fundamental frequency and first harmonic. Here in this case, l is equal to lambda by 4. So, mu is equal to v upon lambda 4 l. This is the fundamental frequency and first harmonic. Now let us take the next possible arrangement where you can have standing waves, sound waves here in the open pipe. This is the next possible arrangement after the fundamental frequency and after the fundamental frequency, it is first overtone. First overtone here also we will write first overtone. So, fundamental frequency then overtone, fundamental frequency then first overtone. What is the combination of lambda and l? 1, 2, 3, 4 lambda by 4, l is equal to lambda. And what is mu is v upon lambda that is l. So, this is first overtone. What is the harmonic here? For first overtone, what harmonic we will call? The fundamental frequency is first harmonic, no doubt on that. But first overtone, which harmonic do we call? So, for this, use this formula. The harmonic is equal to overtone frequency divided by fundamental frequency. Oortone frequency is v upon l and fundamental frequency is v upon twice l. So, you get to. So, this is second harmonic. See the difference. Now in this case, first overtone lambda by 4 lambda by 4 lambda by 4 lambda by 4. So, l is equal to 3 lambda by 4 or lambda is equal to 4 l upon 3. What is the frequency? He is equal to v upon lambda is 4 l into 3. It will be like this. 3 v upon 4 l is the first overtone frequency. What is the harmonic? Corresponding harmonic. Harmonic would be overtone frequency upon fundamental frequency. It is 3 v upon 4 l. And what is the fundamental frequency? It is v upon 4 l. So, it is 3. So, it is third harmonic. So, first overtone here is third harmonic and first overtone here is second harmonic. See the difference. First harmonic, second harmonic. Here you get first harmonic and third harmonic. So, it is odd multiple. Here it is the integer multiple. It is in continuous. Continuum. Let us take this case. This is second overtone. How many lambda 1 2 3 4 5 6 lambda upon 4? So, l is 3 lambda upon 2. Lambda is equal to twice l upon 3. So, mu is equal to v upon twice l into 3. This is the frequency of this second overtone. And what is the harmonic? Harmonic is equal to this divide by fundamental frequency. Which will be 3. Third. So, it is third harmonic. So, in case of open pipe, you have fundamental frequency which is first harmonic. You have first overtone which is second harmonic. You have second overtone which is third harmonic. Here you have fundamental frequency first harmonic. Fundamental, first overtone and third harmonic. And let us find what is the overtone here, frequency here. This is second overtone. And how many lambda 1 2 3 4 5 lambda upon 4? 5 lambda upon 4. So, mu will be equal to v upon 4 l. This is 5. So, this is the frequency of first overtone. And what is the harmonic? Harmonic would be equal to this frequency divide by fundamental frequency. This frequency will be 5. See, first harmonic, third harmonic and fifth harmonic. Here first harmonic, second harmonic and third harmonic. So, you cannot write harmonic straight away. Here it is ok. First overtone, second harmonic, second overtone, third harmonic. But here it is not so straight forward. So, try to remember this that harmonic should be calculated by dividing the overtone frequency with the fundamental frequency. I hope this clarifies some of the doubts about the harmonics, overtones and fundamental frequency. Thank you.