 So, we have discussed the standing wave generated by the transverse wave and we have taken one dimensional wave on a string when we talked about the standing wave of the transverse wave. Now, we are going to discuss the standing wave generated by the longitudinal wave. What is the best example of standing wave when it comes to musical instrument for the sound wave? It is not standing wave. Oh, it is not standing. Fluid. So, not even fluid. It is a sound wave. It is a sound wave. Sound is travelling inside the air. You do not need a string. So, we are going to take the longitudinal standing wave on a pipe. We are going to take a pipe and see the situations that will be arising because of that. There will be one end closed, both end open, both end closed. Something like that. Please write down longitudinal standing wave on a pipe. Situation number 1, both ends are open. End of the pipe is L. Please draw the standing wave. The open end will act like an anti-node always. Open end will be anti-node. Close end will be node. Wherever the reflection happens, there it will be a node when the standing wave gets formed. So, that is why the close end is the node. Draw the first wave possible here. You will say one line like this, one line like that. That is 0. That is nothing. After that what? I am not sure what to draw. Just like you have drawn here. Same way if you draw here, minimum possible frequency. Here draw. Open end will be anti-nodes. Listen. Your node is basically compression. Anti-node is extension. Now, see here, it is a longitudinal wave. So, you cannot draw it like a transverse wave. Are you getting it? You cannot draw it like a transverse wave, sine wave. But we are just trying to find out the frequency. And we know the formula or equation look very similar. So, just to visualize it in a better way, we will draw the longitudinal wave as if it is a transverse wave. But in reality it does not look like that. Are you getting it? So, the first possible frequency will be like this. So, if length is l, what will be the fundamental frequency? Tell me frequency. 1 by 2 l root 2 t by mu. All of you? Something terribly wrong. What? How do you tell me? L by 2 is how much? Sorry, lambda by 2 is l. So, lambda is 2 l. What about the velocity of wave here? It is under root 2. It is under root of v by rho. v could be gamma p whatever. It is not root t by mu. It is not a transverse wave. Long longitudinal wave, the velocity is root of v by rho. You have to use that. So, fundamental frequency is what? 1 by 2 l t by rho. This is the fundamental frequency. What about the next one? First, over tone. How it will look like? So, you said that the anti-node is a low pressure. It is an expansion. It is not a compression. Why? Just a convention. But like if I actually check. So, like if I actually check the pressure in the middle and at the tops, then would I find higher pressure? No, no, no. In the middle it will be higher. It will be higher. Yes. Because there is a reflection. Reflection happens when it gets compressed and then it reflects off. In standing wave it is always like that. Sir, how would that like for a long wave? One will vibrate like this, other will vibrate like that. It will be like this. They will together vibrate. All the particles together will vibrate like this. All will open up together and come back together. Okay, what is the next frequency? How it will look like? It will look like this. So, this is one complete wavelength or not? Is it one complete wavelength? Lambda by 4, lambda by 4, lambda by 4, 4 lambda by 4. So, your wavelength is l only. So, frequency is 2 by 2 l root of b by rho. What is this called? First overtone and which harmonic? Second harmonic. Between these two there is no other frequency possible. What about the nth harmonic? n by 2 l root b by rho. So, if you have something in between rows, then will there be this wavelength between? What are you saying? Like if I have some frequency in between. No, that is not even possible. It will not resonate with it. The length will not allow it to happen. The only frequency with which it will resonate is this one or that one or the next one like that. So, it will not be standing. It will just damp away. Have you seen that example of resonance when the strings are hanging like that? The last example that you have taken SHM, the force oscillation. So, the one which is oscillating will affect the most, the one which has the same length. So, it will immediately start resonating. Others will not even respond. So, that frequency will not even, you know, this will not get affected by that frequency. The structure will not allow it. The natural frequency is not matching with that. Getting it? Now, please write down one end closed. Do it your own now. Tell me the generic formula after doing yourself. So, what is the same as one? Please do it yourself. One end closed. Properly do it. Draw the... The fundamental will look like how? This will be the fundamental. Right? So, mu is... How many times will you say the same thing? How many times? How many times will you say the same thing? This question is same as that question. I am asking what it is. Tell me the same. Then, same kind. B by rho. T by mu. Huh? Is it the same thing? This is the fundamental frequency or the first harmonic. The second possible frequency is 3 by 4 L root of B by rho. So, the generic formula is 2 minus 1 times 4 L. This is 2 N minus 1th harmonic. So, even harmonic does not exist in this case also. Even harmonic does not exist in this case as well. Got it? Any doubts which I may want to clear? No doubts. So, now two end close situation, I don't need to discuss. Sir, but in that how the wave is generated? Hit it from the top. You put a bomb inside. I am joking. But the frequency of the bomb should match with one of these modes of vibration. Otherwise, it will just damp the wave. Silent. Not silent. It will... It will not resonate. It will just... A small noise will come and then goes out. Sir, both ends are close. It will be like first and okay. Then both ends will be... It looks like a transfer. When you analyze it, but it doesn't... It is not like this in reality. It is not like... It is a longitudinal wave. You are analyzing it by drawing as if it is a transverse wave. Okay? Now, we will write down end correction. End corrections. So, the effective length of the pipe... The effective length of the pipe L effective is experimentally found out to be L0 plus 0.3 times the diameter of the pipe. This thing is end correction. So, wherever in the formula L is there, instead of L, you should write L0 plus in L plus 0.3D. Wherever L is, it behaves as if the length is more than L. How much more? 0.3 times diameter time. 0.3 times diameter more than the actual length. Why that happens? Because of the... You can say there is an edge. So, you can say there is an edge effect. And the wave behaves very weirdly at the edges. I will just give you one real example here. Suppose this is you. And this is someone else. This someone else is shouting. This wall is perfectly dampener. It will not allow any voice to travel across. So, it is a soft wall. The rubbers are there. Both sides will damp every noise. But if this shouts, this guy can hear. Why is that? Because the wave goes here and it bends. At the edges, the wave bends. So, actually what we expect is the wave will go like that, isn't it? But it doesn't behave like this. Similarly, if there is an obstacle there and there is a light source over here. You will expect that the light should not reach in this zone at all. But the light will reach over here as well. The light bends at the edges. So, there will be some edge effect. How the derivation of this? No one knows. It is experimentally found out to be L plus 0.3 times the diameter because of the edge effect.