 So, let us take a question from your NCRT, write down y is equal to 0.005 sin of this, this is in meters 80 radians per second, 80 radians per minute, so they are all in the SI units. You need to calculate these things amplitude, wavelength, time period and frequency, you need to calculate displacement at x equal to 30 centimeter and t equal to 20 seconds. Solve it, step forward numerical, you must be getting it right, you step forward 0.005 meters 5 by 40, which is how much, 0.078 meters, find out the time period and then tell me the frequency. So, it is time period is 2 by 30 and t equal to 3.14, can you take rest 3 by 30, 3.13. So, it is time period is 2 by 30 and t equal to 3.14, can you take rest 3 by 30, 3.13. 2.09 is the time period, frequency, inverse of this 0.46, 0.48, the unit is hertz. So, it is root 5 plus 1 by 4. No, it is 36 and 88. Solve it, solve it, no one is getting answer, no one is capable to get the answer. So, how much comes inside sign of this 36 inside minus 36, what do you get, now I have to understand that this is beyond 2 pi or minus 2 pi. So, I will first bring it between 0 and 2 pi, alright. So, how many times I have to add pi to make it, add 2 pi to make it come between 0 and 2 pi? 5. 5 pi is how much? 5 times 2. 5 pi is how much? 15. 15. So, why are you adding 5 pi? 5 times 2 pi. 11 times. 11 times. 5 times of 2 pi, so that is 10 pi, which is 31.4. So, you can go further in, I can do it 12 and then subtract. Let us see. So, you can add 31.4 without affecting its value, yes or no? Yeah. Right? So, let us add it. So, what will come inside? Minus of? 4.6. 3.6. 4.6. Ok. Now, I can add 2 pi. 2 pi is how much? Roughly? 6.28. 6.28. So, add 6.28. How much it will come? 4.6, this is 8. 1.6. 1.6. So, this is 0.005, sign of 1.68. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 1.6. 0 and t equal to 0, the value of y is a by root 2, a is the amplitude. You can assume omega and k to be present. k omega are given. Oh, okay then done. You should not say that only one question sir has done in this topic sir. Two questions. So, value of phi is? Pi by 4 or 3 pi by 4. Pi by 4. Or it can be the other. So, y is equal to k x minus omega t plus pi by 4. Okay, right now, speed of travelling wave, speed. Have you played that game Need for Speed? Yes sir. Right on speed of travelling wave. So, we are going to talk about the transverse wave first. Now, what we have just learned, speed of it is equal to omega by k. Right, it is omega by k. Similarly, acceleration is equal to dv by dt. But still, we use force equal to mass m acceleration to find out the acceleration. Why can't we get acceleration as dv by dt? See, it is different actually when you write down the, so velocity is omega by k is the formula. Now, that is assuming that you know the equation of wave. But what if you don't know the equation of wave? Equation of wave is not good to you. Then you need to find out the velocity of wave by applying some physics. You need to understand what kind of medium it is. Okay, what is the force applied on it. And then depending on that, you determine the velocity of the wave. Okay, so velocity of the wave that is what we are finding out. It is like finding out velocity of a person when the person is inside the car. If you know the displacement of the person after certain time, you can find out the displacement by time as velocity. Okay, at the same time, if you know what kind of force is applied on the car and using that you can find the acceleration of the car and then velocity after some time. Okay, so why I am taking this example of a person inside the car because the velocity of the person inside the car depends on the property of the car, not on the person. Similarly over here, write down the velocity of the wave velocity of the wave depends on the property of medium only. It does not matter what kind of wave it is as in whether it is sinusoidal or triangular. We are talking about transverse wave though. Velocity of the wave depends on what kind of wave as in transverse or longitudinal but what is the shape of the wave that is immaterial. With how fast you are moving one end of the string up and down like that, it doesn't matter. How big a stone you throw in the water, it doesn't matter on that. The velocity of the wave depends only on the property of medium, whether you are throwing stone on the water or on the oil. Okay, whether the string which is tied, whether that string is very light or it is very heavy, whether it is very stiff or very elastic. So velocity of wave only depends on the property of the matter. And let's take example of a string transverse wave in a string. Now suppose I am plucking it from here and I am moving this end up and down. How should I move this end up and down so that sine wave get generated? It should be in SHM. Every point should be doing SHM. So you force this point to SHM from your hand, every other point will automatically start doing SHM. Got it? Now the disturbance will travel from this point forward like this. Now what kind of property the string will have? It will have inertial property and elastic property. Understood? So property of the medium is defined as, please write down, it is inertial and elastic. When I talk about inertial, what I mean to say is that inertial represents mass. Okay, it represents mass in a way. Now if I take a bigger string, will my mass increase? No. Mass will increase, inertia will increase but will velocity get affected if I take a bigger string or a shorter string? No. But it should depend on some sort of inertia. So basically the only thing that is constant between the bigger and the smaller string is mass per unit length. So inertial property is quantified as mass per unit length. This is represented by letter mu. Mu is mass per unit length. Okay? This is inertial property. Now elastic property, how should I quantify the elastic property? By the way, what is elastic means? Elastic means what? The amount of force or amount of resistance it can generate to come back to its original shape. Yes or no? That is how you can define the elasticity. So if it generates more amount of force for smallest of the change in shape, it is more elastic because it is trying very hard to go back to its original shape. So that is why steel is more elastic than rubber. Okay? So elasticity can be quantified as the resistive force that gets generated. And in a string that resistive force is tension. Okay? So this is the force with which the string tries to regain its original shape and size. Okay? Now the thing is that velocity will be 0 if either of inertial or elastic property becomes 0. If it is not inertial then what will happen? But the particles have 0 mass so when particles are doing SHM, when it comes to the mean position, force is 0. So why it will come down? It will stop as soon as force becomes 0. It does not have any inertia. Okay? So it will not perform an SHM. So inertia is required. Okay? And tension is required because the thing is that this particle which is there has to stretch the adjacent one also. If one is getting stretched it has to pull the adjacent one also then only the shape will get transferred from one point to the other point. Are you getting what I am trying to say? Okay? So if this point is moving along with it the adjacent point will also move because of elasticity. Okay? Now tell me velocity should be directly proportional to or velocity should increase when tension increases or decrease when tension increases? Increase. So velocity should be proportional to tension raise to power A let us say, T raise to power A. I don't know whether it is directly proportional to T or T raise to power 2 or T raise to power 3 or whatever it is. Okay? So I am writing T raise to power A and what about inertia? There could be some doubt whether inversely or directly so let's take it as mu to the power B. Now it could be inversely if B comes out to be negative. I don't know. Okay? So combining these two I can say that velocity is some constant K times mu to the power B and T to the power A. Now using dimensional analysis get me the value of A and B. A is half B is minus half. So basically velocity comes out to be K under root T by mu. K is a dimensionless constant and the value of K comes out to be equal to 1. So V is equal to under root of T by mu. So velocity of the transverse wave on a string is given by this equation. It has nothing to do with the shape and size of the wave. It is fixed depending on what is the medium property. Understood? No doubts.