 the frequency due to the motion of source or observer, there will be someone who is creating sound and someone who is listening to the sound, listener is observer, reader is the source, okay. So if source and they start moving actual frequency they will not hear, the observer will not hear the actual frequency, observer will hear some other frequency, okay. And if you find out the relation between what is the frequency, the observer will hear based on how fast they are moving, observer can have an instrument to calculate the frequency and if the observer knows what was the original frequency, he can calculate what is the velocity of the source, are you getting it? So using this Doppler effect, radar, sonar, all these things are based on this, okay, in fact they are using Doppler effect on light also, you know what is red shift, the galaxies are moving far away from each other, the apparent frequency is moving towards the frequency of the red, okay, so that will happen only when they are moving with a certain velocity away from the observer, who is the observer, the earth is the observer, you are the observer, who is observing the light from the galaxy, okay. So you know if you know the actual frequency of the star in the galaxy and you know what frequency you are getting, if you have the mathematical formula, you can calculate based on these two information, what is the velocity of the galaxy, similarly what is the velocity of the enemy aircraft or what is the velocity of the ship when it is moving in the sea, okay. What happens is that in radar one frequency is thrown in the air, okay, suppose I throw 300 hertz frequency in air, it will get reflected from a moving aircraft and I will get that frequency back, depending on how fast that aircraft is moving and where it is moving, I get a different frequency, so if I have the formula or equation with me which will relate what is the actual frequency, what frequency I will get and what could be the velocity of that aircraft, I will calculate the velocity of the aircraft, okay, simple equation is used and this is a very effective method of doing all of these things, radar, sonar and redshift, okay, this is what we are going to here, this is what we are going to do, so here we have one source, one observer, so we are going to take a simple scenario, one source is there, one observer is there and they are moving close to each other, away from each other and things like that, okay, so please write down situation one, source is stationary, observer is moving, so we are not considering both of them are moving, one by one we will consider and then club it, okay, so let's say this line represents source, there is a source, what happened, so you could just use relative velocity, no, because the sound is travelling in the medium, sound, source is not sound, sound velocity doesn't depend on velocity of source, it depends on the medium, there are three things moving, sound is also moving, listen here, there will be source, there will be observer, let's say the distance between them is L0, okay and the observer is moving away from the source with a velocity of V0, you take it, now I am going to find out what is the frequency the observer will hear, okay, the frequency that source is throwing away is N0, the observer will get N, I want to find out what is N depending on N0 and V0, got it, speed of sound is given as C, now you need to listen to this carefully because this derivation, most of us will not get it, okay, because it is slightly tricky, see, I am going to find out the time intervals between which the observer will receive the pulse, okay, let's, if I say that time period of pulse is T0 here, the frequency is 1 by T0, okay, if time period is T here, the frequency with observer will observe N is 1 by T, simple, right, so let's say that at T equal to 0, the first pulse has left from here, okay, so at what time the pulse will reach here, tell me what could be the time here, what will be the time, pulse is moving with what velocity, C and this is moving with V0 velocity, so relative velocity is C minus V0, distance is L0, distance of approach, so time it will take to travel, the first pulse will reach at a time of L0 divided by C minus V0, okay, now second pulse will start from here at what time, T equal to 0 was the first pulse, second pulse will be at T equal to T0, good, so time period is T0, so after T0, next pulse will go, so if I know what time it reaches there, time period over here will be T2 minus T1, if I find out the time it reaches here is T2, this second pulse, T2 minus T1 will be the time period, so what is T2, now tell me what is T2, L0 plus, so see by the next pulse when it starts, the distance between them grows by a distance of V0, T0, yes or no, by the time next pulse is thrown from this side, the observer will move a distance of V0, V0, so now the distance become L0 plus V0, T0, so T2 will be what? No, no, it's T0, time has already gone plus L0 plus V0, V0, C minus V0, okay, now just let's do this thing, let's find out T3, so third pulse will leave from here at what time, T equal to 2 T0, how much this have moved further, T0, T0 more, it is moving with constant velocity V0, so by the time third pulse is thrown from here, this observer would have moved by 2 V0, T0 total distance, so T3 would be 2 T0 is gone plus a distance of L0 plus 2 V0, T0 divided by C minus V0, okay, so basically it is receiving pulse at T1, then T2 and then T3, so time period of receiving pulses will be T2 minus T1 or T3 minus T2, just check both of them are equal or not, okay, both of them are equal, how much? T0 plus V0 plus V0 by C minus V0, C T0 by C minus V0, combine it, just add it up, so it will be, this minus that will be T0 plus V0 T0 by C minus V0, so take T0 common, it will get C by C minus V0 times T0, this is what you will get, and here also you will get the same thing, after every this time period, it will receive pulses, any doubt, so time period is this, so frequency will be N will be equal to inverse of this, C minus V0 by C times 1 by T0, 1 by T0 is what, original frequency, original frequency N0, so this is what the observer will hear, inverse of time period, time period is this, inverse of time period is frequency, so 1 by T0 will come, the 1 by T0 is original frequency, T0 is original time period of the pulse, any other doubt? T2 is a time when the second pulse which has started from here at T0 reaches there, but after T0 the observer would have moved further by distance of V0 T0, so total distance will be N0 plus V0 T0, any other doubt? Yeah, it's very easy right? Yeah, because I am telling you, okay write down, source is moving, observer is stationary, final formula is directly at the end, this is just intermediate formula, source moving and observer at rest, so this is the source again, and this is the observer, let's say length is L0, so you remember right whatever we have done, now assume that the source is moving this side with velocity of V s, speed of sound is C, can you derive it yourself, upper end frequency? Sir, we take V0 positive when it's moving towards the upper end. Don't introduce sign convention right now, we have derived it properly, when it was going that side, okay we'll come back to that, but right now you derive for this scenario, the first pulse, T1 will be what? The first pulse will be L0 by C, it will be C or C plus V s, it will be C only, okay velocity of sound depends only on the medium, got it? Because speed of sound, it doesn't matter what source is doing, speed of sound depends on the medium, it depends on the medium property, okay, like for example if I run and shout, speed with which the sound will travel will be 330 only, my running will not affect the velocity of the sound, okay, now second pulse. Sir, previous case the relative velocity have taken between the sound and the observer, observer is observing that sound, but now observer is at rest, so relative velocity between sound and the observer is speed of sound only, observer has zero velocity, the sound is reaching observer, sound is not reaching source, got it? So T equal to T0, second pulse is released, what is the time? L0 minus V0 T0 by C plus T0. So T2 will be equal to T0 plus V s T0 divided by C, what about T3? 2 T0, okay, so now let's talk about the time period, time period received by the observer is T2 minus T1, which will be equal to T3 minus T2, there is how much? T0 minus V s T0, okay, so T2 minus T1 will be T0 minus V s T0 by C, this is what you are getting? Is it same as T3 minus T2? Okay, so this will come out to be C minus V s divided by C times T0, so the apparent frequency is inverse of this time period, this is modified time period, so 1 by T is the apparent frequency is C divided by C minus V s times F0, what if the velocity was like this? Because this is receiving the pulse released by it at T1, second pulse is received at T2, third pulse is received at T3, so after every regular time interval of T2 minus T1 or T3 minus T2 it is receiving the pulse, from here after every T0 pulse is going, so time period of this is T0, after every T2 minus T1 this is receiving, so time period of that is T2 minus T1, so actual time period is T0, but that guy is seeing as T2 minus T1, so this is the modified frequency for the Doppler's effect, so please write down, no, before that what if velocity of source is like this, then what will happen? It will be L0 plus Vst0, plus here, plus here, plus here, plus here, okay, are you getting it? No, no, just not that simple, so please write down something if the observer and source, if the observer and source are moving towards each other, if the observer and source are moving towards each other, then both are contributing to increase the apparent frequency, understood? So basically if they approach each other frequency will go high, if they move away from each other frequency will decrease, now look at the formula here, all of you, in this scenario the source is approaching observer or going away, approaching, so you can see that it is increasing, denominator it is negative, but if source goes away it becomes C plus Vs, now look at the earlier equation before that, when observer was moving source was at rest, thus the observer was going away, observer going away, so it was C minus Vo, in the numerator it was minus, so the frequency is going down, if observer comes close to the source it would have been C plus V0 by C, getting it, so it is a very simple thing that if they approach each other frequency will rise, if they away from each other frequency will go down, velocity of source will come in the denominator, velocity of observer will come in the numerator, these things if you remember it will be done, and one more thing here we are assuming that they are moving along the same straight line, what I am trying to say is take an example of aircraft flying over someone's head, suppose this is you and aircraft is here flying with velocity V, and you are hearing the sound created by the aircraft, so who is source, aircraft is a source, so velocity of source is what, V, no it is not that simple, you need to join the line between source and observer, and find out the component of velocity along this line, so if this is theta you have to take V cos theta, with V cos theta it is going away from the observer, did I get it understood, what was right, always separation or approach, V sanitary will not create anything, it is going away and it is source, so it will be C divided by C plus V cos theta, apparent frequency will decrease it is going away, but if it is exactly at the top of the head, the component of velocity in that direction is 0, so right now you will hear the exact same frequency if it is exactly above the head.