 After reflection we have written equation of wave also, so we were talking about super position, think of super position, correct, write down super position, what is super position better? Collision of two waves, in the layman terms, collision of two waves, okay, what was the first example that we have taken when the two waves are moving in the same direction and meeting each other, but there amplitude is same, frequency is same, the wavelength is same, velocity is same, only difference is phase. We found out what will happen if two waves travel in the same direction, what will happen then, they will create a third wave of amplitude, phi by 2, where phi is the phase difference, depending on the phase phi, the resulting amplitude can be 0 also, okay, so we have discussed what will happen if two waves moving in the same direction will meet, now we are going to discuss if two waves traveling in opposite direction and meet, two waves can be generated very easily if they are traveling in the same direction, but traveling in opposite direction, very common way is reflection, when a wave is traveling like that, it can reflect off from that wall and started coming in this direction and this wave is continuously going in that direction and once wave started getting reflected, two waves are automatically generated, one is coming this way, other is coming that way, okay, so we have also discussed about what kind of reflections are there, okay, we have talked about hard reflection and soft reflection, but we have talked about only about the transverse wave, okay, by the way going back to the superposition when two waves are going in the same direction, the way we have derived for the transverse wave with the longitudinal wave add exactly the same way or different way, instead of y what will be there, y is equal to a sin kx minus omega t is for the transverse wave, instead of y it will be s, it will be s, so s is a displacement from the mean, we have discussed it or not, we did discuss, take care, so let's discuss it once, we will discuss how this situation of transverse and longitudinal are similar, once you know that the situation is similar, every time we learn anything about the transverse wave, you can understand how it will be for the longitudinal as well, you don't need to study longitudinal separately, okay, so transverse wave looks like this, this is transverse wave, this is one of the example of transverse wave, a sinusoidal wave, okay, what we are tracking in transverse wave, we are tracking y as a function of x and t, so this equation is y is equal to a sin kx minus omega t, let's say, this is one of the wave equation, okay, what is y, y is what, of what, of the particle, particle of what, particle of the medium, when the wave is telling particle starts moving and if it is a transverse wave particle will move up and down, so this wave when it goes forward, like this, exactly as it is when the wave moves forward, what will happen to this particle over here, it will go down, this particle over here it will move up, this particle will go down, particles can't move forward, particles will just move up and down, they are moving in a very synchronous manner and it appears as if particles are moving, but in reality it's a disturbance that is moving, particle are just moving up and down, okay, so basically particles are doing SHM yes or no, if suppose you don't agree that they are not doing SHM, but they must be doing oscillation at least, if not simple oscillation whichever you know wave you take particles must do oscillation, because it should be a periodic motion, it should come up and down like that, okay, so if you put the value of x to be let's say 1 centimeter, if you put x value as 1 centimeter, you will get a SHM equation K x0 will become a constant, so you get an SHM equation A sin omega t plus theta, it is an SHM equation, so sinusoidal wave, all the particles in the medium are doing simple harmonic motion, okay, and what is the location of the mean position for those particles, y equal to 0, on this line mean position of all the particles lie, yes or no, right, amplitude of SHM is amplitude of the wave only, okay, so what we are tracking, we are tracking the displacement of the particle from its mean position, that's all, okay, now the way the longitudinal wave will look like is this, suppose I am taking a spring as an example, longitudinal wave is travelling, so there will be zones of compression and rare fraction like that, so the compression and rare fraction will move forward, okay, so particles what they are doing, they are moving back and forth in the direction of the velocity of the wave like this, in the longitudinal wave, okay, where are their mean positions, their mean positions will be at different x coordinate, what will be the y equal to 0 in this case, entire wave lies in the y equal to 0, there is no movement other than y is equal to 0, entire movement is on y is equal to 0, okay, so y has no meaning when it comes to longitudinal one dimensional wave, so what should I track here, instead of y, displacement of the particle from its mean position, so that I am taking as a third variable, this displacement I am taking it as s, okay, here it came out very nicely, it came out to be y, y coordinate, but here I can't put any coordinate because the mean position are at different x coordinates, but I will be tracking the same thing which I have tracked in the transverse wave, which is displacement from its mean position, okay, so the equation for the longitudinal wave will be s equal to a sin a x minus omega t, what this will tell me, this will tell me displacement from the mean position for a particle which is at a distance of x at a time t, what is the difference between this equation and that equation, right hand side there is no difference, only left hand side is a difference, even left hand side philosophically or qualitatively it is the same thing, okay, so we have mathematically derived what will happen if two waves travelling in the same direction they superpose, okay, we assumed it is a transverse wave, what if they were longitudinal wave, then this will be s1 and s2 will be a sin kx minus omega t plus phi, so when you add it, you will get net displacement s1 plus s2, will it exact same thing or not, you will get the exact same thing, your amplitude will be 2a cos phi by 2, exact same thing, are you getting it, okay, so we don't need to worry about how longitudinal wave will superpose when the two waves are travelling in the same direction exactly same, fine, so we have discussed about the reflection of the transverse wave, soft reflection in the hard reflection, let's talk about reflection of the longitudinal wave, then we will discuss what will happen if two waves travel in the opposite direction and meet, right down to reflection, there is no categorization as such soft or hard reflection, it is only one kind of reflection, okay, it goes, hits an obstacle and comes back, so basically if I draw the sound wave it will be what, compression of the gas molecule is represented by lines which are close to each other, this is the rare fraction, this is compression, this is how sound wave will move, sound wave particles get compressed, standard like this, okay, so now it is compressed and then it hits the obstacle, so after hitting the obstacle what will happen, right now wave is moving like this, when it will get reflected there will be compression will get created near the wall or rare fraction, compression only, compression only, okay, so there will be compression only, so the only difference is the direction of the motion, there is no phase change that has happened, okay, there is no phase change that has happened, so if phase of this wave is k x minus omega t, what will be the phase of that wave, k x plus omega t that's all, because it is travelling in opposite direction, so this will be a sin k x minus omega t, this will be a sin k x plus omega t, okay, but when it was a transverse wave and there is a hard reflection, the phase changes to k x plus omega t plus pi, but if it was a soft reflection the phase remains k x plus omega t only, there is no plus pi, did we discuss what is the relation between distance travelled in the phase, lambda is corresponding to 2 pi that we have discussed lambda correspond to 2 pi, okay, so why do we need to know the relation between the path travelled and the phase, see it is easy to calculate the distance travelled, you take a scale and measure it, but you can't calculate the phase just like that, so the relation between phase and the distance travelled will enable you to find out the phase of the wave, tell me this, suppose there is a reflector here, a sound source, a wave gets generated, is this reflector, goes there and another sound wave goes like this, this sound wave meet over here, there is this, this is a sensor, this is transmitter, this transmits two sound waves let us say, one is in this direction, other goes in that direction, they meet here, okay, let us say this distance is L1 that is L2 that is L3, okay, you need to find out relation between L1, L2 and L3, so that you don't hear anything here, the sensor doesn't hear anything, the wavelength is given as lambda, how can L1 plus L2 be equal to L3, is it triangle right, did we discuss about the path difference should be what when there is a constructive difference, how much should be the path difference, in these are times lambda, if this constructive, destructive it will be 2n plus 1 into lambda by 2, if it is destructive the path difference, so do it here, okay shall we do it, the path difference is L1 plus L2, this is the path travelled by the wave 1 minus L3, path travelled by the upper waves, okay, this is the path difference or not, there is some error, tell me what it is, oh so it got reflected, so then the phase is going to reverse, no it doesn't reverse, it will get shifted by L1 plus L2 plus lambda by 2, you have to add lambda by 2, because of phase shift happens pi because of reflection, so lambda correspond to 2 pi, lambda path correspond to 2 pi, so pi correspond to lambda by 2, so lambda by 2 is extra path that has added to it because of the reflection itself, okay, so when this path difference is equal to 2n plus 1 times lambda by 2, there will be destructive difference and you will not be able to hear anything, L1 plus L2 minus L3, if this become equal to n lambda, have you understood this, why is, due to reflection, how much phase get added up, pi phase, okay, pi phase gets added up and I know that 2 pi phase is how much path lambda, so pi phase is lambda by 2, it acts as if it has travelled an extra distance of lambda by 2, it is not travelling lambda by 2, but because of reflection it behaves as if lambda by 2 has been added up, okay, so I know that 2 pi phase is how much path lambda, so pi phase is lambda by 2, it acts as if it has travelled an extra distance of lambda by 2, it is not travelling lambda by 2, but because of reflection it behaves as if lambda by 2 has been travelled extra and this is hard reflection or soft reflection, this is hard reflection, so this is what we have discussed, okay, nothing new, we discussed it, right, last class only, okay, see these I have questions are more there in class 12th, these are not there in 11th, but if you pay attention here, maybe 12th will become easier for you.