 Hi, I'm Zor. Welcome to Unizor education. Today we will talk about the reflection of waves and we're talking about longitudinal waves. It's waves inside the medium like, for instance, air, sound waves. That's a perfect example. So we will talk about a reflection of these waves. This lecture is part of the course called Physics for Teams presented on Unizor.com. I suggest you to watch this lecture from the website because you will get into this lecture through the menu and menu basically describes the whole course and its logical connection between lectures. They're supposed to be in certain sequence because obviously some material which is presented in one lecture is used later on in subsequent lectures. There is also another course called Math for Teams on the same website which is a prerequisite. You have to know Math if you want to study Physics. The website is completely free. There are no advertisements. You don't really have to even sign in unless you would like to get involved in process, educational process with certain supervision, maybe teachers or parents and it's all explained basically on the website how to use this as a process but at the same time you're free to listen to any lecture obviously. Also every lecture has very nice notes, practically like a textbook. Each lecture is like a chapter in the textbook. Also the website has exams for those who are interested in challenge. Okay, now back to waves. Now I'm talking right now about waves in the medium but primarily I'm concentrating on the simplest kind of waves, the flat waves. I'm not talking about spherical distribution like whenever we're singing or talking about something. The model which I'm using is a cylinder relatively thin with a piston on the top and air inside, air or any other gas or whatever. So our first experiment is to quickly and short movement, quick and short movement down of the piston. So what happens if it just moves down very quickly? I did explain in the previous lectures that it creates the waves of pressure because it actually squeezes this particular layer immediately under the piston and the pressure is not dissipated immediately throughout the whole thing. It's only squeezing the molecules of air immediately under it and they being squeezed and having piston on the top so they can't really go anywhere up so they press down and the pressure in the air is basically a chaotic movement of the molecules which are hitting each other. So whenever you are making this short push down, short and quick push down, the chaotic movements of the molecules becomes less chaotic. It has certain direction so they move a little bit more down since we are pressing from the top down and they transfer their energy and their pressure therefore to next layer and that's how the wave goes down. So all the wave goes down, one layer goes, transfers the energy to another so the molecules are not really moving all the way down. They are just shaking around certain neutral position and now the wave goes down and that's where I actually stopped before. Now let's think about what happens if they have reached the bottom. Well, if they have reached the bottom it's basically kind of similar to whatever happens on the top. So whenever it's on the top the molecules have more pressure immediately under the piston and the pressure actually means intensity of the movement. They cannot go up because this is the hard surface of the piston. Same thing happens here. So whenever the wave of high pressure reaches the bottom, we have exactly the same picture in this, they cannot really go anywhere down so they transfer their energy back up. And what happens? Well, there is another wave which is coming as a reflection wave from the bottom up. So if we will do just one quick push, this wave goes down all the way, reflects from the bottom and the energy starts transferred upwards from one layer of molecules to another. And then what happens? Well, if piston is not moving anymore it reaches the top and does exactly the same thing. It cannot go anywhere up. So the energy of the top layer whenever it reaches this higher pressure, it will start pushing down and the wave goes down. And it goes up and down, up and down all the time. Obviously it's ideal situation. In practical life doesn't happen. Energy obviously is dissipating among the molecules and gradually the pressure will equalize the whole thing. There will be no waves. But we're not talking about this type of behavior as the time goes on. Basically it's like you have certain oscillations in the medium which has friction or something like this. So we're not talking about this. Our purpose right now is to talk about reflection. So what happens with the wave which goes down, it reflects. And then it goes up, it reflects again. Okay. Now let's consider the next step in our experiments. Let's think that this piston is not just moving down for a very short period of time, but it's oscillating. Let's say it's a harmonic oscillation, some kind of oscillation. Short ones and quick ones. So it produces certain waves. So every push down produces certain wave. And the wave goes down. And then there is a next wave which is following the first one because our piston is oscillating. What does it mean? It means that the waves will go down. High pressure, low pressure, high pressure, low pressure. That's how it will be here. And these waves go down. Now immediately after they reach the bottom, well each wave, each wave now reflects from the bottom and there is another wave goes up. And again it's one wave after another goes up. So if this process is continuous, so we're continually oscillating the piston. There is a continuing reflection from the bottom. We have basically two different movements. One movement of pressure in waves goes down, another goes up and reflects again and again and again. I mean it's really complex and chaotic because every molecule of the air is supposed now to participate in all these different movements. It participates in the movement of the wave down with the pressure and then there is a movement of the up. So certain molecules are pressing up, certain molecules are pressing up down. It's very chaotic. Okay. Now there is another small complication. If this is harmonically oscillating piston, now the reflection will be after a certain time, which means that we might not actually go in phase. There is a difference in phase whenever this one, let's say reaches the maximum. This does not necessarily reach the maximum. It all depends on the wave lengths and the lengths of the cylinder. If they are not really somehow evenly divided into each other, then we will have certain shifting phase and that even complicates the picture more. Now I would like to really talk about this complexity and related to a very practical situation. Let's say you're designing opera house. Opera house means that whenever somebody is singing on the scene, everybody should listen and hear quite well every word. But now imagine that all these sound waves, they are reflecting from everywhere and there is a difference in phase obviously whenever you're reflecting something because all depends on the length. So if these reflections are really not taken care of properly by designer, but by architect, the opera house will not be suitable to sing. Now there are some famous opera houses and what's important, people were really thinking quite intensely about how to design these opera houses in such a way that the sound will really sound nice for everyone who really listens from all these seats around the main scene. So there are different ways to achieve the goal of proper hearing of the sound. In most cases the purpose is to suppress the reflection and all these velvety seats and lots of different curves maybe which are introduced in the architecture of the whole opera house. They're all supposed to somehow dissipate the reflection so it doesn't really go to the people. Even this room actually, I did have a similar problem because I have an opposite wall. I'm talking about this wall and there is an opposite wall. Now if I don't take care of this, the sound will reflect from the opposite wall and it will go to a microphone again and it will be a little bit fuzzy, so to speak. So what did I do? Well, number one, I'm using a directional microphone which means it's directed towards me and so it really accepts the sound which goes from this direction. Also to reduce the reflection, I have closets on the opposite side of this room so that wall actually has two large closets. I open them up and there is something in it. So whenever my sound goes that way, it goes into the closets and considering there is a lot of stuff over there, it just reflects inside and doesn't go back. So I don't have as much reflection if I open these closets. So these are all very important measures to improve the quality of the sound and the quality in this case depends on this reflection thing. So we have to take care of it somehow. Okay, now in this particular case we were talking about reflection of the wall which is of the surface which is perpendicular to the direction of the of the flat wave. So the wave is flat basically, it's all basically parallels or all the molecules of air are simultaneously going up and down, up and down, they are oscillating. Now what if my reflecting surface is not perpendicular? So let's see, you have something like this. These are two different molecules of air. This is the front, so they are together, they're oscillating together. Now what do they need? It's at 45 degree surface to reflect from. So what happens? Will my flatness of the sound be preserved? Well let's just think about this will reflect here, this will reflect here. Now this is at 45 degrees to this direction. So we know that these angles are the same, right? These are parallel. So obviously by the time this molecule goes here and here, this molecule goes all the way here, right? Because this is equal to this. This segment is equal to this segment. So the time this molecule comes to this point is the same as this molecule comes to this point. They now continue as a flat wave because they are the same. So flatness is basically preserved. Now what if it's not 45 degrees? What if it's something like this, let's say? So we go this and this. Let's go this and this. Well, the parallelism is definitely preserved because the angles are the same. But now if you will connect this to this, you will see that the difference, there is no difference between lengths from here. Let's say this is A, this is B, this is A, this is B, this is C. The difference for the molecule A to go to point A and then to point C is exactly the same as the distance from this particular point to the B. If you will perpendicular here, you will see that these are equal segments. So this is equal to this, the distance to A is equal to distance to D and then you add this C and then you add from D to B. So when this molecule is at point C, this molecule is at point B and again the flatness of the front is preserved. So this is just a little geometry. I don't want to prove anything, I mean it's really very trivial. Okay, so this is a reflection from any kind of a surface, not necessarily perpendicular like here. But there is one very important phenomenon which can be observed in case you do have a perpendicular reflecting surface. Whenever you go with the wave goes here, then it's reflected back. Now there is a difference in phase obviously. Is there a difference in frequency? No. In a period? No. The wave which goes down has exactly the same period and exactly the same wavelength as the reflected wave which goes up because it's just synchronously good. Up and down, up and down. So the same wavelength, the same period, okay, and the same speed obviously because it depends only on the colleges of the air. So now let's imagine some kind of a thin layer of air. Whenever there is a wave which goes through this thin layer of air, whenever it goes down, what does it mean? The wave goes down. It means that neighboring air molecules present certain pressure and they're just trying to push a little bit down. Then this pressure is down, etc. But in any case, there is a pressure down when the wave goes down. Now then there is something which is a surface perpendicular to the direction of the propagation waves and there is a reflecting wave. Now what does it mean, reflecting wave? Again, it means that at a certain moment in time these molecules immediately under this layer will push it up. And since everything depends on the difference in phases, there is a situation. There is, you know, certain combination of conditions between this length and the wavelengths when these two events happen simultaneously. So the pressure down and the pressure up are happening at the same time. So what's the result of this? Well, the result of this is that this layer will be squeezed. And obviously you understand that if this layer is squeezed, the neighboring layers will be rarefied. They will be thinner. So this will be thicker air and around the next layers above and beyond, above and below will be thinner. So that's quite an interesting moment because the same happens here as well. And this is the wavelengths. So we will have some kind of a thin air and then thick air, thin and thick. And at some moment the thick air will be squeezed, as I was saying, all the thick layers will be squeezed. But then after a while, after half a period, half a period, basically, it will start expanding. And what happens? Now this layer will expand and this, which used to be thin, now will become squeezed from both sides. So I think the very good picture of this is imagine a codon. You know what a codon is? It just expands and contracts, right? So imagine a certain number of codons, which are connected sidewise. So whenever the first, the third, the fifth, etc., every other codon, they're squeezing. Then obviously the second, the fourth, the sixth, so the even numbers, the codon numbers will be stretched. And then the situation is reversed. Whenever the odd numbers are stretched, the even numbers will be squeezed. So that's how, actually, this happens and that's exactly how it looks when the phase of the reflected wave is corresponds in some way, corresponds to the phase of the coming from the piston waves. And this phenomenon is called standing waves, because in this particular case, there is also change of pressure. But if you don't have this bottom, if it's bottomless, then the waves are going down all the time. High pressure goes down a little bit all the time. And in this case, when there is such a surface and the distance is properly aligned with the wavelengths, we will have the areas of the high pressure not moving, but actually standing still at this moment. And that will be high pressure, but then it will change to low pressure because the high will be in the neighborhood. Then again, high will be in this layer and lower will be this layer. And then the pressure will change this way. So the high pressure will basically not move down. It will just stay up and higher and lower will stay in place. It's called standing waves. One more consideration which I wanted to mention. Whenever we are talking about reflection, we are not talking about molecules actually moving all the way down and all the way up. It's not the molecules which are moving. Imagine, for instance, the billiard. Whenever you're hitting one ball with another, if it's a straight up, if it's a direct hit, the ball which you have hit will hit that next ball and then the next ball will start moving. But this one, the first one, will stop. So the energy is transferred, but not by the same ball, by two balls actually, maybe three balls or whatever number. Same thing happens with molecules of airs. Molecules of airs are not going all the way down and all the way up. They're just moving a little bit. Consider there are springs between the molecules. So whenever one molecule moves through the spring, it actually pushes the other molecule. But the first one stays relatively in the same neighborhood. They're not really moving all the way down. Well, there is a chaotic movement and gradually molecules do change their position significantly. For instance, if I will open, for instance, some perfume in this particular place, the person over there eventually will feel the smell. So the molecules will definitely travel long distance. But not when we're talking about these very short oscillations, like a sound, for instance. During the sound oscillations, molecules are relatively stable in their neighborhood. They're just moving enough for a very, very short distance to push other molecules to oscillate and transfer energy. And they move the same way in their neighborhood. They're oscillating only around a certain point, but push the energy forward just through these oscillations, through these little, well, you can imagine, springs which connect molecule to molecule. But again, actually, it's just a chaotic movement and they're hitting each other. But this hitting is directed towards distribution of the sound. In this case, it's a thin, relatively thin cylinder. So distribution goes all the way down. Now, if I'm talking, for instance, distribution goes all around. So it's not really the same kind of a model. But anyway, it's something similar because in any direction, I can actually imagine that there is certain, like a cylinder, which has a flat wave. It's not really flat, obviously. It's a spherical, but every angle can be considered relatively as a relatively flat wave. It goes this direction, that direction, that direction, etc. Okay. That's basically it. The only thing I just wanted to add that if this is a situation when we have a standing wave, well, obviously, the difference between accordions, I will use this particular term. The difference in accordions is half of the lambda. So two accordions, one goes like stretching and at the same time, another goes squeezing, represent a wavelength lambda. So one accordion is half a lambda. And obviously, whenever the pressure goes up in one accordion, that's half a period. And then it goes down. That's another half a period. So it's t, t over two, and then another t over two. So these are periods. And these are, that's basically, that's basically all I wanted to talk about reflection. So it's very important, especially reflection of the sound is very practical. And people really do have to take care of it. That's it. Thank you very much. Please read the notes for this lecture. It goes on the physics 14 course. You have to go to waves, then waves in medium. And then when you open the waves in medium manual, you will see the reflection in waves chapter or lecture. Okay. Thank you very much. And good luck.