Particles in Waves
So we hear sounds around us, we listen to music and we appreciate music separately from sound separately from noise but there are a few questions that I have. First one being, why do we have two ears? Wouldn’t one ear just do? We could hear probably. Well of course some of you might be answering, we need to ears so I can hear from both sides. While that could be true or it may not. Let’s find out. It’s one of the answers or one of the questions hidden inside this chapter for you. And the other one of course being what exactly is common between dolphins and bats? They look pretty different right? There couldn’t be something that’s so different looking than bats and, and dolphins. But what is it that connects. Something in common between the two of them. And what exactly is this sound? We hear it. We say that I can hear something. Would all animals agree with us if we told this is sound and this is not sound? Would a dog agree with us? Would a snake agree to our definition of sound? So one more question and one of the last questions, one of the many other questions in fact that are hidden inside this chapter are what exactly is this matchbox phone? How does it work? You have a matchbox, you connect a thread to it, put another matchbox at the end. Somebody whispers at this end. Quite far away you take it far away and still somebody puts their ear on the other end and they are able to hear the sound. Which we know is not true if somebody whispers here without this right. If somebody whispers here and somebody tries to listen to it quite far away, they can’t hear it. So what exactly does this matchfo.. matchbox, couple of matchboxes with a thread do such that sound can be heard? So as you learn new things in this chapter, you’ll begin to find that answering these questions and many a, many more are going to be that much more easy and let’s find out how.
But in order to answer any of these questions we need to go back into probably one of the most fundamental ideas of physics, in fact fundamental dichotomies of physics which is particles and waves. There are certain waves in which you can look at the world as particles are you can look at the world as waves. Now, let’s, let’s imagine that you want to send a message to somebody, right? And you, you could do it this way, you could whisper it to somebody in somebody’s ear, you can tell it to someone and then they can run to the other person and tell them. And that way you have conveyed the message, right? But that’s not the only way in which information can spread in this, this world. Because you can imagine if it’s this way. Instead of the first case let’s imagine now that there are a line of people between you and the other person continuously and now what you do is that you whisper whatever you want to say to the person next to you. Right? And that person whispers it to the person next to him and that person whispers to the person next to him and so on and eventually what begins to happen is that the person you intended the message for gets the message. In this case has information spread from you to that person? Yes it has. Has any particle in one sense of the word has any object actually physically gone from here to there? It’s not right? So in the first case of course it did. There was a person running from here to there, but in the second everybody just turned to the next person and then whispered. The information still went. So if you were to imagine dropping a stone into a very clear lake, right? A calm lake that is completely still. You drop a little stone there, it begins to send off a circle and you would have surely seen this. When that circle is going the question you will begin to have is who really is going? Who are those little water people running around in a circle scared by your little stone? Who exactly are they? Is that are there really water particles going around in circles, are they really moving? To test this of course we can do something pretty interesting. That if you were to take a little cork that floats, a little sponge ball or if you are really mean you c.. a little piece, little ant, I don’t know if ants float, you put them on a little leaf and put them. You leave them there what can begin to happen is that you will notice that when the circle passes them, when the circle of water, that ring that you see, passes them, they do not move rightwards or left. They do not move along the plane of water at all. They just bounce up and come back down. So you begin to realize that sometimes information or water appears to spreading because even on a wheat field, right, if you, there is a windy day there is a field and you see that there is a wind blowing on that field. You will see little lines that are seen to be going on that field when you look at it from the top. Right? You will see that there are, there is something going on but you know that the, every single piece of wheat, every single plant is actually rooted to the ground which means that it’s not moving this way or that way. But overall on top you see that something is moving across the field. What exactly is this? So the sense that we have right now is that things can move even without the actual particles moving physically from one place to another. They can just do something very small where they are but we see that as if something is moving. So in the case one where we showed you a person runs and gives the message that is called a particle, where a particle transfers from one place to another. Second case where something apart from a particle transfers, we call it a wave.
And we are now going to talk about certain types of waves because we have kind of already told you a little bit about water waves and about how we have moved on a wheat field and things like that. We are going to tell you how these two waves can be different. The first thing of course is that there is no particles moving from one place to another and that’s when, when information travels without that it’s a wave. Now let’s begin to ask this question, right? Let’s imagine now, let’s imagine that the particles are moving, where about their position, whichever their position is. They are moving about that just kind of vibrating around it, up and down or sideways, this way or somewhere like that. They are not really moving but just vibrating about that point. Now what are the two possibilities that we have? I might want my message to go from this point to this point and everybody in this, in that whole line of people that we imagined could either maybe say sit down and stand up, right? And how would that look? If you were to imagine this now, right? Imagine a group of people standing in a line, right, and at the first count the first person sits down and they are all holding each other shoulder to shoulder, right. So in one sense they are all connected. One person sitting is not independent of another person. So if he sits he starts pulling the person next to him. So it’s kind of like a bond. So there is a particle here that human being, there is kind of bond between and the next through his shoulder and he begins to sit down, the next person feels of force, he begins to sit down and as he’s sitting down the person next to him feels the force and it keeps going that way what would you observe? Every single person here is actually just sitting up and down. He is never ever, ever moving slightly towards his right or towards the left. But when you watch this happening what will you see? You will see something that is going from one side to the other. Something that looks like a wave and what we call a wave. Right. Because you would have played with this sometime as well because if you were to take this and compare this with something you have played with very commonly. Take a piece of string, do a little whip, you see something going across the string and coming back. Right. It comes back sometimes when it hits the wall but at least you see it going. In that case as well all the particles of the string are just going up and down exactly similar to what you see over here where people are just sitting up or going sitting down or going up and not anything else, but the wave as it is moves this way. So in this case the wave motion is in one direction and the motion of the particles that make up that wave is in the perpendicular direction, just like in the threat case, right. You do a thread every, you do a whip to a thread, you whip a thread, every particle goes up and down but the wave as it is moves this way. So they are perpendicular. The particles move that way, the wave goes that way. And when that happens we call it a transverse wave which is just a name that we give whenever particles and the wave are perpendicular. Awesome. So is there any other kind of wave?
Let’s try to find out. We will take this and set it aside and let’s begin to think about what else could we do? Let’s take the same people analogy. So we take a group of people and you make them stand shoulder to shoulder. In this case, instead of, in the first case what did we do? We took the first guy, pressed him on his head right? So that it kind of sent off a wave throughout. In this case what we will do is that we will hold this guy right, and instead of trying to push him down or up we will shove him towards the other people and then pull him back. Now what’s going to happen when you do that? So you’re beginning to shove him towards the other guy, so the other guy, the second guy in this situation begins to feel a force and he pushes the next and pushes the next and so on. Yeah, that sense off something like a domino effect. It starts to push people. But the moment you’re doing that, the moment it’s going, in just some amount of time you begin to pull the guy back and because he is connected to the next person on his shoulder he’s going to pull back the next guy as well. So he begins to pull him, right? And now what happens? Every single person is pulled backwards as well. And what would this look like? Yeah, everybody over here is going a little bit away from their position but coming back. Yeah that’s what they are doing. They’re not moving to, too far away from where they are, but the wave as it is, is moving. And in this case the particles are moving parallely to the direction of motion of the wave. In the previous case it was perpendicular. Here it is parallel. And exactly would you have seen this? In a very common way you would have seen this very often if you have ever played with a slinky, or that little spring toy that you play with. So you take that and if you were to push a little bit on one side and pull it back you would see a little kind of a wave that goes around and comes back. Sometimes it comes back and it reflects on the other surface. But at least you would see it going that way. Now what exactly is going that way? You have succeeded in compressing this spring a little bit and then elongating it. That little compression compresses the next part, then the next part, then the next part and each compre… the compression travels along that slinky and then as that compression travels there is also what’s we call a lack of you know you compress it you can also elongate it. There is an elongated part that follows it. Right. So instead of this spring being uniform as it would be if you just leave it. You compress it, some part of it and elongate some part of it. And then that begins to travel. So in this case, what you observe is that the particles travel in a particular direction that is parallel to the direction of motion of the wave itself.
Poof. So two cases here. First one was called transverse, it still is. The second one what we call longitudinal. So when the wave and the particle move parallel to each other we call it longitudinal waves and when the particles move perpendicular to the wave we call it a transverse wave. Interesting. So these are just names we give to differentiate between these two because they are fundamentally different in many aspects. They are very, very different in the way they behave and that’s one of the reasons why we do this. Even though they have a lot of similarities, which we are going to see in some time. So now let’s, let’s see if we have kind of understood this concept in a nice manner. How many of you watch sports here? So if you do, almost surely you will know about this phenomenon called the Mexican wave. Right. There is a huge stadium of people and it begins from one side and it spreads across the entire stadium. It’s a beauty to watch. What kind of, is it a wave first of all? It’s called the Mexican wave. Yeah. It’s probably is a wave. There is no particle moving but you see something moving. So from your understanding what do you think it is? Is it a transverse wave or is it a longitudinal wave? That’s right, yeah. Each of the people over there, each person over there is actually just standing up and sitting down. He might, if he is really enthusiastic, he might do something with his hands but all he needs to do is stand up and sit down. Right. But as people start doing it in order, what you begin to observe is that a wave that’s tra.. transverse, that is travels in the entire stadium. Yeah. Each person of course just sits up and down. It is a transverse wave. Now, that we have done what it is that’s required for you to understand what these particles and these waves are, these concepts are extremely crucial to understand all the physics because everything that you learn about will probably fall into one of these two boxes. Or we will try to fit it within one of these two boxes. We will. But before you believe in the certainty of this all let’s add one little bonus to this for the extremely keen ones because you’re going to begin to question this in a few years.
And that is, is everything in the world either a wave or a particle? Well it turns out first of all that we have one more third kind of wave. We have transverse waves, we have longitudinal waves and we have one more third kind of wave which we are going to talk about. Yeah. But before we do that, there is one little classification called mechanical waves and non-mechanical waves. Right. Mechanical waves are those that require something like we saw here. Every single thing we saw till now are mechanical waves. People pushing, Mexican waves, little springs, little threads, because everywhere there is something mechanical, something that is a particle that is actually moving up and down or side wards. But we don’t need that. An example for this is light. You could take it in vacuum and light would just travel and the question was what exactly is light moving up and down? What is exactly moving up and down when light is moving? And the answer really is nothing and lots of people couldn’t accept that the answer was nothing. They just couldn’t do that. They believed in something called the ether that exists all over the universe which was moving when light was moving. But it turns out that you don’t really need an ether for light to move. We don’t need to imagine an ether for light to move. So for the really keen ones there are, all the waves are kind of classified into mechanical and non-mechanical waves. Mechanical waves that require a medium to propagate and non-mechanical waves that don’t require one. And on top of this we have what’s called, what are called matter waves which you will learn about in some time, quite some time, which are pretty interesting because it’s one way of looking where every particle can be kind of seen as a wave with a particular wavelength. So it, all this is me trying to tell you that whenever human being try to fit in nature within the boxes that we create, nature inherently, it becomes arrogant and shows us that we can never do that. It kind of always steps out of those two boxes we create and say there are particles that behave both wave, both as waves and particles, neither is wave nor particles. Things like that. Which begins to really tell us that our categorical wave separating in this world may not really work well at, at certain points where there is a break. Where things begin to start having a smooth flow between one to the other. Because in the previous chapter we saw that solids and liquids have a nice smooth transition between them. There are objects that behave both like solids and little bit like liquids. Powdery substances. So similarly, even when it comes to matter and waves, particles and waves, there are things that behave like particles, like waves, in other words they don’t obey our categories. In fact another interesting example for a wave, is that you’ve gone to an amusement park, and there are these things called wave pools there right. And you go stand in one of them, especially in the deep parts, not in the shallow parts because it doesn’t really work that well in the shallow parts. In the deep part, if you are standing and if the wave is generated, you will notice that every single person standing there, little heads, will all bob up and come back down when the wave passes them. If you have noticed this, you will realize that what kind of wave was generated. A transverse wave of water where every water molecule is pushed up and down. So with that, along with that, even the people went up and down but the wave as it is propagated horizontally. So a very real life example of what we notice as waves. Now the thing about waves is that when a wave propagates, every particle in that wave is only influenced by that person or that particle right next to it. It doesn’t really care too much about the history of how this was created. Not directly. Of course the person who is starting it is indirectly influencing this particle. Right. But as far as this particle knows, all it knows is that the person next to me is pulling me down or pulling me up or whatever, so I go down, and by doing that I also pull the next person up or down or whatever. So it’s really a, a very local thing where each particle interacts with the next one and so on and so on its transferred throughout. So in a wave, each particle kind of cares only about who is right next to it and in one sense influences who is right after it.