https://youtu.be/-SMwe8oTdtw
PHYS 1101: Lecture Twenty-Five, Part Two
Our new material in this lecture has to do with waves. We’re very familiar with them in day-to-day life. From a physics perspective, what’s at the heart of a wave is it’s nothing more than what we call a disturbance that’s moving through what, in physics, we’re going to think of as the medium.
In other words, when you drop a pebble into a pond, and you see these ripples on the surface of the water that spread out around that location where the pebble fell in, the disturbance is that ripple in the water, those circular waves that are spreading out. The medium is the water. It’s the material in which this wave is moving through. We’re going to learn in next lecture about sound. That’s nothing more than a wave that propagates through the medium of air, the air molecules that make up the atmosphere.
In this lecture we’re going to look at waves travelling on strings. And you’ll see one of your quiz questions, I even have you thinking about a wave in the context of people, when you’re sitting in a ball game, and you see a wave spread through the crowd. The wave, the motion of this disturbance you describe as the wave, and the medium would be the people. Okay. These are the key features that are true with any wave.
At the heart of it, there’s no new physics. In essence, at the beginning of every wave I have to have some sort of initial disturbance. Think of this as a source. I have to have something that moves, and because of that motion it exerts a force on, it influences the nearby neighbor in this medium, the neighbor then in turn influences its neighbor, and this propagation of this force, and of this interaction is what gives rise to this overall effect of the disturbance propagating along, or moving along.
Let me show you an animation, or a simulation of a very dramatic type of wave–a tsunami. This animation I’m going to show you was generated by a scientist that studies tsunamis, and he simulated the consequence of a large earthquake that happened in 1960 in Chile that’s down here on this map.
The consequence of that tsunami was this water wave that then propagated through the Pacific Ocean. The disturbance is this jarring of the earth that then pushed against the water, and in this simulation he’s showing how that disturbance then keeps exerting a force on the neighboring water molecules, and in turn that keeps happening, and this propagates.
That was Hawaii that you see just got blasted by it, and eventually it reached over here to Japan. This was a Japanese scientist that did this study, or simulation. For the purposes of this demonstration that he did, he greatly magnified the size of the water here, or this ripple compared to the size of the earth, but that’s just so you could see it well. But it’s a good visual though, of a dramatic type of a wave, a tsunami.
It’s the same physics, though. It starts with some disturbance that generates an initial kick, or a force exerted in this medium, in this case, the water. That force then ends up being passed, or exerted on neighbor, to neighbor, to neighbor, and that’s what continues on and builds up to just be this wave, the disturbance. Let’s look at an animation that’s offered through your textbook where we can study the basic features of a wave more carefully, and we can vary some of the parameters.
You can look at this simulation yourself. If you go through WebAssign, into the online version of the textbook, you’ll notice for chapter 16 there’s a simulation section there, and there’s one simulation for this chapter called, it’s just labeled, “C 16.1 Traveling Waves.” That’s the animation I’m going to show you now.
What we have here is a plunger that’s acting on a source. This plunger, when I hit go, does nothing more than move up and down. This disturbance, this initial source here of course, exerts a force on this string, which is attached to this plunger. That string, of course, each segment you can picture is attached to a neighboring segment, which attached to a neighboring segment, and so on. And there are real contact forces between all those segments, and it’s that contact force that gives rise to the propagation of this. Let me reset this and play it for you.
You see, it starts with the plunger going up and down. As a consequence each segment of the string right beside the plunger has to go up and down, but you see, as that effect propagates down the string, it gives rise to this visual effect of something moving to the right. So here I have a snapshot that I’ve taken of that scenario that you just watched.
Now, the thing that jumps out the most at you, I think, as you watch it, is this visual picture of these crests moving to the right. That’s one kind of motion that’s characteristic of a wave. That’s what you really saw in the animation of the tsunami, right? Your eye was drawn to watching the crest of the wave as it moved along the ocean. A separate kind of motion that happens at the same time is to focus on a single segment in this medium. Imagine a red spot that’s painted onto one little section of this string and to look at the motion of this segment.
So this spot that’s attached to the string, we’re going to have to appreciate that it has very different motion than what your eye really watches and sees, which is the crests that move to the right.
So we’re going to break this up into first focusing on a careful analysis of a single spot in the medium, in this case on the string, and watch the motion of that red spot, and let’s think about what it’s doing. Then we’re going to look at the next type of motion, which is that of the wave itself, where we can simplify it to picture we’re following the crest of a wave.
What’s the behavior of that crest, and what sets that characteristic motion? What determines it? Step one, though, let’s focus on the motion of this red spot.