Introduction to mechanical waves
Introduction to waves
Let's say I've got a rope. That's my rope. And what I'm going to do is, I'm going to take the left end of the rope, and I'm going to jerk it up, and then back down. And we're going to talk about what happens or what possibly gets formed. So if I take it up over here, it's going to, obviously, take the string to the right of it up with it. And the string is going to look something like this. It's going to look something like that. Now I'm going to immediately jerk it back down. And as it passes, let's see what the rope will look like when the left-hand point is at its original position again. So the left-hand point-- I've pulled it back down. But in the last time period, this part of the rope had some type of an upward velocity. You could imagine that way. And even after that point, even though this left-hand point starts getting pulled down, this point right here still has some upward momentum. So it's still going to keep moving up, maybe at a slower pace because it's starting to be tugged down by the rope on its left. So it's going to look something like that. And it's going to bring the rope to its right with it. So the rope will look something like this. The rope might look something like that. And then I'm going to take this guy-- this was just an intermediate position on the way to being pulled all the way down here. So what's the rope going to look like now? Well. This guy, he had some momentum that got him there. But then all of that velocity will essentially go to zero because he's being tugged by the rope to the left. And now, he's going to switch directions. And he will have gotten here, at that point. The point on the line that was here-- on the purple period of time-- it had some upward momentum. So it's just going to keep going, on maybe a slower pace. It'll be there and it will bring the rest of the rope to the right of it with it. So now my rope is going to look something like this. And then finally, where I'm going to jerk the rope back to its original position-- so this left-hand point is going to be there. This guy, in the previous time period, was moving down rapidly. So he might get there ready to switch directions again. This guy will start moving down. This guy, right here, he had some upward momentum. So he's going to be up in this position now. And he's going to be ready to switch directions. So finally, when I've done this whole cycle, when I've moved up, down and back there again, my rope might look exactly like this. And I could let go of the rope. I could just leave this little left point right there. And this the lump is going to propagate along the rope. Because in the next moment of time, what's it going to look like? This guy is going to be pulled up by this left-hand point. So he'll go back to his resting position. This guy's being pulled down right here by the part of the rope to the left of him, so he's going to be pulled down. This guy's being pulled down. But this guy had some upward momentum in the time period before, so he will have moved up. And so, the very next time period, my rope is going to look something like this. And this disturbance in the rope, if I do nothing else, and if I don't lose energy to heat and friction and all that, it'll just continue moving down the rope. If I look at the rope at some future period in time, maybe not that far down, the rope will look something like this. And if I were to keep watching it, I'll see this disturbance. I keep using the word disturbance, because there's really no better word to use for it. I'll see this disturbance or perturbation, or whatever you want to call it, moving along the rope. When we think about what a wave is, we essentially-- I kind of jumped the gun-- I keep calling this is a disturbance, because I didn't want to use the word, wave. I want to say, well what really is a wave? And a wave really is just this disturbance that's propagating down the rope. So this is a good time to actually define a wave. A wave. Because once I define it, I can start calling this a wave, as opposed to a disturbance propagating down the rope. So a wave is a disturbance propagating through space. And you might see other definitions of a wave. One of the most typical ones is energy or a disturbance propagating energy through a medium. And when they say medium, it's what is the wave going through? So in this example, the rope would be our medium. But the reason why I don't want to use that definition of a wave is because in future videos, we'll learn about electromagnetic waves and those don't propagate through any medium. They propagate through a vacuum. So to keep things as general as possible, we'll just call it a disturbance that propagates through space. And it usually transfers energy. What do I mean by transferring energy? On this left hand part of the rope, I gave a little energy the rope. I moved it up, down, and then back again. And then after I did that, that up, down, back again is happening successively to every point to the right on the rope. So if I waited long enough, at this point on the rope right here, it's going to move up, down, and then back again. Exactly what I did over here is going to happen to this point on the rope. And then later on, it's going to happen to some other future point on the rope. So that energy that I originally put on the left-hand side of the rope is being transferred down the rope. If I had some type of object here sitting on the rope, maybe when the wave-- when the disturbance- passes by it, this thing could get flipped into the air; it might get pushed into the air, and go into a higher potential energy. So this disturbance is transferring energy in this case. Now, what I've drawn here isn't the only type of wave you can have. I mean my definition is fairly general. But the definition is more general than just what I've drawn here. For example, you could have a sound wave. If you just look at all of the molecules of the air, they have some density that looks something like that. And now let's say I had some type of a membrane-- maybe it's a speaker-- that jolts this left-hand side of the air. So it just pushes-- so let me see if I can draw this. Let's say I had some type of surface here that just really quickly jolts-- that just moves it in that direction, and then just comes back. So similar to what I did here, I go up and down. But instead of doing that, it just pushes the air and then pushes back. So what's going to happen? Right after it pushes it, the air molecules that it pushes up against are going to jam together. They're going to get compressed. Right here, all these air molecules that were right on the surface, they're going to get pushed next to all these air molecules that are right there. And then when it pushes back, or when the membrane goes back, you're going to have fewer air molecules here, because you're going to have a low density here. And then these guys, that are all scrunched up together, they're going to want to get away from each other. They might even run into each other. And so these guys are going to run into those guys, who are going to run into the next guys. And so on and so forth. And after these guys bump into those guys, those guys are going to go back to where they were. So essentially, you're going to have this disturbance that's going to be a set of molecules compressing, or bumping into, its neighboring molecules. So if you look at this at some future period in time, all of a sudden, this area might look normal. Let me clear it and draw it just the way it I started. So this area might look normal. But that compression of the particles might have reached right over here. And not only that, we saw that right after the compression, you usually have this area of low pressure. So if I were to really draw this wave, and actually, if this membrane were to keep doing it over, and over, and over again-- so it kept going forward and back, forward and back, or right and left, right and left-- what you would have is a series of compressions. The air would just have a series of compressions. So that's one compression. You'd have another compression right there. Another compression right there. And then, in between the compressions the air is less dense. The air is less dense like this. And what we've essentially just generated is a sound wave travelling through air. So this right here is a sound wave. And this type of wave, where the direction of the disturbance is the same, or along the same axis as the direction in which the wave is travelling-- the wave is travelling in that direction-- this is call a longitudinal wave. So sound waves sound through air, they're longitudinal waves. Sometimes called a compression wave. Same thing. Compression wave. Because it's caused by compression. Our example of the string, this is called a transverse wave. Because the disturbance, the movement of the medium, is going in a direction transverse to-- or at an axis that's transverse to-- the direction of our movement. We're moving in that direction, to the right. Actually, our wave is moving to the right, but the actual medium is moving up and down. Our medium is moving up and down. That's why this is called transverse. While here the medium is moving left and right while the wave moves to the right. So it's along the same axis. So we're dealing with the compressional or longitudinal. Now in this first example, I just did one cycle. I just jerked up, down, and back again. And I created this one disturbance. And we can call this, when you just do it once, you can view this as a wave pulse. If I kept doing that-- if I just went up, down, back again, up, down, back again, and I kept doing it periodically, over and over again, then I would generate a periodic wave. And my string would look something like this. Well actually, it would look something that right there, where that's the disturbance generated from our first time that we moved this left-hand part of our string. So this right here is a periodic wave. In the next video, we're going to talk about a lot of the properties of a periodic wave. How the wavelength, and its frequency, and its period relate to its velocity, and all of that. But I'll leave that alone in this video. But I just wanted you to appreciate what I think is a concept that we use in everyday life. So it's a wave, it's a sound wave, and all that. But it's a fairly abstract notion where we talk about a wave, we're really just pointing to a disturbance that's moving, usually along a medium, at least when we visualize it, but not always. But we're just pointing to this disturbance. And this disturbance could take many forms. It could be a transverse disturbance if we're dealing with a string. It could be a disturbance in terms of the density of air molecules in terms of a sound wave. And there is a relation. So if you wanted to just plot the density here by position-- if I were to mathematically represent this compression wave right here-- let's say that this line represents just resting before the sound wave hits, that's just your normal density. If we were to plot the density it might look something like this. Over here, we have very high density. Over here, we have very low density. Over here, we have very high density. And if you were to plot it, it would look a lot like that transverse wave that I did with the rope at the beginning of this video. And that's why they're even grouped together. Because mathematically, even though a compression wave looks very different, or you might visualize or conceptualize it very different than a transverse wave, mathematically, they're essentially the same thing. You have this quantity. In this case, it's the density of the air varying over time. In this case, it's the height, or the position, or how much your displacement from your resting position-- that's the quantity varying through time, that disruption is travelling over the course of the medium. That's why we call both of these things waves. Anyway, I'll let you go here. And in the next video, we'll talk a little bit more of the properties of periodic waves.