字幕表 動画を再生する 英語字幕をプリント Hi. It's Mr. Andersen and today I'm going to talk about waves. Our lives are dominated by waves. Right now you're listening to me and so you're picking up sound waves from the speakers in your computer. Since you're watching me, that's electromagnetic waves. If you're listening to this on wifi then you're using radio waves to pick up that signal. So what is wave? A wave if we define it is simply a disturbance that moves through space and time. It's a good way to take energy or information and move it from point A to point B. So waves are really important. But there are a few properties that you need to understand about waves before you really get it. First of all you should understand that waves come in two different flavors. There's transverse waves and longitudinal waves. Transverse waves, an example of that, if you were to tie a string to a tree and then just move the string up and down you'd be creating a transverse wave. How does that work? Well the string would be moving up and down. But the wave would actually be traveling perpendicular to that. And since this is perpendicular motion we call that transverse wave. And this does kind of look like a T on its side. And so that's a good way to remember what a transverse wave is. A longitudinal wave, an example of that would be the sound you're listening to. It doesn't oscillate perpendicular to the motion. It actually oscillates in the direction of the motion. And so this video shows you some longitudinal waves. What's happening? Well the oscillation is in this direction. And the motion is in this direction as well. And so that's a longitudinal wave. It could be like this in water waves. Or it could be air waves as well. But that's a longitudinal wave. There are some properties you should understand about waves as well. And in fact there's a relationship that's worth memorizing. And that is V equals f times lambda. What does that mean? Speed of a wave equals the frequency of the wave times the wave length. We always measure speed in meters per second. We measure frequency in hertz which is one divided by time. Or one divided by a period or second. It's called a hertz. And then wavelength is going to be measure in meters. So let me kind of go through these three properties of a wave. If you're looking at wave speed it's easier to measure wave speed when you're just looking at one wave. And so let's say for example that we're measuring a wave and we want to see how long it takes to move from point A, we'll say over here, to point B which is over here. Well let's put the wave in motion. Let me time it. One one thousand two one thousand three one thousand. So let's say it takes 3 seconds to move from point A to point B. And let's say that that's 3 meters to make the math easy. Well it's now moving 3 meters in 3 seconds and so it would have a wave speed of one meter per second. Another thing that's interesting to look at in this animation is that the actual particles on the wave don't move as fast as the wave. The closer you get to the surface, if you're a surfer, the faster you could move. But a lot of those particles are barely moving at all. And so the energy is being travelled through the medium. But the medium is not actually being travelled. Next thing is going to be called frequency. Frequency is how often waves come. And so the definition for that is one wave divided by T which stands for the period. In other words if we have one wave every one second, then we would call that a frequency of one Hertz. So let me put this animation in and run. So right here we've got a series of lights. So the light at the bottom, it's blinking every 0.5 second. And so it's period is 0.5 seconds. And so it's 1 divided by 0.5 or 2 hertz. Let's say we have a wave that come this often, every 2 seconds. So we have a wave. And then one one thousand, two one thousand, wave. So that would have a frequency of 0.5 hertz. In other words the faster the waves come the bigger the frequency is going to be. The larger the frequency is going to be. And if you're listening to my voice, you're listening to thousands of hertz, if not tens of thousands of hertz in my voice. And so those waves are oscillating really, really quickly. Much quicker than these flashing lights right here. Last thing in a wave is lambda. And what lambda simply is going to be wave length. Wave length, well first let's look at this wave right here. In a transverse wave it's going to have a crest which is going to be the top. It's going to have a trough which is right here at the bottom. And then we're going to have the node which is right in the middle. And so from crest to crest we call that one wave length. And what you'll find is it's going to be the same distance from here to here, here to here. In other words how long a wavelength is is going to be lambda. Or that's going to be the wavelength of a wave. Now to really measure and play around with the waves, I would encourage you to do this. This is a simulation. It's found at phet.colorado.edu. They do some wonderful science animations. And this one is called waves on a string. So let me go find that for a second. So here would be a wave that you can kind of play around with. So what you can is we can grab this string of beads and I can move it up and down. And I can move a wave from this side to that side. Now what you'll find, it's hard for me to do this very well. Let me try that again. Is that the energy is being travelled from or is traveling from point A to point B. But the beads aren't traveling. So it's just being transferred through that medium. So this would be a typical wave. Let me just make a quick pulse like that. So what's happening here? Well that wave is moving down and then it's just moving right out the door. Let's kind of reduce the damping for just a second and see what happens. Alright. So we even have more of a wave that's moving down. Now let's actually put a fixed end on that. So now what I'm going to do is I'm going to actually send a wave down. And let's see what happens to it. Ah. The wave is being reflected or it's bouncing back. And this is a characteristic of waves as well. I'm going to put a damper on that for just a second. So let's see what happens when I send a wave and then I send another wave. Well what happens when they hit? That's kind of hard to see. Let's try that again. Let's say if I send a wave. And then I send another wave, well, what happens when they hit? Well when they hit they actually cancel each other out. It's hard to see. Let's see if we do it this way. Let's make a loose end now. What happens if I have a loose end? We send that down. That's cool. The wave actually comes back on the same side. So now let's send a wave and now another wave down. What happens when they hit? Well what's happening is they're actually taking the energy of both waves when they collide and then we're adding to that. So we have that, that's called constructive interference. So now let's kind of oscillate our waves. So let me keep the dampening like that. Let's go back to no end at the end. And now let's set it to oscillate. So now what do we have in a wave? Well, in this wave we've got a high amplitude. So amplitude is going to refer to how big the wave is. So let's reduce that. So amplitude is how high it's moving up and down. Frequency is going to be how fast it occurs. So right now the frequency is 50 hertz. What does that mean? We have one divided by, what would that be. One divided by 0.02 seconds. And so we're getting 50 waves per second. So that's going to be a high frequency. If I increase the frequency, so we're going to have more waves per second or 50 waves per second. And I get it really cranking, now we have 84 waves per second. Or 84 hertz. What happened to the wave length when I did that though? So what happened to the wavelength? Well as I increased the frequency I decreased the wavelength. So let's go back here. What happens when I decrease the frequency? So now it's only 24 waves per second. Now the wavelength gets really really longer. So what do we remember? Well v, so if we go back to our equation, v, which is speed, equals frequency, which is how many hertz it is times lambda. So what does that mean? If we increase the frequency, if we increase the frequency then the wavelength is going to go down. Now a cool thing can happen if we actually add a fixed end to that. We start to get constructive interference. And so what's happening now? Waves that are going down are meeting waves that are coming back. And so if we increase the amplitude a little bit we can actually get some really big waves. Now let's decrease the dampening. And now we've got waves that are almost standing waves. Or dancing waves at this point. If we really reduce the dampening, then this is going to get crazy out of control. And so that's waves on a string. And that's phet. So let's go back to the keynote for just a second. And so there are a few more properties that you should understand about waves. And the next thing is what happens when they move from one medium to another. So there are essentially three things that can happen. Four, but let's just talk about these three. It could be absorbed as well by the material. But first is reflection. So what happens with a reflected wave? In this case we're using a laser, which is coherent light. So we have light moving in this direction which is a wave. It hits the surface that's reflected and we get a reflected wave. And this reflect, angle of reflection is equal to the angle of incidence. So the waves are simply bouncing off of it. So when you're looking at a mirror, those would be reflective waves that are coming back to you. Now another thing that can happen when it moves from on medium to another, in this case we're going from air it looks like to a lens or the this could be filled with water. It's being refracted. What does that mean? It's being bent. And so as the light moves in this direction, it's a wave, it hits this and it's actually slowing down and that's bending or refracting the wave. Now you can also see here that some of that is being reflected. But we certainly have a lot of refraction here or bending of a wave. And then the last thing that occurs is something called diffraction. When you move waves through a small opening, the waves will actually bend. And that's called diffraction. So they're bending through this opening. Or they could be bending around the bend as well. So let's say you're listening to music and you're right over here, that sound wave is actually going to bend around so you can hear it. Now which waves are you going to hear bend more easily? Well the high frequency waves, the high pitches will actually move right through. But the low frequency will actually bend more quickly. And so that's why when you hear a car coming by and they're listening to really loud music you'll hear that boom, boom, boom, boom, boom. You hear that low frequency sound because it's diffracted more readily to get out of the car. But the high pitches or the higher frequency noises, they don't get diffracted as much. So you don't hear them. Last thing I want to show you is you can solve simple problems. And so let's say this is a real world example. Let's say we have a tsunami which is a giant wave in the ocean created by an earthquake. Let's say it has a wavelength of 210,000 meters. So that's 210 kilometers between waves. That's a huge wave length. And let's say it has a frequency of 0.00067 hertz. That would be like 1 wave coming every 25 minutes. Now calculate the speed of the wave. Well how would you do that? Well we remember our equation, v which is wave speed equals frequency times wave length. We have to look at our units so we know frequency and it's in hertz and so we're fine. We know wavelength and that's going to be in meters. And so we're fine. So to figure out that the wave's speed, we simply multiply the frequency times the wavelength to figure out the wave speed. And I did this earlier. When you take 210,000 times 0.00067 what you get is 140, if we do significant digits right. Because both of those have 2 significant digits. 140 meters per second. Now most of us don't understand what meters per second are. So we can roughly take that times 2.2. And so a tsunami that has that large of wavelength and that small of frequency is going to move at about 310 miles per hour. And so these things move really really quickly. And that's why it's important that we know and get to higher ground when we hear the tsunami warnings going. And so that's waves. And I hope that's helpful.