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• 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.

Hi. It's Mr. Andersen and today I'm going to talk about waves. Our lives are

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# 波 (Waves)

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Wayne Lin に公開 2021 年 01 月 14 日