0:53

That you might want to check it out, see what it's all about.

The subtitle is Space, Time and the Beauty that Causes Havoc.

So it sort of puts them side by side, looks at their life and

their work together and draws some parallels and things like that.

So Arthur I Miller, Einstein, Picasso, I just have to

be thinking about that since I mentioned Picasso offhand last time.

Maybe that's why I did it subconsciously, I was thinking about that.

I'm not sure, but there you go.

Einstein, Picasso, Arthur I Miller.

As you may know, there are dozens,

hundreds of books on Einstein out there and many of them are very good.

You can explore that.

Later in the course, we'll talk about some books to continue on with in

terms of Einstein if you're interested in pursuing it more.

But now, we're on to a few more words about waves part three.

Key facts about the speed of waves, I think I mentioned this in an earlier

video clip, but just to make sure they're using speed and

velocity interchangeable for those who've had a little physics you'd know.

Technically, there's a difference between velocity,

the concept of velocity and speed.

Speed being the magnitude of velocity.

Velocity having a direction, as well as a magnitude.

So again,

we're not going to have to be too concerned about those exact definitions.

So we'll say, speed of waves, velocity of waves.

Speed of light, the velocity of light, will be meaning the same thing.

So, three key facts.

Number one,

key fact Is the speed

depends on the medium.

So, what do we mean by that?

Well, consider water waves again, maybe we have a long tank, we're going to

generate some waves in this tank with our hand or some sort of paddle device.

If we replace the water in the tank with another type of fluid,

another liquid that had different properties,

in particular maybe had different viscosity, different density.

The speed of the waves we can generate is going to be different compared to

the water.

At a certain point, if you have molasses in there,

you can't really generate waves at all or they'll die out almost immediately.

But the idea being is that the speed of waves, this patterned disturbance

propagating through a medium is going to change depending on the medium itself.

Another example would be vibrations,

which is a wave-like phenomenon in a steel bar or something like that.

The more rigid the steel bar is, the faster the waves are going to travel,

everything else being equal.

If it's a softer type of a bar or whatever,

then the waves are not going to travel as fast.

So key point, the speed of the waves depends on the medium.

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Second point is if we have a moving source,

we're going to add on to this in a second here.

What do we mean by moving source?

We're going to go back to our idea of a tank, long tank of water maybe.

And we have a paddle device or our hand,

we're going to generate waves by moving it up and down.

And one key thing to remember, I mentioned this, actually,

I think in part one of the video clip, but remind ourselves here is that

if we have this paddle device and we're generating waves and they're traveling

down our tank into our bathtub or swimming pool or whatever it happens to be.

The water molecules themselves are not moving with the waves.

The wave that's traveling is a pattern or disturbance within the medium,

which is the water in this case.

The actual water molecules are moving up and down in that peak an trough.

So say, you've got some water right here.

I start generating my waves, so the water molecules at this point as a peak comes,

there's going to move up and then thrust they going to move down and

then up and down.

So, the water molecules are moving up and down and

the wave pattern is traveling that way.

So when I'd like to talking about the speed of whatever the medium of this

compose as this moving through,

as the speed of the pattern the disturbance moving through the medium.

So then when we having a moving source here,

as I've got my paddle device moving up and down.

Instead of having it be stationary watching the waves go along and

I'm outside here measuring the velocity of the waves,

I'm going to start moving that paddle device.

So, let's think about what's going to happen here.

We said that the speed of the waves depends on the medium by moving the paddle

device, I'm not changing the properties of the medium in any way unless I move it up

and down so fast, it starts heating the water or something like that, but

we'll assume we're not doing anything like that.

So the peaks of the waves, imagine the peaks

of the waves going out here as I move the paddle device along.

That means I'm generating a new peak before this peak has traveled,

as far as it normally does.

So what happens is the peaks, as they move along here are closer together than if

the paddle device was just normally stationary like this,

generating the peaks that go by.

So in other words, generated peak.

It gets to here.

And normally,

the wave length would be that long if the paddle device is not moving.

But in this case, I have moved the paddle device a little bit more over this way

as the wave has traveled out and now I am jetting a new peak right here.

And so that distance is shorter, just because I am moving the paddle device,

the source of the waves along.

So, the peaks going in this direction sort of bunch up a little bit.

And actually, the peaks if we extend our tank the other direction as well,

the peaks are going to extend out a little bit more.

So, imagine a paddle device in the middle where and

joining waves going in both directions.

If I don't move the pedal device, everything's the same.

If I start moving the pedal device in this way,

the peaks are going to be bunched up a little bit more.

And over here, they're going to be spread out a little bit more.

So in this direction, I'm shortening the wavelength a little bit.

In this direction, I'm extending the wavelength a little bit.

So when I have a moving source

just to emphasize here,

no change in wave speed.

There's no change in the wave speed, because the medium,

properties of the medium are not changing.

What is changing is the wave length and we're dealing in just a simple

basic case here, leaving out a lot of complicating circumstances.

But essentially, here's my wave generator.

My paddle device as it moves this way, the distance between the peaks

gets a little shorter and they get spread out this way.

So in this direction, the waves, the wavelength is shorter and

it's longer out this direction.

Well, remember,

the relationship we had from part one of our few words about waves?

We said, the velocity of a wave, the waves we're considering at

least is the wavelength lambda times the frequency f.

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If the wavelength is getting shorter in order for

the velocity to remain the same, the frequency has to be higher.

Do an example.

Let's just say, this is 24.

Say, velocity was 24 meters per second and

I said, the wavelength was 4 meters,

frequency was 6 inverse seconds.

Some of you may know the units of frequencies are hertz.

So when we talk about megahertz, that's millions of hertz.

So we won't worry about the details here, but just the idea.

4 times 6, 24 hours.

So now I'm saying as a paddle device moves along here,

the wavelengths are getting shorter.

Let's say, they go from four to three.

So, that means the frequency has to increase.

So I'm going to have a situation where it's 3 times 8,

that's why it shows the numbers here.

So, I can do it easily.

So, 3 times 8 is still 24.

So the velocity stays the same,

the wavelength is compressed a little bit, gotten shorter.

So the frequency has gone up and whether you realize it or not,

you probably have encountered this in real life or at least seen it in the movies.

Think about a train whistle.

If you have a train whistle and the train is coming towards,

you have sound waves coming towards you from the train whistle.

The velocity of the train is a moving source.

So, the train is a moving source with a certain velocity towards you.

The source of the sound waves, as we've been talking about the velocity

of the sound waves toward you does not change.

They are still coming towards you at the same rate.

They won't get there any faster to you.

But because it's a moving source towards you,

the movement of the train compresses the wavelengths of the sound out in

front of it as it travels away from the front of the train.

And that means shorter wave lengths, higher frequency.

So that's why when the train whistle coming toward you, you hear it.

It's a higher pitch.

Then as it passes by you, now you're behind the moving source just on my paddle

device, I was moving the other direction though.

Paddle device was moving this way.

Shorter wavelengths here, longer wavelengths behind it.

Same idea for the train whistle whether it's moving this way or that way,

it doesn't really matter.

We're pretending its coming this way.

So here comes a train toward you,

it's compressing the sound wavelengths in front.

Which means a higher frequency, higher pitched sound, as it moves by,

what do you hear?

The pitch drops [SOUND] like that, more or less.

And that's because behind the moving source as it moves away from you,

the wavelengths spread out a little bit.

Meaning that you have a bigger wavelength.

This number becomes bigger, the frequency, therefore,

has to be smaller to keep the velocity the same, the whole thing the same.

And therefore, you have a lower pitch sound.

And some of you again may know that this is something called the Doppler effect.

Doppler effect, so that's just a little side note.

And actually, there is a sort of relativistic Doppler effect.

We're not going to get to that in this course, but it is important.

The important point here is that wave speed depends on the medium.

When you have a moving source,

it does not change the speed of the wave through the medium.

It changes other things, it changes the wavelength, the frequency,

it does not change the speed of the waves.

And this is important and you may say, well,

why are we doing all this with wave stuff?

It's important, because we mentioned Einstein had two postulates,

two principles that he enunciated in his special theory of relativity.

One of them was the principle of relativity.

The second one was essentially number two here, our number two.

He called it the principle of light constancy.

And essentially, it was a that moving source is no change in the wave speed and

light was recognized as a wave.

So I said, hey, with a moving source, there's no change in the speed of light.

13:16

What do we mean by this?

Well, again, let's go back to our water tank.

So here's our water tank here and we have our paddle device generating waves flowing

down the tank, and we're measuring the velocity of the waves there.

And as we just finished saying with our number two, if I move the source of

the waves through the water, it doesn't change the velocity of the waves.

The frequency in wave length change, but not velocity.

But now, let's think of another situation.

Here's my paddle device, here's my tank and

I'm measuring the speed of the waves as it go along.

What happens if I move the whole thing?

So in other words, the medium is moving as well as the waves.

In that case, when I have a moving medium the velocity is due at in a sense.

So before I set the whole thing in motion,

I'm measuring the speed of the waves as I go along here.

And then maybe I have it on rollers or something, on wheels, I start moving

the whole thing and then I measure the speed of the waves going by me.

And pretty intuitively and intuition is correct here,

you'll see the speed of the waves increase.

They'll be going by you at their normal speed plus the speed

that the whole thing is moving by you.

So with a moving medium,

then the wave speed changes as

an observer is measuring it.

Now in terms of the median here, another way to think about this.

We've done our water tank example, but

it's also the difference between say, journeying waves in a pond or

a lake and a flowing river or if you're able to set the lake in motion sense.

So if it's in the lake or pond, again, just generate the waves that

are flowing along here if you have that same situation in a river.

Let's say, the river is flowing this way.

So I'm generating my waves here and they're travelling along,

but then everything is in motion as well.

All the water molecules and everything are flowing this way.

And so that adds velocity to the velocity of the waves,

if I'm on the bank measuring those waves go by.

Or intuitively also, if I'm going upstream, up against the current.

So I'm watching the device here on a boat,

as it goes up the current generating waves.

The flow current of the water will retard

the velocity of the waves trying to go upstream.

That's one case where our intuition actually is correct there,

that the wave speed will change.

If the whole medium is moving, the wave speed will change.

Why is this important for our purposes?

Because in the next video clip, we're going to talk about something

called the luminiferous ether and that is the supposed medium for

light waves and Einstein actually got rid of it later on.

We'll see how that happened, but

there are two key experiments that we need to talk about.

Because one of them, known as the Michelson-Morley

experiment gave one result in terms of how the ether worked and

how light waves worked traveled in the ether and

a second experiment involving something called stellar aberration.

Stellar meaning stars and aberration,

we'll figure out what that means, gave an opposite result.

A result that contradicted the Michelson-Morley experiment.

And both of them were well-understood and so I was like, this we're just nonplus.

They couldn't figure out what we do with this.

How do we understand this and

they came up with a number of very innovative ideas, very creative ideas, but

it was still a big mess and they tried and tried and tried.

And eventually, that was one of Einstein's great triumphs by attacking

it sort of from a different perspective.

He was able to show that these things actually were not in contradiction even

though they seemed to be, but by coming from perspective where they're not in

contradiction, then you get all kinds of other interesting and weird results.

So, that's where heading with these.

These principles are going to be key in understanding these two different results,

the Michelson-Morley experiment and stellar aberration.

And so, I'll be covering those over the next few video clips.