0:03

In the next few video clips, we're going to be concentrating on waves.

And some of the key concepts behind them.

Our goal here is to understand one of Einstein's two

key postulates that enunciated in his theory of relativity, and

that would be the principle of light constancy.

The other one, of course, being the principle of relativity.

So, the principle of relativity and the principle of light constancy.

To understand the principle of light constancy, we need to know

a little bit more about light, and light especially as it acts as a wave.

And thus, we need to go over a few of the concepts of dealing with waves.

So, we'll say a few words about waves here in this video clip and

then a couple more after this one.

I've listed some of the key terms we will cover here,

so you can write those down if you would like as we go along here.

Many of them you've probably heard before, but you may not quite be sure exactly how,

1:02

exactly what is a wavelength, what is frequency and so on and so forth.

These are terms we often use in everyday language, or

semi everyday language, I suppose.

But if you really had to define it you might say,

hmm not quite sure exactly what that means.

So We're not going to go into the whole long theory of waves,

the different kinds of waves and so on and so forth.

We're just trying to hit the key concepts that we need to understand

Einstein's approach here.

So, what I've drawn here is a typical periodic wave,

a periodic wave is something that repeats its pattern.

In fact, we could say for our purposes a wave is a disturbance in a medium that

propagates along or propagates through that medium, travels through that medium.

Classic example of course, would be water waves.

1:52

And we could imagine, for this situation here, let's imagine we have a tank or

something like that, or a pond, or whatever you want to imagine, and

the dotted line here represents the normal, still water level,

the water level when nothing is happening.

And then maybe we, put our hand in there, or have some sort of device where we can

start moving it up and down, creating the ripples, creating the waves that will then

travel propagate outwards from our source of disturbance.

That would be our wave source, just our hand moving up and down,

creating these waves going out and we will draw situations such as this.

Obviously, we really need to do it in three dimension,

it will get a little more complicated and the waves might die out as we go along,

but we're imagining an idealized situation here as we often do in physics.

And so, this would be the peaks and

troughs of the water wave as it propagates along.

So, here would be the still water level, goes up and then you have a trough,

and up and down and up and down and up and down and so on and so forth.

3:58

in this case we'll do air, is the motion is back and forth.

For sound waves actually, you have areas of higher density,

where the air molecules group together more, and then area is lowered in and so

this be high density area, lower density, high density, lower density.

But it's the movement of the medium, the air molecules in that case are back and

forth this way in the direction the wave is going.

So, it's longitudinal with the wave and so, there's certain concepts like

that in terms of different types of ways transverse, longitudinal and so on and so

forth we will actually need that but you may think you know water waves and

sound waves they are different this is one of the ways they are different.

Okay so we're going to talk about essentially,

transverse waves because light waves are transverse waves so we'll [INAUDIBLE]

about a little bit later on in this video clip but in a later video clip but

let's get some of these key concepts down again a medium is involved so

in this case we're going to imagine it's water a periodic

wave is something where the pattern or disturbance repeats itself.

You know peak and trough, peak and trough, and

again we're just assuming that it doesn't die out or anything like that.

It just continues on like that.

5:19

Some other key concepts, the amplitude of the wave, the amplitude of the wave is,

maybe you might guess, is just the up and down distance measured usually from

the center still point as it were, if we're thinking about our water.

So the amplitude in this case would be this distance there,

or that distance there.

So, a wave with higher amplitude means you got higher up and

down motion of the water molecules as the pattern, the disturbance goes along.

The wave length, the term we've all heard but

what exactly does it mean in this case?

The wave length Is a distance and it is essentially the distance,

the easiest way to think of it is the distance between two peaks.

So for example, from here to here.

6:14

It's going to be the wavelength The wavelength.

And a symbol, we won't really have to use these symbols too much, but

if you've had a little physics before, you may remember a common symbol for

wavelength is the Greek letter lambda, lowercase lambda there.

So that's the wavelength.

Technically, the wavelength is the distance between

any two points that are on the same part of the pattern, so

we could also move to the wavelength from this point to that point and if it's truly

a periodic way where everything is just repeating itself exact same situation.

Then this distance here, between those two points is the same as the distance

with two peaks is the same as this between see two troughs there, the negative peaks.

And so on and so forth.

So that's the concept of a wavelength.

So when we talk about a short wavelength wave, it means it's compressed more.

You have more oscillations up and down within a certain sort of, in length,

say, one meter, or one foot, or whatever you wanted to measure with.

Okay, so a short wavelength means you have more of these up and

down oscillations in a given length,

because that means the actual distance between two peaks is going to be smaller,

then, if you can get more of the up and down oscillations in a certain distance.

A long wavelength wave is going to be something where,

you know, just the opposite.

It's going to be farther distance, longer distance, between the two peaks, or

between the two points on the wave, so a short wave length, long wave length.

What about, then, the period, the period now, we're imagining here that.

Again, some of you who may have taken physics before know there's such things as

standing waves.

If you, you can get them going in your bath tub maybe or on a string.

Waves on a string.

Where they just sort of look like they're stationary and not doing anything.

And in this case, so we're going to assume our waves are travelling waves, so

the disturbance is actually travelling along here.

You could see the waves flowing through the water as it were.

And so, the period then is as we're watching,

let's just say this is our reference point right here.

So here we are, standing right here, and

we're watching the wave travel by us like that.

And the period then, it will stop.

The period's going to be the time it takes

from one peak until the next peak gets to us.

Right? So often measured in seconds,

but any unit of time.

So the period's going to be measured in seconds or minutes or hours or years or

whatever you want but, often in seconds, okay.

So, that gives you an idea really of how fast sometimes the wave is

traveling depending on a few other things as well but that's the idea of the period.

So a period is measured in,

we'll just say it's measured in seconds, or as they said in a unit of time.

So wave length measured, we'll say wave length is measured in meters,

centimeters, millimeters, nanometers if you want.

Period measured in seconds.

Now, another concept is the frequency.

The frequency, in fact, often the period,

I said we use the Greek letter lambda for wavelength.

Often, the period we use just a capital T for since it's measured in seconds.

The frequency is, if you think about it, maybe you think, what's frequency?

How frequent is something, okay?

Well, what that really is saying here is, how frequent are the up and

down oscillations?

That's what frequency means in the context of a wave.

How frequent are those up and down oscillations?

How fast are they occurring in a sense, as this wave goes by me?

So a high frequency wave

is going to be one with a lot of oscillations in one second.

I'm standing here and I'm counting the number of oscillations per second I

see the number of up and down movements that my wave is making as it goes by.

If it's a lot of oscillations in a second, then, I say,

that's a higher frequency wave.

If it's fewer oscillations in a given time period, in this second,

or whatever it might be, that's a lower frequency wave.

Okay, and, in fact, frequency, I'll just put it over here

10:58

another common letter is the Greek letter nu for that.

We'll just use f though, just remind ourselves for frequency there.

And it turns out if you think a minute here,

there's a relationship between period and frequency.

All right, let's think about that a minute, so we said the frequency is how

many up and down motions we get, how many oscillations we get in one second.

All right.

The period is how long it takes between peaks, so

if I have a high frequency wave right,

so a high frequency wave meaning, I have a lot of up and down oscillations per second

It means the distance between peaks must be pretty short.

The period must be small.

Must be a small number if the frequency is high.

And if frequency is low, meaning I don't have as many oscillations per second,

that means the period must be longer.

There's a longer time between each peak.

And so, I'm not getting as many oscillations per second.

In fact, there is an exact inverse relationship between period and frequency.

We can write period equals one over the frequency.

12:06

So that if the frequency is a big number, we can talk about a high frequency wave or

a high frequency anything, it means that the period is going to be very small,

got a big number down here, one over a big number makes this a very small number.

On the other hand, if I say I have a low frequencies something like a low frequency

sound right coming out of our bass speakers or whatever.

This number is going to be much smaller, one divided by a small number gives

me a bigger number here in general and so the period is going to be longer then.

So high frequency, short period, low frequency, longer period.

There's also a relationship between certain kinds of waves,

like periodic waves we're talking about here, between the wavelength and

the frequency and the velocity wave.

We're not going to try to prove this or anything, we're just going to state

it as a fact, and that is, if I've got a certain velocity.

13:49

Frequency, note that if period is in seconds,

frequency has to be inverse seconds, okay?

because they're inverse, really constant this relationship here.

So, frequency has units of one over seconds or

sometimes we call, so that, we'd be write it like this in this sort of exponential

notation inverse seconds but one over seconds has this inverse of period.

And wavelength, remember, is a length, as the name implies.

So lambda is meters, okay.

So given those facts of what the units are for each of these, what the dimensions

are, dimensions of distance over time, or inverse time, or distance for

each of these, and we're told that there's a simple relationship between them.

Let's just think about this a minute and say, well velocity is meters per second,

look what happens if I take the wave length and

multiply it by the frequency, we get it in meters per second.

I have meters per second, multiplied by one over seconds, and

that gives me meters per second.

In fact, that is the relationship here, we'll write it down here,

a little more room.

The velocity, this is for our periodic wave here,

and technically even there's such a thing called harmonic wave, again for

those of you who might have had a little physics before.

If you haven't don't worry, we're not going to have to use that concept.

We just want to get the basic concepts of waves here.

Velocity is going to be lambda, the wavelength, times the frequency.

Because velocity is meters per second.

Lambda is in units of meters, frequency is in units of one over seconds so,

the there s down there per seconds,

all right just to make that clear, s being our abbreviation per seconds.

And so, this is just meters per second and

this is the relationship right here so this is the key relation.

It's the velocity of the waves we'll be talking about

is simply the wavelength times the frequency.

And so know what happens here, if lambda gets big, let's say for a given velocity.

So say, we have a given velocity wave traveling along If lambda is big,

that means frequency has to be smaller to make this work.

And so on and so forth with that, you can go the other direction too.

You can have a high frequency wave, big frequency, means short wavelength.

Okay? Short wave length, big frequency.

Small wave length, big frequency.

Or big wave length, lower frequency.

Let's use the term for that, so

low frequency, big wave length, short wave length, high frequency.

16:51

Okay, and we'll mention those a little bit more, maybe when we get to the light year.

But those are the key concepts of our waves now.

A few words about waves just, what wavelength is?

The whole concept of a wave as pattern or disturbance propagating through a medium

and again water is a classic example that we can use for that and then just,

some of these simple relationships with ways between velocity,

wavelength, frequency and of course we got period in here as well.

Lambda times frequency is the same thing as, so

we could say also v equals Lambda

divided by period, another way to write this,

because its frequency here, period is one over the frequency,

frequency is also one over the period the, other way around.