In the last video we talked about the idea that if I start
with some type of a string there, and if I were to take
the left end of the string-- I could just have equally have
done the right, but if I take the left end of the string and
jerk it up, then all the way down, and then back to its
resting position, it'll generate this disturbance in
the string.
And the disturbance might initially look like this after
I've done that jerking up and down once.
And that disturbance is going to propagate down the string.
It's going to move down the string like that.
Let me color this in black.
So this is right after I do that first cycle-- that first
jerking up and down.
The string might look something like that.
And if we wait a little while, the string might look
something like this, assuming that I only did that once.
The string might look something like this, where
that pulse has actually propagated down the string.
That pulse has propagated down the string.
And in the last video, we said, hey, this disturbance
that's propagating down the string, or propagating down
this medium-- although it doesn't necessarily have to
have a medium- we called this a wave. And in particular,
this wave right here, this is a pulse.
This is a pulse wave because we only have, essentially, one
perturbation of the string.
Now if I kept doing that-- if I kept going up and down, and
up and down, essentially, if I periodically did it at regular
intervals, then my string would look
something like this.
Doing my best to draw it neatly.
It might look something like this, where once again, the
perturbations are going towards-- the disturbances are
going to move to-- the right.
They're going to move to the right with some velocity.
And what I want to do in this video is really focus on this
type of wave. This type of wave right here, which you can
imagine, since I'm periodically moving this left
side up and down, up and down, and creating these periodic
movements in the wave, we call this a periodic wave. This is
a periodic wave. The motion is repeated over and over again.
So what I want to talk about is some of the properties of a
periodic wave. Now, the first thing you might say is, hey,
how far are you jerking it up and down?
How far are these movements from rest?
So if this is the resting position right there, how far
are these movements above the resting position and below the
resting position?
And we call that the amplitude of the wave. So that distance
right there- I'll do it in magenta-- that distance right
there is the amplitude.
Sometimes mariners will have an idea of wave height.
Wave height, they normally refer to from the bottom--
from the trough-- of a wave to its peak.
Amplitude, we're talking about from the resting
position to it's peak.
So let me label peak.
I think you know what peak means.
Peak is the highest point on the wave. That's the peak.
And that's the trough.
If you're in a fishing boat and you wanted to see how big
a wave is, you'd probably care about the wave height-- not so
much if your boat's sitting down here, you have to care
about this whole distance.
But anyway, we won't talk too much about that.
So that's the first interesting idea behind a
wave. And not all waves are being generated by Sal
jiggling a string on the left-hand side.
But I think you get the idea that these waves can represent
many different-- this graph can represent many different
types of wave forms. And this, essentially, displacement,
from the resting position, or from the zero position, that
is your amplitude.
Now the next question you might ask is, OK, I know how
far you're jiggling this string up and down, but how
quickly are you doing it?
So how long does it take for you to go all the way up, all
the way down, and back again?
So how long for each cycle?
Cycle is me going up, down, back again.
How long for each cycle?
Or you might say how long for each period?
We're saying this is periodic.
Each period is each repetition of the wave. So this idea of
how long for each cycle, we call that the period.
And this is going to be a unit of time.
Maybe I'm doing it every two seconds.
It takes me two seconds to go up, down, back again.
Up, down, back again.
That's going to be two seconds.
A very related term is, how many cycles
am I doing per second?
So in other words, you could say, how many
seconds for each cycle?
We could even write that.
So for example, a period might look like something like 5
seconds per cycle.
Or maybe it's 2 seconds per cycle.
But what if we're asked how many cycles per second?
So we're asking the opposite question.
It's not how long, how many seconds does it take for me to
go up, down, and back again.
We're saying in each second, how many times am I going up,
down, back again?
So how many cycles per second?
That's the inverse of period.
So period, the notation is normally a big
capital T for period.
This is frequency.
It's normally denoted by an F.
And this, you're going to say cycles per second.
So if you're going 5 seconds per cycle, that means you're
doing 1/5 of a cycle or, 1/5 of a cycle per second.
All I did is invert this right there.
And that make sense.
Because the period and the frequency are inversions of
each other.
This is how many seconds per cycle.
How long does one up, down, back again take?
And this is how many up, down, back agains
are there in a second?
So they are inverses of each other.
So we could say that frequency is equal to 1 over the period.
Or you could say that period is equal
to 1 over the frequency.
So if I told you that I'm vibrating the left end of this
rope at 10 cycles per second-- and, by the way, the unit of
cycles per second, this is a hertz, so I could have also
written this down as 10 hertz, which you've
probably heard before.
10 hertz just means 10 cycles per second.
If my frequency is 10 cycles per second, my period is going
to be 1 over that.
So 1 over 10 seconds per cycle, which makes sense.
If in 10 times, I can go up and down, a whole up, down,
back again, if I can do that 10 times in a second, it's
going to take me 1/10 of a second to do it each time.
Now another question we might ask ourselves is, how quickly
is this wave moving, in this case, to the right?
Since I'm jiggling the left end of the string.
How quickly is it moving to the right?
So the velocity.
So to do that, we need to figure out how far did the
wave go after one cycle?
Or after one period?
So after I jiggled this once, how far did the wave go?
What is this distance from this resting point to this
resting point there?
And we call that a wavelength.
And there's a lot of different ways you can define a
wavelength.
You could view a wavelength as how far the initial pulse went
after completing exactly one cycle.
Or you could view it as the distance from one peak to
another peak.
That is also going to be the wavelength.
Or you could view it as a distance from one trough to
the other trough.
That's also the wavelength.
Or in general, you could view the wavelength as one exactly
equal point on the wave. From that
distance to that distance.
That is also one wavelength.
Where you're completing, between that point and that
point, you're completing one entire cycle to get exactly
back to that same point.
And when I say exactly back to that same point, this point
doesn't count.
Because this point, although we're in the same position,
we're now going down.
We want to go to the point where
we're in the same position.
And notice over here, we're going up.
We want to be going up again.
So distance is not one wavelength.
To go one wavelength, we have to go
back to the same position.
And we're moving in the same direction.
So this is also one wavelength.
So if we know how far we've travelled after one period--
let me write it this way; wavelength is equal to how far
the wave has traveled after one period.
Or you could say after one cycle.
Because remember, a period is how long does it take to
complete one cycle.
One to complete up, down, and back again notion.
So if we know how far we've traveled, and we know how long
it took us, it took us one period, how can we figure out
the velocity?
Well, the velocity is equal to distance divided by time.
For a wave, your velocity-- and I could write it as a
vector, but I think you get the general idea.
Your velocity-- what's the distance
you travel in a period?
Well, the distance you travel in a period is your wavelength
after one up, down, back again.
The wave pulse would have traveled exactly that far.
That would be my wavelength.
So I've traveled the distance of a wavelength, and how long
did it take me to travel that distance?
Well, it took me a period to travel that distance.
So it's wavelength divided by period.
Now I just said that 1 over the period is the same thing
as the frequency.
So I could rewrite this as wavelength.
And actually, I should be clear here.
The notation for wavelength tends to be the
Greek letter lambda.
So we could say velocity is equal to
wavelength over period.
Which is the same thing as wavelength
times 1 over my period.
And we just said that 1 over the period, this is the same
thing is your frequency.
So velocity is equal to
wavelength times your frequency.
And if you know this, you can pretty much solve all of the
basic problems that you might encounter in waves.
So for example, if someone tells you that I have a
velocity of-- I don't know-- 100 meters per second to the
right, so in that direction-- velocity you have to give a
direction-- and they were to tell you that my frequency is
equal to-- let's say my frequency is 20 cycles per
second, which is the same thing as 20 hertz.
So literally, if you had a little window where you're
only able to observe this part of your wave, you'd only
observe that part of my string.
If we're talking about 20 hertz, then in 1 second, you
would see this go up and down twenty times.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20.
In exactly one second, you would see this go
up and down 20 times.
That's what we mean by the frequency being 20 hertz, or
20 cycles per second.
So, they gave you the velocity.
They gave you the frequency.
What's the wavelength here?
So the wavelength, in this situation-- you would say the
velocity-- your velocity is equal to your wavelength times
your frequency.
Divide both sides by 20.
And actually, let me make sure I get the units right.
So this is meters per second, is equal to lambda times 20
cycles per second.
So if you divide both sides by 20 cycles per second, you get
100 meters per second times 1/20 seconds per cycle.
And then this becomes a 5.
This becomes a 1.
So you get 5, and then the seconds cancel out.
So you get 5 meters per cycle.
So this is equal to 5 meters per cycle, which would be your
wavelength in this situation.
So it's 5 meters.
You could say 5 meters per cycle, but wavelength implies
that you're talking about the distance per cycle.
So in this situation, if this is moving to the right at 100
meters per second and this frequency-- I see this moving
up and down 20 times in a second-- then this distance,
right here, must be 5 meters.
Likewise, we can figure out the period very easily.
The period here is just going to be 1 over the frequency.
It's going to be 1/20 seconds per cycle.
So using these formulas-- and I don't want you to memorize a
formula, it should be intuitive for you.
And hopefully, this video made it a little bit intuitive.
But using this, you can really answer almost any question if
you're given two of these variables and you need to
solve for the third.
Anyway, hopefully you found that helpful.