Let's say I've got a rope.
That's my rope.
And what I'm going to do is, I'm going to take the left end
of the rope, and I'm going to jerk it up,
and then back down.
And we're going to talk about what happens or what possibly
gets formed.
So if I take it up over here, it's going to, obviously, take
the string to the right of it up with it.
And the string is going to look something like this.
It's going to look something like that.
Now I'm going to immediately jerk it back down.
And as it passes, let's see what the rope will look like
when the left-hand point is at its original position again.
So the left-hand point-- I've pulled it back down.
But in the last time period, this part of the rope had some
type of an upward velocity.
You could imagine that way.
And even after that point, even though this left-hand
point starts getting pulled down, this point right here
still has some upward momentum.
So it's still going to keep moving up, maybe at a slower
pace because it's starting to be tugged down by
the rope on its left.
So it's going to look something like that.
And it's going to bring the rope to its right with it.
So the rope will look something like this.
The rope might look something like that.
And then I'm going to take this guy-- this was just an
intermediate position on the way to being pulled all the
way down here.
So what's the rope going to look like now?
Well.
This guy, he had some momentum that got him there.
But then all of that velocity will essentially go to zero
because he's being tugged by the rope to the left.
And now, he's going to switch directions.
And he will have gotten here, at that point.
The point on the line that was here-- on the purple period of
time-- it had some upward momentum.
So it's just going to keep going, on maybe a slower pace.
It'll be there and it will bring the rest of the rope to
the right of it with it.
So now my rope is going to look something like this.
And then finally, where I'm going to jerk the rope back to
its original position-- so this left-hand point is going
to be there.
This guy, in the previous time period,
was moving down rapidly.
So he might get there ready to switch directions again.
This guy will start moving down.
This guy, right here, he had some upward momentum.
So he's going to be up in this position now.
And he's going to be ready to switch directions.
So finally, when I've done this whole cycle, when I've
moved up, down and back there again, my rope might look
exactly like this.
And I could let go of the rope.
I could just leave this little left point right there.
And this the lump is going to propagate along the rope.
Because in the next moment of time, what's it
going to look like?
This guy is going to be pulled up by this left-hand point.
So he'll go back to his resting position.
This guy's being pulled down right here by the part of the
rope to the left of him, so he's going to be pulled down.
This guy's being pulled down.
But this guy had some upward momentum in the time period
before, so he will have moved up.
And so, the very next time period, my rope is going to
look something like this.
And this disturbance in the rope, if I do nothing else,
and if I don't lose energy to heat and friction and all
that, it'll just continue moving down the rope.
If I look at the rope at some future period in time, maybe
not that far down, the rope will look something like this.
And if I were to keep watching it, I'll see this disturbance.
I keep using the word disturbance, because there's
really no better word to use for it.
I'll see this disturbance or perturbation, or whatever you
want to call it, moving along the rope.
When we think about what a wave is, we essentially-- I
kind of jumped the gun-- I keep calling this is a
disturbance, because I didn't want to use the word, wave. I
want to say, well what really is a wave?
And a wave really is just this disturbance that's propagating
down the rope.
So this is a good time to actually define a wave. A
wave. Because once I define it, I can start calling this a
wave, as opposed to a disturbance
propagating down the rope.
So a wave is a disturbance propagating through space.
And you might see other definitions of a wave. One of
the most typical ones is energy or a disturbance
propagating energy through a medium.
And when they say medium, it's what is
the wave going through?
So in this example, the rope would be our medium.
But the reason why I don't want to use that definition of
a wave is because in future videos, we'll learn about
electromagnetic waves and those don't propagate through
any medium.
They propagate through a vacuum.
So to keep things as general as possible, we'll just call
it a disturbance that propagates through space.
And it usually transfers energy.
What do I mean by transferring energy?
On this left hand part of the rope, I gave a
little energy the rope.
I moved it up, down, and then back again.
And then after I did that, that up, down, back again is
happening successively to every point to the
right on the rope.
So if I waited long enough, at this point on the rope right
here, it's going to move up, down, and then back again.
Exactly what I did over here is going to happen to this
point on the rope.
And then later on, it's going to happen to some other future
point on the rope.
So that energy that I originally put on the
left-hand side of the rope is being
transferred down the rope.
If I had some type of object here sitting on the rope,
maybe when the wave-- when the disturbance- passes by it,
this thing could get flipped into the air; it might get
pushed into the air, and go into a
higher potential energy.
So this disturbance is transferring
energy in this case.
Now, what I've drawn here isn't the only type of wave
you can have. I mean my definition is fairly general.
But the definition is more general than just what I've
drawn here.
For example, you could have a sound wave. If you just look
at all of the molecules of the air, they have some density
that looks something like that.
And now let's say I had some type of a membrane-- maybe
it's a speaker-- that jolts this
left-hand side of the air.
So it just pushes-- so let me see if I can draw this.
Let's say I had some type of surface here that just really
quickly jolts-- that just moves it in that direction,
and then just comes back.
So similar to what I did here, I go up and down.
But instead of doing that, it just pushes the air and then
pushes back.
So what's going to happen?
Right after it pushes it, the air molecules that it pushes
up against are going to jam together.
They're going to get compressed.
Right here, all these air molecules that were right on
the surface, they're going to get pushed next to all these
air molecules that are right there.
And then when it pushes back, or when the membrane goes
back, you're going to have fewer air molecules here,
because you're going to have a low density here.
And then these guys, that are all scrunched up together,
they're going to want to get away from each other.
They might even run into each other.
And so these guys are going to run into those guys, who are
going to run into the next guys.
And so on and so forth.
And after these guys bump into those guys, those guys are
going to go back to where they were.
So essentially, you're going to have this disturbance
that's going to be a set of molecules compressing, or
bumping into, its neighboring molecules.
So if you look at this at some future period in time, all of
a sudden, this area might look normal.
Let me clear it and draw it just the way it I started.
So this area might look normal.
But that compression of the particles might have reached
right over here.
And not only that, we saw that right after the compression,
you usually have this area of low pressure.
So if I were to really draw this wave, and actually, if
this membrane were to keep doing it over, and over, and
over again-- so it kept going forward and back, forward and
back, or right and left, right and left-- what you would have
is a series of compressions.
The air would just have a series of compressions.
So that's one compression.
You'd have another compression right there.
Another compression right there.
And then, in between the compressions
the air is less dense.
The air is less dense like this.
And what we've essentially just generated is a sound wave
travelling through air.
So this right here is a sound wave. And this type of wave,
where the direction of the disturbance is the same, or
along the same axis as the direction in which the wave is
travelling-- the wave is travelling in that direction--
this is call a longitudinal wave. So sound waves sound
through air, they're longitudinal waves.
Sometimes called a compression wave. Same thing.
Compression wave. Because it's caused by compression.
Our example of the string, this is called a transverse
wave. Because the disturbance, the movement of the medium, is
going in a direction transverse to-- or at an axis
that's transverse to-- the direction of our movement.
We're moving in that direction, to the right.
Actually, our wave is moving to the right, but the actual
medium is moving up and down.
Our medium is moving up and down.
That's why this is called transverse.
While here the medium is moving left and right while
the wave moves to the right.
So it's along the same axis.
So we're dealing with the compressional or longitudinal.
Now in this first example, I just did one cycle.
I just jerked up, down, and back again.
And I created this one disturbance.
And we can call this, when you just do it once, you can view
this as a wave pulse.
If I kept doing that-- if I just went up, down, back
again, up, down, back again, and I kept doing it
periodically, over and over again, then I would generate a
periodic wave. And my string would look
something like this.
Well actually, it would look something that right there,
where that's the disturbance generated from our first time
that we moved this left-hand part of our string.
So this right here is a periodic wave.
In the next video, we're going to talk about a lot of the
properties of a periodic wave. How the wavelength, and its
frequency, and its period relate to its velocity, and
all of that.
But I'll leave that alone in this video.
But I just wanted you to appreciate what I think is a
concept that we use in everyday life.
So it's a wave, it's a sound wave, and all that.
But it's a fairly abstract notion where we talk about a
wave, we're really just pointing to a disturbance
that's moving, usually along a medium, at least when we
visualize it, but not always.
But we're just pointing to this disturbance.
And this disturbance could take many forms. It could be a
transverse disturbance if we're dealing with a string.
It could be a disturbance in terms of the density of air
molecules in terms of a sound wave. And there is a relation.
So if you wanted to just plot the density here by position--
if I were to mathematically represent this compression
wave right here-- let's say that this line represents just
resting before the sound wave hits, that's
just your normal density.
If we were to plot the density it might look
something like this.
Over here, we have very high density.
Over here, we have very low density.
Over here, we have very high density.
And if you were to plot it, it would look a lot like that
transverse wave that I did with the rope at the beginning
of this video.
And that's why they're even grouped together.
Because mathematically, even though a compression wave
looks very different, or you might visualize or
conceptualize it very different than a transverse
wave, mathematically, they're essentially the same thing.
You have this quantity.
In this case, it's the density of the air varying over time.
In this case, it's the height, or the position, or how much
your displacement from your resting position-- that's the
quantity varying through time, that disruption is travelling
over the course of the medium.
That's why we call both of these things waves.
Anyway, I'll let you go here.
And in the next video, we'll talk a little bit more of the
properties of periodic waves.