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In the last video we talked
about the idea that if I start

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with some type of a string
there, and if I were to take

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the left end of the string-- I
could just have equally have

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done the right, but if I take
the left end of the string and

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jerk it up, then all the way
down, and then back to its

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resting position, it'll generate
this disturbance in

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the string.

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And the disturbance might
initially look like this after

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I've done that jerking
up and down once.

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And that disturbance is going to
propagate down the string.

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It's going to move down
the string like that.

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Let me color this in black.

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So this is right after I do that
first cycle-- that first

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jerking up and down.

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The string might look
something like that.

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And if we wait a little while,
the string might look

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something like this, assuming
that I only did that once.

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The string might look something
like this, where

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that pulse has actually
propagated down the string.

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That pulse has propagated
down the string.

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And in the last video, we said,
hey, this disturbance

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that's propagating down the
string, or propagating down

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this medium-- although it
doesn't necessarily have to

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have a medium- we called this
a wave. And in particular,

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this wave right here,
this is a pulse.

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This is a pulse wave because we
only have, essentially, one

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perturbation of the string.

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Now if I kept doing that-- if I
kept going up and down, and

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up and down, essentially, if I
periodically did it at regular

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intervals, then my
string would look

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something like this.

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Doing my best to
draw it neatly.

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It might look something like
this, where once again, the

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perturbations are going
towards-- the disturbances are

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going to move to-- the right.

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They're going to move to the
right with some velocity.

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And what I want to do in this
video is really focus on this

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type of wave. This type of wave
right here, which you can

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imagine, since I'm periodically
moving this left

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side up and down, up and down,
and creating these periodic

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movements in the wave, we call
this a periodic wave. This is

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a periodic wave. The motion is
repeated over and over again.

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So what I want to talk about is
some of the properties of a

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periodic wave. Now, the first
thing you might say is, hey,

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how far are you jerking
it up and down?

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How far are these movements
from rest?

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So if this is the resting
position right there, how far

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are these movements above the
resting position and below the

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resting position?

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And we call that the amplitude
of the wave. So that distance

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right there- I'll do it in
magenta-- that distance right

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there is the amplitude.

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Sometimes mariners will have
an idea of wave height.

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Wave height, they normally refer
to from the bottom--

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from the trough-- of
a wave to its peak.

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Amplitude, we're talking
about from the resting

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position to it's peak.

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So let me label peak.

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I think you know what
peak means.

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Peak is the highest point on
the wave. That's the peak.

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And that's the trough.

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If you're in a fishing boat and
you wanted to see how big

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a wave is, you'd probably care
about the wave height-- not so

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much if your boat's sitting down
here, you have to care

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about this whole distance.

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But anyway, we won't talk
too much about that.

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So that's the first interesting
idea behind a

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wave. And not all waves are
being generated by Sal

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jiggling a string on
the left-hand side.

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But I think you get the idea
that these waves can represent

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many different-- this graph can
represent many different

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types of wave forms. And this,
essentially, displacement,

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from the resting position, or
from the zero position, that

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is your amplitude.

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Now the next question you might
ask is, OK, I know how

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far you're jiggling this string
up and down, but how

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quickly are you doing it?

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So how long does it take for you
to go all the way up, all

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the way down, and back again?

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So how long for each cycle?

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Cycle is me going up,
down, back again.

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How long for each cycle?

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Or you might say how long
for each period?

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We're saying this is periodic.

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Each period is each repetition
of the wave. So this idea of

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how long for each cycle, we
call that the period.

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And this is going to
be a unit of time.

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Maybe I'm doing it every
two seconds.

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It takes me two seconds to
go up, down, back again.

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Up, down, back again.

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That's going to be
two seconds.

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A very related term is,
how many cycles

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am I doing per second?

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So in other words, you
could say, how many

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seconds for each cycle?

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We could even write that.

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So for example, a period might
look like something like 5

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seconds per cycle.

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Or maybe it's 2 seconds
per cycle.

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But what if we're asked how
many cycles per second?

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So we're asking the
opposite question.

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It's not how long, how many
seconds does it take for me to

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go up, down, and back again.

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We're saying in each second, how
many times am I going up,

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down, back again?

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So how many cycles per second?

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That's the inverse of period.

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So period, the notation
is normally a big

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capital T for period.

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This is frequency.

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It's normally denoted by an F.

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And this, you're going to
say cycles per second.

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So if you're going 5 seconds per
cycle, that means you're

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doing 1/5 of a cycle or, 1/5
of a cycle per second.

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All I did is invert
this right there.

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And that make sense.

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Because the period and the
frequency are inversions of

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each other.

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This is how many seconds
per cycle.

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How long does one up, down,
back again take?

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And this is how many up,
down, back agains

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are there in a second?

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So they are inverses
of each other.

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So we could say that frequency
is equal to 1 over the period.

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Or you could say that
period is equal

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to 1 over the frequency.

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So if I told you that I'm
vibrating the left end of this

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rope at 10 cycles per second--
and, by the way, the unit of

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cycles per second, this is a
hertz, so I could have also

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written this down as 10
hertz, which you've

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probably heard before.

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10 hertz just means 10
cycles per second.

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If my frequency is 10 cycles per
second, my period is going

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to be 1 over that.

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So 1 over 10 seconds per cycle,
which makes sense.

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If in 10 times, I can go up and
down, a whole up, down,

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back again, if I can do that
10 times in a second, it's

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going to take me 1/10 of a
second to do it each time.

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Now another question we might
ask ourselves is, how quickly

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is this wave moving, in this
case, to the right?

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Since I'm jiggling the left
end of the string.

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How quickly is it moving
to the right?

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So the velocity.

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So to do that, we need to figure
out how far did the

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wave go after one cycle?

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Or after one period?

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So after I jiggled this once,
how far did the wave go?

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What is this distance from this
resting point to this

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resting point there?

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And we call that a wavelength.

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And there's a lot of different
ways you can define a

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wavelength.

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You could view a wavelength as
how far the initial pulse went

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after completing exactly
one cycle.

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Or you could view it as the
distance from one peak to

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another peak.

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That is also going to
be the wavelength.

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Or you could view it as a
distance from one trough to

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the other trough.

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That's also the wavelength.

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Or in general, you could view
the wavelength as one exactly

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equal point on the
wave. From that

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distance to that distance.

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That is also one wavelength.

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Where you're completing, between
that point and that

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point, you're completing one
entire cycle to get exactly

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back to that same point.

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And when I say exactly back to
that same point, this point

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doesn't count.

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Because this point, although
we're in the same position,

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we're now going down.

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We want to go to
the point where

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we're in the same position.

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And notice over here,
we're going up.

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We want to be going up again.

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So distance is not
one wavelength.

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To go one wavelength,
we have to go

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back to the same position.

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And we're moving in the
same direction.

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So this is also one
wavelength.

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So if we know how far we've
travelled after one period--

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let me write it this way;
wavelength is equal to how far

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the wave has traveled
after one period.

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Or you could say after
one cycle.

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Because remember, a period is
how long does it take to

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complete one cycle.

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One to complete up, down,
and back again notion.

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So if we know how far we've
traveled, and we know how long

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it took us, it took us one
period, how can we figure out

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00:09:54,750 --> 00:09:56,350
the velocity?

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Well, the velocity is equal to
distance divided by time.

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00:10:02,175 --> 00:10:09,450


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00:10:09,450 --> 00:10:12,340
For a wave, your velocity--
and I could write it as a

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vector, but I think you
get the general idea.

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Your velocity-- what's
the distance

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you travel in a period?

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00:10:17,650 --> 00:10:23,390
Well, the distance you travel in
a period is your wavelength

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00:10:23,390 --> 00:10:27,640
after one up, down,
back again.

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00:10:27,640 --> 00:10:30,210
The wave pulse would have
traveled exactly that far.

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That would be my wavelength.

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00:10:31,910 --> 00:10:34,830
So I've traveled the distance of
a wavelength, and how long

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00:10:34,830 --> 00:10:36,850
did it take me to travel
that distance?

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00:10:36,850 --> 00:10:39,180
Well, it took me a period
to travel that distance.

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So it's wavelength divided
by period.

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00:10:42,170 --> 00:10:46,320


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00:10:46,320 --> 00:10:50,790
Now I just said that 1 over the
period is the same thing

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00:10:50,790 --> 00:10:51,410
as the frequency.

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00:10:51,410 --> 00:10:54,910
So I could rewrite this
as wavelength.

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And actually, I should
be clear here.

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00:10:57,570 --> 00:11:00,540
The notation for wavelength
tends to be the

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00:11:00,540 --> 00:11:01,810
Greek letter lambda.

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00:11:01,810 --> 00:11:06,550
So we could say velocity
is equal to

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00:11:06,550 --> 00:11:09,510
wavelength over period.

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Which is the same thing
as wavelength

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times 1 over my period.

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And we just said that 1 over the
period, this is the same

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thing is your frequency.

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So velocity is equal to

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wavelength times your frequency.

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00:11:25,600 --> 00:11:28,090
And if you know this, you can
pretty much solve all of the

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00:11:28,090 --> 00:11:31,470
basic problems that you might
encounter in waves.

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00:11:31,470 --> 00:11:34,400
So for example, if someone
tells you that I have a

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velocity of-- I don't know-- 100
meters per second to the

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00:11:42,520 --> 00:11:45,940
right, so in that direction--
velocity you have to give a

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00:11:45,940 --> 00:11:54,410
direction-- and they were to
tell you that my frequency is

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00:11:54,410 --> 00:12:00,770
equal to-- let's say my
frequency is 20 cycles per

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00:12:00,770 --> 00:12:04,370
second, which is the same
thing as 20 hertz.

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00:12:04,370 --> 00:12:08,790
So literally, if you had a
little window where you're

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only able to observe this part
of your wave, you'd only

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observe that part
of my string.

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00:12:15,160 --> 00:12:18,020
If we're talking about 20 hertz,
then in 1 second, you

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00:12:18,020 --> 00:12:19,960
would see this go up and
down twenty times.

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00:12:19,960 --> 00:12:23,020
1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17,

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00:12:23,020 --> 00:12:24,410
18, 19, 20.

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00:12:24,410 --> 00:12:26,280
In exactly one second,
you would see this go

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00:12:26,280 --> 00:12:27,510
up and down 20 times.

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That's what we mean by the
frequency being 20 hertz, or

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00:12:30,960 --> 00:12:32,590
20 cycles per second.

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00:12:32,590 --> 00:12:33,495
So, they gave you
the velocity.

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They gave you the frequency.

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What's the wavelength here?

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00:12:36,380 --> 00:12:39,380
So the wavelength, in this
situation-- you would say the

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00:12:39,380 --> 00:12:45,130
velocity-- your velocity is
equal to your wavelength times

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00:12:45,130 --> 00:12:47,780
your frequency.

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Divide both sides by 20.

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00:12:49,380 --> 00:12:52,470
And actually, let me make sure
I get the units right.

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So this is meters per second,
is equal to lambda times 20

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cycles per second.

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00:13:02,450 --> 00:13:05,610
So if you divide both sides by
20 cycles per second, you get

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00:13:05,610 --> 00:13:14,010
100 meters per second times
1/20 seconds per cycle.

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00:13:14,010 --> 00:13:16,490
And then this becomes a 5.

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00:13:16,490 --> 00:13:17,370
This becomes a 1.

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00:13:17,370 --> 00:13:21,760
So you get 5, and then the
seconds cancel out.

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00:13:21,760 --> 00:13:23,680
So you get 5 meters per cycle.

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00:13:23,680 --> 00:13:30,830
So this is equal to 5 meters per
cycle, which would be your

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00:13:30,830 --> 00:13:32,150
wavelength in this situation.

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00:13:32,150 --> 00:13:34,350
So it's 5 meters.

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00:13:34,350 --> 00:13:37,130
You could say 5 meters per
cycle, but wavelength implies

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00:13:37,130 --> 00:13:39,810
that you're talking about
the distance per cycle.

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00:13:39,810 --> 00:13:44,760
So in this situation, if this is
moving to the right at 100

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meters per second and this
frequency-- I see this moving

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00:13:47,440 --> 00:13:50,830
up and down 20 times in a
second-- then this distance,

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00:13:50,830 --> 00:13:53,700
right here, must be 5 meters.

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00:13:53,700 --> 00:13:57,050
Likewise, we can figure out
the period very easily.

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00:13:57,050 --> 00:13:59,710
The period here is just going
to be 1 over the frequency.

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00:13:59,710 --> 00:14:06,470
It's going to be 1/20
seconds per cycle.

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00:14:06,470 --> 00:14:10,190
So using these formulas-- and I
don't want you to memorize a

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00:14:10,190 --> 00:14:13,350
formula, it should be
intuitive for you.

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00:14:13,350 --> 00:14:15,470
And hopefully, this video made
it a little bit intuitive.

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But using this, you can really
answer almost any question if

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00:14:18,380 --> 00:14:22,770
you're given two of these
variables and you need to

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00:14:22,770 --> 00:14:23,990
solve for the third.

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00:14:23,990 --> 00:00:00,000
Anyway, hopefully you
found that helpful.