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What we're going to do in
this video is think

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about two wave sources.

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But one of them is going to be
stationary and the other one

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is going to be moving.

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And just to have a concrete
number, it's moving at 5

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meters per second
to the right.

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And what we're going to think
about is where are the crests

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of the wave that it's
been releasing for

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the last 3 or 4 seconds?

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So let's say that in both cases,
they are releasing a

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wave. So the velocity of the
wave is going to be 10 meters

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per second.

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You could visualize this, maybe,
as a sound wave, but

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sound and air move much, much,
much, much faster than 10

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meters per second.

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But this'll make the
math work out easy.

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Especially relative to this
guy, who is moving to the

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right at 5 meters per second.

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And that's the whole point, to
give you the intuition and

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make the math really
simple here.

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And both of these guys are going
to be, the wave that

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they're emitting is at
10 meters per second.

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And the period of the wave
is going to be at

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1 second per cycle.

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And if the period is 1 second
per cycle, you take the

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inverse of that-- the frequency
of the source, I

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guess you could call it, of the
wave, as being emitted is

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going to be the inverse
of this.

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The inverse of 1 is just 1.

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But 1 cycle per second.

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If it takes a second for a
cycle, it's also in 1 second,

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you're also going to see 1
cycle, so 1 cycle per second.

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So let's think about what's
happening here.

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So let's think about where--
let's say it emitted a crest

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of it's a wave exactly
1 second ago.

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Where is that crest
going to be now?

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Let's think about the stationary
character.

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Well, this guy emitted
a crest 1 second ago.

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It's moving outward.

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So this is outward.

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It's movie outward radially.

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We need to give a direction if
I'm giving a vector quantity.

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So it's moving outward at
10 meters per second.

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So if it emitted it 1 second
ago, it's going to be 10

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meters radially outward
from the source.

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So maybe that is right
over there.

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Well, let me draw it a little
bit neater like that.

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So that's where that
crest will be.

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Now what about this guy?

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Where's the crest that this
guy emitted 1 second ago?

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You might want to just draw a
radius 10 meters around this

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guy as well.

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But he wasn't here
1 second ago.

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He was 5 meters to the left.

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Remember, he's moving 5 meters
per second to the right.

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1 second ago, he was 5
meters to the left.

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So maybe that places him
right over there.

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So the crest that he emitted 1
second ago isn't going to be

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10 meters from this guy.

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It's going to be 10
meters radially

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outward from that guy.

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So this is where he is now.

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That's where he was 1 second
ago, where he emitted this

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crest that has now traveled
10 meters away.

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This a little inexact,
so I could draw it a

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little bit like that.

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This is 5 meters.

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That's 10 meters away.

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But you get the general idea.

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Now let's keep going.

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Let's think about the crest
that both of these guys

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emitted 2 seconds ago.

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This guy's been stationary
the whole time.

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If he emitted it 2 seconds
ago, it's traveling at 10

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meters per second.

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It's going to be 20 meters
radially outward from the

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center, from the source.

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So it will look something
like that.

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I'm just drawing the
crest of the waves.

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If you think of water, a pebble
being dropped into the

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pond, these are just the high
points on the wave that

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spreads radially outward from
where the pebble was dropped.

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Now this guy, once again, you
can't just draw a circle

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around this because he wasn't
here 2 seconds ago.

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He was right here.

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He was right here
2 seconds ago.

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1 second ago, he was 5
meters to the left.

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A second before that, he was
5 meters more to the left.

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So that wave that he emitted
then is going to be 20 meters

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radially outward from
this point.

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So the center isn't going
to be that or that.

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It's going to be that point
where he was 2 seconds ago.

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So what about the crest that
either of these of sources

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emitted 3 seconds ago?

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Well, it would be 30 meters
radially outward, so another

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10 meters from the last one.

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So it will be out here.

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It will be out there
just like that.

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This guy has been stationary
the whole time.

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But what about this guy?

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He wasn't here 3 seconds ago.

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He was here.

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Right?

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1 second ago, here.

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2 seconds ago, there.

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3 seconds ago, there.

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So we're going to be
30 meters radially

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outward from this point.

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So once again, I can just copy
and paste this right here.

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And it should be centered
around that point.

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Now, let's think a little bit
about what the perceived

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frequency of this wave would be
for a couple of observers.

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So we could put an observer
here, really

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anywhere around this guy.

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We could put an observer
right here.

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And then we could put another
observer right here.

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Now, what's this guy
going to perceive?

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Well, every second he's getting
a pulse-- well,

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there's a couple of things
to think about.

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First of all, what is the
wavelength of, at least this

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wave right here.

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Well, every second, he's
emitting a pulse.

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So, a second ago, the pulses
out there would

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have traveled 10 meters.

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And then he emits
another pulse.

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So the pulses are going to be 1
second apart, but since they

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traveled 10 meters in that 1
second, they are also going to

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be 10 meters apart.

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So the wavelength,
in this case, is

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going to be 10 meters.

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The distance between these
crests are 10 meters.

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Now what about this situation
right here?

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It depends on what side, whether
the source is coming

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towards you or whether it's
going away from you.

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That's the situation
with this guy.

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When it's moving towards you,
it's emitting a pulse-- so

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let's say it emitted a pulse
right here-- and then, it

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moves 5 meters to
the right before

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emitting the next pulse.

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So instead of them being 10
meters apart, in this case,

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this guy has closed
the distance by

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5 meters over here.

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So these pulses are only going
to be 5 meters apart.

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So over here, the wavelength
is only 5 meters.

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You can see it visually.

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This distance right here is
half of this distance.

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These are 5 meters apart.

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And on the left-hand side, if
you're on the side of the

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source that the source is moving
away from, it would be

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10 meters, but every second the
source is also moving 5

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more meters away from you.

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So this perceived wavelength
right here is

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going to be 15 meters.

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And we can see it visually.

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That's the whole reason why
I drew it this way.

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Now what's going to
be the perceived

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frequencies for this?

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Well, this guy has one crest
passing him right now.

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It's going to take exactly 1
second for the next crest to

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get to him because
it's traveling at

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10 meters per second.

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So he is going to perceive 1
crest, or 1 cycle per second,

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or a frequency of 1 hertz,
which makes sense.

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This is stationary.

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They're both stationary relative
to each other.

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And we're also talking about
classical physics.

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We're not getting to relativity
and all that.

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But the observed frequency is
the exact frequency that was

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emitted by this guy
right there.

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Now what about this situation?

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Each of these crests are 5
meters apart for this guy.

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If you imagined that this was
some type of a train coming

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towards this guy, each of these
crests are only 5 meters

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apart, but they're traveling
at 10 meters per second.

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So how many crests are you
going to see in a second?

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Well, you're going to
see two of them.

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This one's going to take 1/2 a
second to return you, and then

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in the next 1/2 a second, this
one's going to get to you.

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Or you could say this one takes
1/2 second to reach you,

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and this is going to take
1 second to reach you.

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So you're going to see two.

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So there's two ways
to think of it.

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You could say your period in
this situation is 1/2 of a

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second per cycle.

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Or you could invert it and you
could say that the frequency--

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I mean we could put the observed
frequency-- is going

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to be 2 cycles per second.

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And already notice, this guy's
experiencing a higher

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frequency then this guy over
here, because these wave

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fronts or these crests are
just passing by him more

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frequently.

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Because this guy is moving in
the same direction as this

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guy, they are closer together.

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Now this guy's going to
experience the opposite thing.

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Let's say that this crest
is just passing him by.

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How long will it take for
the next crest to

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cover that 15 meters?

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Well, they're going at
10 meters per second.

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It's going to be 1.5 seconds per
crest. That's going to be

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the observed period
for this guy.

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You have to take the inverse of
that-- that's 1.5 is 3/2,

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that's 2/3 of a --or you could
say crest or 2/3 of a cycle

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per second.

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So when the source is moving
away from this observer, the

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frequency, or the perceived
frequency, is the lower than

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00:09:24,270 --> 00:09:28,520
the frequency of the actual
emitted wave. When the source

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is moving towards the
observer, the

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frequency is higher.

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This might seem some like some
type of bizarre thing but

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you've experienced it before.

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00:09:35,770 --> 00:09:38,230
It's called the Doppler
effect, which you've

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probably heard of.

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And that's exactly what you
experience when you sit at,

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maybe, a train crossing.

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Be careful not to
sit too close.

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And as a train is approaching
you, you noticed-- say it has

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its horn going on.

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It'd be very high-pitched.

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And then right when it passes
you, and it starts moving away

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from you, it has a
much lower pitch.

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And that perceived pitch, that's
your brain and your

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00:10:03,680 --> 00:10:05,660
ears' way of sensing
frequency.

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So when the train is coming
toward you, it's a high pitch,

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high frequency.

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When it's going away from you,
low pitch, low frequency.

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And hopefully, drawing it out
this way gives you a visual

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understanding of why that is;
why these points on the cycle,

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or these crests, are closer
together when it's moving in

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your direction then when they're
farther apart-- when

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it's moving away from you.

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In the next video, we'll do
these with more abstract

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numbers so we can actually
figure out generalized

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formulas for relating the
observed frequency with the

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emitted frequency.

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