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- [Voiceover] You are straight up partying

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at the rock show here.

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But you're a little close to the speakers,

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it's getting a little loud.

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You need a break here, your
ears are starting to hurt.

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So you back up and my question is,

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it sounds like a stupid question,
but I don't think it is,

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why does the sound seem softer,
when you're further away

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from a speaker compared to
when you're close to a speaker.

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And be careful, there's
actually two distinct reasons

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for this, so let's make
sure we're clear about this.

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It's not so dumb of a question.

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Here's a speaker.

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Now, this speaker is going to emanate

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sound waves out away from it.

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And I'm gonna represent
that sound wave like this.

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Let's draw a circle around
it, here's the sound wave.

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To make things simple,
let's just say it sends out

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one burst of a sound, it's not sending out

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repeated sound waves, let's just say

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there's one burst of the sound.

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This is what the sound wave looks like

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at a given moment, the wave front.

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And if you wait a little
while, that wave front's gonna

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emanate outward.

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So, here's the sound wave after
some later amount of time.

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Here's the sound wave, if
you wait a little longer.

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And if you wait a little longer,

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the sound wave might look like this.

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These are all the same sound wave,

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these are just at
different moments in time.

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So, the question was, to remind
you, if someone's over here,

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close to the speaker, why
do they notice the sound

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that's louder from a person over here

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farther from the speaker.

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And one reason has to do
with what's called intensity.

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The intensity is defined
to be the power per area.

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So, this sound this
speaker is sending out,

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a certain amount of power,

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and that's divided by a
certain amount of area.

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So, right here that power is
divided by this much area,

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that power is spread
out over this much area.

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But the sound wave's
gonna emanate outwards.

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And that means this power
is gonna get spread out

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over a larger and larger area.

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So, now that same amount
of power is spread out

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over a larger area.

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And this keeps going, the further away

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the sound wave gets, the larger the area.

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So if you're way back here,
now that same amount of power

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is spread over a much larger area.

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And this is one reason why
the sound's gonna get weaker,

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'cause if you divide by a larger area,

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if you take that same amount of power,

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you divide by a larger area,

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that intensity is gonna get smaller.

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Notice, your ear doesn't
sample the whole wave,

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your ear just samples the part

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that actually gets into your ear.

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If your ear could hear the whole wave,

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if you could sample that
whole amount of power,

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yeah, maybe that would sound just as loud.

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But you only get a piece of it.

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So, you're just measuring how
concentrated that sound is,

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not the total amount of sound
that is on the whole surface.

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So, how much less is it gonna be?

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If someone's standing twice as far away,

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if this person is at a
distance D from the speaker,

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and some other person is
at a distance two times D

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from the speaker, twice as far.

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For this person up here,
if this person here

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is an intensity I, what intensity will

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this person over here experience?

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Will they hear half I, fourth
of an I, an eighth of an I?

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To figure it out, you've gotta remember

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that these sound waves
are emanating in 3D space,

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these are 3D sound waves.

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So, these are really spheres,

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these are spheres of surface area

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that the sound wave's emanating out along,

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and so, gotta remember what
the area of a sphere is.

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I remember the area of the
sphere; it's four pi r squared.

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This means the intensity is gonna equal

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the power divided by four pi r squared.

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This means, if this person
is twice as far away,

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he's twice the radius
away, that means the area

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that the power's been spread out over

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is now not just twice as
much area, this is r squared.

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Since this is r squared,
if you double the radius,

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you're getting four times the area.

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This is, actually, the
power over here spread out

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over four times the area.

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Since the same amount
of power's spread out

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over four times the area, this intensity

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is gonna be 1/4 as much.

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If the same power's spread
out over four times the area,

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and if you were three times
further away, over here,

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what do you think the
intensity would be out here?

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The intensity, since you've
got three times the radius,

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you square that three, you're
gonna get a factor of nine.

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This is gonna be 1/9,
the intensity out here.

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This is an important rule:
the intensity is gonna be

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proportional to one over r squared.

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Lots of things in physics are proportional

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to one over r squared, and
intensity is gonna be one of them

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of the sound wave, 'cause
it's spread out over a sphere.

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And that sphere gets
bigger, like r squared.

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This is actually a little
bit of a simplification,

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but this is one reason why
the sound waves get softer

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the further out you go,
because that sound, that power

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is now spread out over a larger area.

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It's an oversimplification,
because, let me show you why.

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It's an oversimplification, because,

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if you had an actual speaker,
an actual speaker is probably

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not gonna be sending out
perfectly spherical sound waves.

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Oops.

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I mean, you wouldn't really want it.

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If you're gonna manufacture a speaker,

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you probably don't want the
sound wave traveling back here

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just as much as it
travels in front of you.

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You want the sound to go
in front of the speaker.

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But it doesn't even matter.

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Even though it might
not be a perfect sphere,

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if it's gonna be part of a
sphere, it's still gonna emanate

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along part of the sphere.

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This is still gonna be in 3D.

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These are gonna be 3D sound waves.

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So, even if the area isn't spread out over

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exactly four pi r squared,

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maybe this is only a third of a sphere,

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maybe only an eighth of a sphere,
a sixteenth of the sphere,

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it doesn't actually matter.

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What matters is you're still
gonna have r squared here.

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And because you're gonna have
r squared, that intensity

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of the sound wave is still going to be

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power divided by something with r squared.

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So, the intensity is gonna be proportional

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to one over r squared.

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It's gonna die out like
one over r squared.

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Let's come back here, oops,
let's come back to this one.

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That's one reason why.

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One reason why the sound gets weaker,

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that power is distributed
over a larger area.

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There's another reason why.

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The other reason why is that...

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I lied again a little bit.

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This power gets diluted
over a larger area,

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but this power, some of
that energy doesn't even

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make it over to the second person.

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Some of that power gets
lost, some of that energy

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gets lost into the air here.

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I don't really like that term,
it doesn't really get lost,

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we know where it is.

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But energy is lost, and by "lost" we mean

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it gets turned into E thermal.

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Thermal energy of the
air molecules in here.

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It's not really lost, it's more
like it's just unavailable.

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It's just stuck in the
random thermal vibrations

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of the air molecules.

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I'm not talking about the
actual coordinated oscillations

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back and forth of the air molecules

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as sound passes through them.

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I'm talking about just random vibrations

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in random directions of the air molecules.

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This takes energy away.

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So, this is one more
reason why this person

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farther away will hear a softer sound.

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Not only does that energy get
spread out over a larger area,

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some of this energy gets lost.

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This has a specific name,
this is called attenuation.

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Attenuation is referring to the fact

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that some energy gets
lost to the medium itself.

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So, whenever energy
gets lost to the medium,

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through which a wave is
traveling, we call it attenuation.

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These are the two independent reasons

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why the sounds will sound softer.

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One, that power's spread
out over a larger area.

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And two, some of the power
doesn't even actually make it

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to where you're at, because it gets lost

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due to attenuation in the medium itself.