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- [Voiceover] If two waves overlap

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in the same medium, we say that

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there's wave interference.

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So this box here could represent a speaker

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and this could be the
sound wave it generates

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or it could represent a
laser and this would be

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the light wave it generates or it could be

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some sort of ripple
tank generator and this

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is the water wave it generates.

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Regardless, if you had a second source

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of a wave and these were to overlap,

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you'd cause wave interference and what

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that would look like would
be something like this.

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So let's say these are speakers.

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I like thinking about
it in terms of speakers,

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I think it's easy to think about

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and I put this speaker right next

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to the first speaker, side-by-side.

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So they'd be creating sound waves

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in this region and I wouldn't really have

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two sound waves necessarily.

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You can think of it as just having

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one total sound wave and how would we

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find the size of that total sound wave?

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Well if I put an axis in here.

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The axis will make it
easier to think about this.

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I'm going to put an axis
through here like this

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What I can do is I can
just ask myself this,

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I'm going to say, what was the value

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of the first wave, so I'm going

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to take that value.

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What was the value of second wave

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and I'm just going to add them up.

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To get the value of the total wave,

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I'd take that value of the first wave

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plus the value of the second wave

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and well I'd just get double in this case.

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I can come over to here okay.

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The value here plus the value there,

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I get double that point.

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It's not going to be as high

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because they weren't as high..

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Then over here I got zero
and zero is just zero.

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and you start to see what's happening.

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I can come down here very low

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or very negative and I
get double that down here

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and if I were to trace this out,

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what I would get is one
big total sound wave

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that would look like this.

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So these have been amplified.

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So that's one possibility.

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When two waves overlap,
you can get this case

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where the peaks match the peaks

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and the valleys match the valleys

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and you get constructive interference.

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So notice how each valley matches

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the valley, each peak matches the peak

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and this is called,
Constructive Interference

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because these constructively combine

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to form one bigger wave.

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So this is Constructive Interference.

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So what would you hear?

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If your ear was over here somewhere

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waiting to hear this sound.

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What you'd actually hear is a loud note.

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This would be much louder than it was.

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It would be twice as loud in fact.

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Which makes sense.

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You've got a second speaker in here.

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It's twice as loud.

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That makes sense.

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What's a little bit harder to understand

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is you can also have something called,

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Destructive Interference.

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What would that look like?

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Well, imagine you had two speakers

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but they looked like this so that the peak

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of the first one lined
up not with the peak

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of the second one but with the valley

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of the second one and the valley of

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the first one lined up with the peak

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of the second one.

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These are out of phase we say.

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Before, when they looked like this.

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These waves we say are in phase,

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because they look identical.

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The peaks match up with the peaks.

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The valleys with the valleys.

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These are out of phase.

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How far out of phase are they?

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We say that these are
180 degrees out of phase.

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So these are 180 degrees out of phase.

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The phase refers to what point on

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the wave cycle is the wave at

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and these two are starting
completely separately

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which is 180 degrees.

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You might think that means 360

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but think about it.

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If you turn around 360 degrees,

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you're actually back where you started.

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If we tried to make these 360 degrees

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out of phase, they'd look identical again

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because I've moved on
so far through a cycle

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that's it's back to where it started

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in the first place.

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So I want to move it 180
degrees out of phase.

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That's exactly the opposite

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So that you get peak lining up with valley

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or if you like radions, this is called

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pi out of phase because pi and 180

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are the same angle.

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Alright so what happens here

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if I take these two speakers?

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I'm going to take this second speaker

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and I line it up right
next to the first speaker.

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I get something that looks more like this.

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Look at how weird this looks.

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These are completely out of phase

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and what's going to happen is

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if I add my little axis to
help me think about this.

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I'm going to add an axis
straight through here.

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Now I play the same game.

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What total wave do I end up with?

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Well, I take this value.

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I'm going to add up the
values just the same.

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I take the value of the first wave

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plus the value of the second wave.

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I add those up, one's a positive

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and one's a negative I get zero

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and then over here zero plus zero is zero

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and then the valley of the first wave

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is lining up with the
peak of the second wave

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and if I add these two points up,

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I get zero again and you probably see

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what's going to happen.

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I'm just going to get a flat line.

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I'm going to get a flat line and I'm

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going to get no wave at all.

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These two waves cancel and so we call this

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not Constructive Interference

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but Destructive Interference
because these have

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destructively combined
to form no wave at all

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and this is a little strange.

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How can two waves form no wave?

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Well, this is how you do it.

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And what would our ear here if we had

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our ear over in this area again,

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and we were listening.

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If I just had one
speaker, I'd hear a noise.

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If I just had the second speaker,

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I'd hear a noise.

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If I have both the first and second

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speaker together, I don't hear anything.

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It's silent, which is hard
to believe but this works.

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In fact, this is how noise canceling

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headphones work if you take a signal

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from the outside and you send in

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the exact same signal but flipped.

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Pi out of phase or 180
degrees out of phase.

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It cancels it and so you can fight noise

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with more noise but exactly out of phase

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and you get silence in here, or at least

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you can get close to it.

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Now you might be wondering how do we

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get a speaker to go 180
degrees out of phase?

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Well it's not too hard.

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If you look at the back of these speakers.

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Let me make a clean view.

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If you look at the back of these speakers,

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there will be a positive terminal

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and a negative terminal or at lease inside

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there will be and if you can swap

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the positive terminal
for the negative terminal

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and the negative terminal
for the positive terminal,

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then when one speaker's
trying to push air forward,

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there's a diaphragm on this speaker

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moving forward and backwards.

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When one speaker is
trying to push air forward

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the other speaker will be trying

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to pull air backwards and the net result

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is that the air just doesn't move

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because it's got equal and opposite

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forces on it and since
the air just sits there,

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you've got no sound wave because

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air has to oscillate
to create a sound wave

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and you get Disruptive Interference.

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So that's how you can create a speaker

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pi out of phase.

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You might be wondering, I don't want

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to mess with the wires on the back

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of my speaker in fact, you shouldn't

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so you don't get shocked but if I've got

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two speakers in phase
like this, I'm stuck,

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I can't get Destructive Interference

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but yeah you can.

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Even if you don't mess with the wires,

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and don't, don't try this at home,

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you can still take this speaker,

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remember before when these where

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in phase we'd just line them up like that,

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Constructive Interference but I don't

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have to put them side-by-side.

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I can start one speaker
a little bit forward

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and looks what happens.

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We start to get waves
that are out of phase.

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So my question is how far forward

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should I move this speaker to get

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Destructive Interference
and we can just watch.

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So I'm just going to try
this and when we get to

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this point there, now we're out of phase.

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Now I have Destructive Interference

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and so how far did I
move my speaker forward?

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If we look at it, here was the front

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of the speaker originally, right there.

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Here's the front of the speaker now.

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If you look at this wave, how much

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of a wavelength have I moved forward.

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The amount of wavelength that you had

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to move forward was 1/2 of a wavelength.

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So if you take two speakers that are

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in phase and you move one

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1/2 a wavelength forward you get

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Destructive Interference again.

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Again, if my ear's over here, I'm not

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going to hear anything.

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Even though these two waves started off

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in phase, move one 1/2
a wavelength forward,

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they line up so that it's Destructive,

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I get no noise but if I take this away.

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We go back to the beginning here.

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Take my speaker, we start over.

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If you move it forward a whole wavelength,

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so I take this here, keep moving it,

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keep moving it and then
Destructive Interference

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Whoa, here we go, Constructive
Interference again.

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That's a whole wavelength.

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So if you move it forward
a whole wavelength.

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Look, there's one whole
wavelength forward.

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So the front of the speaker was here

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now the front of the speaker's here.

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This is an entire wavelength.

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I get Constructive Interference.

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Now I'm going to hear a loud sound again.

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I'm going to hear twice the noise

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that there would be if
I just had one speaker.

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So the moral of this story is that

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even if you have speakers
that are in phase,

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you can get Destructive Interference

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depending on the difference in the length

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that these two waves travel.

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In other words wave two
is traveling this far

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to get to my ear.

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I'm going to call that x2 and wave one

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is traveling this far to get to my ear.

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I'm going to call that x1.

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If I took the difference
between these two,

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I'd be finding the path length difference.

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The difference in path lengths that

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these waves are traveling and that

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would be this amount.

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This is the difference right here.

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I'm going to call it delta x because

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it's the magnitude of the difference

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between these two lengths and we saw

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00:09:49,498 --> 00:09:52,586
that if this equals
lambda it was constructive

266
00:09:52,586 --> 00:09:55,067
and if it equaled a 1/2 a lambda

267
00:09:55,067 --> 00:09:57,866
it was destructive but those
aren't the only values.

268
00:09:57,866 --> 00:09:59,929
We can write down an
important result here.

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00:09:59,929 --> 00:10:03,897
If delta x, the path length difference was

270
00:10:03,897 --> 00:10:07,178
lambda or it turns out 2 lambda will work

271
00:10:07,178 --> 00:10:10,110
or 3 lambda, imagine
moving the second speaker

272
00:10:10,110 --> 00:10:13,273
one more whole wavelength.

273
00:10:13,406 --> 00:10:15,615
Well, you'd be perfectly
back in phase again

274
00:10:15,615 --> 00:10:17,550
because you'd align back up perfectly

275
00:10:17,550 --> 00:10:21,388
or 3 whole wavelengths
again, perfectly in phase.

276
00:10:21,388 --> 00:10:25,084
Any integer wavelength including zero

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00:10:25,084 --> 00:10:26,508
because zero is just the case where

278
00:10:26,508 --> 00:10:29,404
the speaker was right next to speaker one.

279
00:10:29,404 --> 00:10:30,764
Where these two speakers were lined up

280
00:10:30,764 --> 00:10:32,555
right next to each other,

281
00:10:32,555 --> 00:10:35,107
you'll get Constructive Interference.

282
00:10:35,107 --> 00:10:38,151
The waves line up perfectly,
it's going to be constructive

283
00:10:38,151 --> 00:10:42,998
and we saw if, delta x
equals a 1/2 wavelength

284
00:10:42,998 --> 00:10:46,041
it was destructive but
that's not the only case.

285
00:10:46,041 --> 00:10:48,909
Any odd 1/2 integer here.

286
00:10:48,909 --> 00:10:50,567
So I can't do 2 over 2 because that

287
00:10:50,567 --> 00:10:52,151
would be lambda again.

288
00:10:52,151 --> 00:10:57,110
I could do 3 lambda over
2 or 5 lambda over 2

289
00:10:57,110 --> 00:10:59,523
or 7 lambda over 2.

290
00:10:59,523 --> 00:11:02,446
Any of these will give me
Destructive Interference

291
00:11:02,446 --> 00:11:04,780
because they'll cause these peaks

292
00:11:04,780 --> 00:11:06,482
to match up with valleys.

293
00:11:06,482 --> 00:11:07,914
The whole thing would flat line.

294
00:11:07,914 --> 00:11:09,369
I'd get no sound.

295
00:11:09,369 --> 00:11:11,061
This is an important result.

296
00:11:11,061 --> 00:11:12,425
If you've got two speakers that are

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00:11:12,425 --> 00:11:14,521
starting off in phase.

298
00:11:14,521 --> 00:11:16,928
In other words they both
start off the same way

299
00:11:16,928 --> 00:11:19,370
and by that I mean one speaker sends out

300
00:11:19,370 --> 00:11:23,935
it's wave going up, the other

301
00:11:23,935 --> 00:11:25,291
sends out it's wave going up.

302
00:11:25,291 --> 00:11:26,765
There both at the same cycle.

303
00:11:26,765 --> 00:11:30,039
If the only difference is
the path length difference,

304
00:11:30,039 --> 00:11:31,549
this is an important result that let's you

305
00:11:31,549 --> 00:11:33,300
determine whether there's constructive

306
00:11:33,300 --> 00:11:36,839
or destructive interference
but you might ask,

307
00:11:36,839 --> 00:11:38,723
hold on, what if...

308
00:11:38,723 --> 00:11:40,610
See this was assuming there was no phase

309
00:11:40,610 --> 00:11:42,386
difference to start off with.

310
00:11:42,386 --> 00:11:44,467
What if you did the old switcheroo

311
00:11:44,467 --> 00:11:46,107
on the back of one of these speakers

312
00:11:46,107 --> 00:11:47,638
and you swapped the positive end

313
00:11:47,638 --> 00:11:50,019
for the negative end so
instead of coming out

314
00:11:50,019 --> 00:11:54,588
upward, the second one
was coming out downward.

315
00:11:54,588 --> 00:11:56,004
Then what would happen?

316
00:11:56,004 --> 00:11:57,762
Well you might be able to guess.

317
00:11:57,762 --> 00:12:00,818
Now, this results just going to flip-flop.

318
00:12:00,818 --> 00:12:04,927
In other words, if I
look at this case here

319
00:12:05,300 --> 00:12:06,791
Look at, now we start off with speakers

320
00:12:06,791 --> 00:12:10,075
that are out of phase to begin with.

321
00:12:10,075 --> 00:12:12,998
This time, if I start off with zero

322
00:12:12,998 --> 00:12:15,100
path length difference, I get destructive

323
00:12:15,100 --> 00:12:16,700
destructive instead of constructive.

324
00:12:16,700 --> 00:12:19,548
If I move this a whole wavelength forward,

325
00:12:19,548 --> 00:12:20,882
there's a whole wavelength,

326
00:12:20,882 --> 00:12:23,148
I get destructive again.

327
00:12:23,148 --> 00:12:25,819
Two wavelengths forward,
destructive again.

328
00:12:25,819 --> 00:12:27,166
Three wavelengths forward would be

329
00:12:27,166 --> 00:12:28,763
destructive again and so
the integer wavelength

330
00:12:28,763 --> 00:12:31,612
this time are going to
give me destructive.

331
00:12:31,612 --> 00:12:33,051
What about the half integers?

332
00:12:33,051 --> 00:12:35,027
Let's see, I'll go forward
a 1/2 a wavelength.

333
00:12:35,027 --> 00:12:38,025
Look at this, perfectly in phase.

334
00:12:38,025 --> 00:12:39,444
It's going to be constructive.

335
00:12:39,444 --> 00:12:42,867
How about if I go 3 1/2 of a wavelength.

336
00:12:42,867 --> 00:12:45,650
Again, perfectly in phase, constructive.

337
00:12:45,650 --> 00:12:49,651
So, in this case it turns
out if you start off

338
00:12:49,651 --> 00:12:52,193
with speakers that were
already phase shifted.

339
00:12:52,193 --> 00:12:57,193
If one speaker is pi
shifted from the other

340
00:12:57,346 --> 00:12:58,817
then we got another result here.

341
00:12:58,817 --> 00:12:59,888
We've got that...

342
00:12:59,888 --> 00:13:01,137
Well actually I'll just go back to my

343
00:13:01,137 --> 00:13:02,976
previous result, it's easier.

344
00:13:02,976 --> 00:13:06,934
We can just add a little addendum here if

345
00:13:07,135 --> 00:13:12,135
if one speaker is pi phase shifted,

346
00:13:15,977 --> 00:13:20,138
from the other speaker and remember

347
00:13:20,138 --> 00:13:22,984
these don't have to be speakers.

348
00:13:22,984 --> 00:13:25,320
They could be any wave source.

349
00:13:25,320 --> 00:13:27,273
If one speaker's a pi phase shift

350
00:13:27,273 --> 00:13:32,273
from the other speaker then
you just flip-flop this.

351
00:13:32,295 --> 00:13:34,215
Then you just take this rule and now

352
00:13:34,215 --> 00:13:39,074
these give you constructive right here.

353
00:13:39,074 --> 00:13:41,296
These would give you constructive

354
00:13:41,296 --> 00:13:45,050
and these up here would
give you destructive

355
00:13:45,050 --> 00:13:46,419
and so the whole thing just gives you

356
00:13:46,419 --> 00:13:48,501
the opposite result.

357
00:13:48,501 --> 00:13:51,213
Now the whole integer
wavelengths give you destructive.

358
00:13:51,213 --> 00:13:53,580
The 1/2 integer wavelengths
give you constructive

359
00:13:53,580 --> 00:13:56,652
and I have to impress upon you the idea

360
00:13:56,652 --> 00:13:59,149
that this does not just
apply for speakers.

361
00:13:59,149 --> 00:14:01,708
This applies for light and some sort of

362
00:14:01,708 --> 00:14:03,970
double slit experiment or light in

363
00:14:03,970 --> 00:14:06,449
a thin film experiment or sound

364
00:14:06,449 --> 00:14:08,659
with speakers or water waves.

365
00:14:08,659 --> 00:14:11,231
Any time that's the case, this rule holds

366
00:14:11,231 --> 00:14:13,107
in fact, this is the fundamental rule

367
00:14:13,107 --> 00:14:16,548
for almost all wave interference aspects.

368
00:14:16,548 --> 00:14:18,307
Is that the path length difference

369
00:14:18,307 --> 00:14:21,171
along with whether
there's a pi phase shift,

370
00:14:21,171 --> 00:14:23,593
a relative pi phase shift between the two

371
00:14:23,593 --> 00:14:25,107
will determine whether you get

372
00:14:25,107 --> 00:14:28,519
constructive or destructive interference.