Wave Interference

- [Voiceover] If two waves overlap

in the same medium, we say that

there's wave interference.

So this box here could represent a speaker

and this could be the
sound wave it generates

or it could represent a
laser and this would be

the light wave it generates or it could be

some sort of ripple
tank generator and this

is the water wave it generates.

Regardless, if you had a second source

of a wave and these were to overlap,

you'd cause wave interference and what

that would look like would
be something like this.

So let's say these are speakers.

I like thinking about
it in terms of speakers,

I think it's easy to think about

and I put this speaker right next

to the first speaker, side-by-side.

So they'd be creating sound waves

in this region and I wouldn't really have

two sound waves necessarily.

You can think of it as just having

one total sound wave and how would we

find the size of that total sound wave?

Well if I put an axis in here.

The axis will make it
easier to think about this.

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

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

I'm going to say, what was the value

of the first wave, so I'm going

to take that value.

What was the value of second wave

and I'm just going to add them up.

To get the value of the total wave,

I'd take that value of the first wave

plus the value of the second wave

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

I can come over to here okay.

The value here plus the value there,

I get double that point.

It's not going to be as high

because they weren't as high..

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

and you start to see what's happening.

I can come down here very low

or very negative and I
get double that down here

and if I were to trace this out,

what I would get is one
big total sound wave

that would look like this.

So these have been amplified.

So that's one possibility.

When two waves overlap,
you can get this case

where the peaks match the peaks

and the valleys match the valleys

and you get constructive interference.

So notice how each valley matches

the valley, each peak matches the peak

and this is called,
Constructive Interference

because these constructively combine

to form one bigger wave.

So this is Constructive Interference.

So what would you hear?

If your ear was over here somewhere

waiting to hear this sound.

What you'd actually hear is a loud note.

This would be much louder than it was.

It would be twice as loud in fact.

Which makes sense.

You've got a second speaker in here.

It's twice as loud.

That makes sense.

What's a little bit harder to understand

is you can also have something called,

Destructive Interference.

What would that look like?

Well, imagine you had two speakers

but they looked like this so that the peak

of the first one lined
up not with the peak

of the second one but with the valley

of the second one and the valley of

the first one lined up with the peak

of the second one.

These are out of phase we say.

Before, when they looked like this.

These waves we say are in phase,

because they look identical.

The peaks match up with the peaks.

The valleys with the valleys.

These are out of phase.

How far out of phase are they?

We say that these are
180 degrees out of phase.

So these are 180 degrees out of phase.

The phase refers to what point on

the wave cycle is the wave at

and these two are starting
completely separately

which is 180 degrees.

You might think that means 360

but think about it.

If you turn around 360 degrees,

you're actually back where you started.

If we tried to make these 360 degrees

out of phase, they'd look identical again

because I've moved on
so far through a cycle

that's it's back to where it started

in the first place.

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

That's exactly the opposite

So that you get peak lining up with valley

or if you like radions, this is called

pi out of phase because pi and 180

are the same angle.

Alright so what happens here

if I take these two speakers?

I'm going to take this second speaker

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

I get something that looks more like this.

Look at how weird this looks.

These are completely out of phase

and what's going to happen is

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

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

Now I play the same game.

What total wave do I end up with?

Well, I take this value.

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

I take the value of the first wave

plus the value of the second wave.

I add those up, one's a positive

and one's a negative I get zero

and then over here zero plus zero is zero

and then the valley of the first wave

is lining up with the
peak of the second wave

and if I add these two points up,

I get zero again and you probably see

what's going to happen.

I'm just going to get a flat line.

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

going to get no wave at all.

These two waves cancel and so we call this

not Constructive Interference

but Destructive Interference
because these have

destructively combined
to form no wave at all

and this is a little strange.

How can two waves form no wave?

Well, this is how you do it.

And what would our ear here if we had

our ear over in this area again,

and we were listening.

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

If I just had the second speaker,

I'd hear a noise.

If I have both the first and second

speaker together, I don't hear anything.

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

In fact, this is how noise canceling

headphones work if you take a signal

from the outside and you send in

the exact same signal but flipped.

Pi out of phase or 180
degrees out of phase.

It cancels it and so you can fight noise

with more noise but exactly out of phase

and you get silence in here, or at least

you can get close to it.

Now you might be wondering how do we

get a speaker to go 180
degrees out of phase?

Well it's not too hard.

If you look at the back of these speakers.

Let me make a clean view.

If you look at the back of these speakers,

there will be a positive terminal

and a negative terminal or at lease inside

there will be and if you can swap

the positive terminal
for the negative terminal

and the negative terminal
for the positive terminal,

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

there's a diaphragm on this speaker

moving forward and backwards.

When one speaker is
trying to push air forward

the other speaker will be trying

to pull air backwards and the net result

is that the air just doesn't move

because it's got equal and opposite

forces on it and since
the air just sits there,

you've got no sound wave because

air has to oscillate
to create a sound wave

and you get Disruptive Interference.

So that's how you can create a speaker

pi out of phase.

You might be wondering, I don't want

to mess with the wires on the back

of my speaker in fact, you shouldn't

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

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

I can't get Destructive Interference

but yeah you can.

Even if you don't mess with the wires,

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

you can still take this speaker,

remember before when these where

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

Constructive Interference but I don't

have to put them side-by-side.

I can start one speaker
a little bit forward

and looks what happens.

We start to get waves
that are out of phase.

So my question is how far forward

should I move this speaker to get

Destructive Interference
and we can just watch.

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

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

Now I have Destructive Interference

and so how far did I
move my speaker forward?

If we look at it, here was the front

of the speaker originally, right there.

Here's the front of the speaker now.

If you look at this wave, how much

of a wavelength have I moved forward.

The amount of wavelength that you had

to move forward was 1/2 of a wavelength.

So if you take two speakers that are

in phase and you move one

1/2 a wavelength forward you get

Destructive Interference again.

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

going to hear anything.

Even though these two waves started off

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

they line up so that it's Destructive,

I get no noise but if I take this away.

We go back to the beginning here.

Take my speaker, we start over.

If you move it forward a whole wavelength,

so I take this here, keep moving it,

keep moving it and then
Destructive Interference

Whoa, here we go, Constructive
Interference again.

That's a whole wavelength.

So if you move it forward
a whole wavelength.

Look, there's one whole
wavelength forward.

So the front of the speaker was here

now the front of the speaker's here.

This is an entire wavelength.

I get Constructive Interference.

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

I'm going to hear twice the noise

that there would be if
I just had one speaker.

So the moral of this story is that

even if you have speakers
that are in phase,

you can get Destructive Interference

depending on the difference in the length

that these two waves travel.

In other words wave two
is traveling this far

to get to my ear.

I'm going to call that x2 and wave one

is traveling this far to get to my ear.

I'm going to call that x1.

If I took the difference
between these two,

I'd be finding the path length difference.

The difference in path lengths that

these waves are traveling and that

would be this amount.

This is the difference right here.

I'm going to call it delta x because

it's the magnitude of the difference

between these two lengths and we saw

that if this equals
lambda it was constructive

and if it equaled a 1/2 a lambda

it was destructive but those
aren't the only values.

We can write down an
important result here.

If delta x, the path length difference was

lambda or it turns out 2 lambda will work

or 3 lambda, imagine
moving the second speaker

one more whole wavelength.

Well, you'd be perfectly
back in phase again

because you'd align back up perfectly

or 3 whole wavelengths
again, perfectly in phase.

Any integer wavelength including zero

because zero is just the case where

the speaker was right next to speaker one.

Where these two speakers were lined up

right next to each other,

you'll get Constructive Interference.

The waves line up perfectly,
it's going to be constructive

and we saw if, delta x
equals a 1/2 wavelength

it was destructive but
that's not the only case.

Any odd 1/2 integer here.

So I can't do 2 over 2 because that

would be lambda again.

I could do 3 lambda over
2 or 5 lambda over 2

or 7 lambda over 2.

Any of these will give me
Destructive Interference

because they'll cause these peaks

to match up with valleys.

The whole thing would flat line.

I'd get no sound.

This is an important result.

If you've got two speakers that are

starting off in phase.

In other words they both
start off the same way

and by that I mean one speaker sends out

it's wave going up, the other

sends out it's wave going up.

There both at the same cycle.

If the only difference is
the path length difference,

this is an important result that let's you

determine whether there's constructive

or destructive interference
but you might ask,

hold on, what if...

See this was assuming there was no phase

difference to start off with.

What if you did the old switcheroo

on the back of one of these speakers

and you swapped the positive end

for the negative end so
instead of coming out

upward, the second one
was coming out downward.

Then what would happen?

Well you might be able to guess.

Now, this results just going to flip-flop.

In other words, if I
look at this case here

Look at, now we start off with speakers

that are out of phase to begin with.

This time, if I start off with zero

path length difference, I get destructive

destructive instead of constructive.

If I move this a whole wavelength forward,

there's a whole wavelength,

I get destructive again.

Two wavelengths forward,
destructive again.

Three wavelengths forward would be

destructive again and so
the integer wavelength

this time are going to
give me destructive.

What about the half integers?

Let's see, I'll go forward
a 1/2 a wavelength.

Look at this, perfectly in phase.

It's going to be constructive.

How about if I go 3 1/2 of a wavelength.

Again, perfectly in phase, constructive.

So, in this case it turns
out if you start off

with speakers that were
already phase shifted.

If one speaker is pi
shifted from the other

then we got another result here.

We've got that...

Well actually I'll just go back to my

previous result, it's easier.

We can just add a little addendum here if

if one speaker is pi phase shifted,

from the other speaker and remember

these don't have to be speakers.

They could be any wave source.

If one speaker's a pi phase shift

from the other speaker then
you just flip-flop this.

Then you just take this rule and now

these give you constructive right here.

These would give you constructive

and these up here would
give you destructive

and so the whole thing just gives you

the opposite result.

Now the whole integer
wavelengths give you destructive.

The 1/2 integer wavelengths
give you constructive

and I have to impress upon you the idea

that this does not just
apply for speakers.

This applies for light and some sort of

double slit experiment or light in

a thin film experiment or sound

with speakers or water waves.

Any time that's the case, this rule holds

in fact, this is the fundamental rule

for almost all wave interference aspects.

Is that the path length difference

along with whether
there's a pi phase shift,

a relative pi phase shift between the two

will determine whether you get

constructive or destructive interference.