- [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.