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 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'm 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 for me to think about this I
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 the 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
just get double in this case I can come
over to here okay 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 and then over here I got
0 and 0 is just 0 and you start to see
what's happening it 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 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 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'd 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
look 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 a hundred and eighty 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 if you
turn around 360 degrees you're actually
back to where you started if we tried to
make these 360 degrees out of phase they
look identical again because I've moved
one so far through a cycle that 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 radians this is
called pi out of phase because pi and
180 are the same angle all right so what
happens here if I I take these two
speakers I'm going to take the second
speaker and I line it up right next to
the first speaker I get something looks
more like this 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 not 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 once positive
1/2 negative I get 0 and then over here
0 plus 0 is 0 and then the value of the
first waves lining up with the peak of
the second wave and if I add these two
points up I get 0 again and you probably
see what's going to happen I'm just
going to get a flat line I 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 combine 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
hear if we had our ear over in this area
again we were listening if I just had
one speaker I'd hear a noise if I just
have 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
cancelling 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 they'll be a positive terminal
and a negative terminal released 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 is trying to push air forward
there's a diaphragm on the speaker
moving forward and backwards when one
speaker is trying to push air forward
the other speaker will be trying to
whole 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 destructive interference so
that's how you can create a speaker pie
out-of-phase well 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 then 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 were in phase we 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 look at 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 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 wave length have I moved
forward the amount of wavelength that
you had to move forward was one half of
a wavelength so if you take two speakers
that are in phase and you move one
one-half of a wavelength forward you get
destructive interference again again if
my ears over here I'm not going to hear
anything even though these two waves
started off in phase move one half 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 at what
destructive interference and now whoa
here we go
constructive interference again that's a
whole wavelength so if you move it
forward a whole wavelength there's
on whole wavelength forward so the front
of the speaker was here now the front of
speaker's here this is an entire
wavelength I get constructive
interference now it's going to 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
constructive or 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 X 2 and wave 1 is traveling this
far to get to my ear I'm going to call
that X 1 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 1/2 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 to
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
backup perfectly or three 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 1
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 1/2 wavelength it was destructive
but that's not the only case any odd
half integer here so I can't do 2 over 2
because that would be lambda again I can
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
flatline I'd get
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 its
wave whoops one speaker sends out its
wave going up the other sends out its
way of going up to both of the same
cycle if the only difference is the path
length difference this is an important
result that lets 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 switcheroo on the
back of one of these speakers and you
swapped the positive end for the
negative end so that 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
started off with zero path length
difference I get destructive instead of
constructive if I move this a whole wave
length forward there's a whole wave
length I get destructive again two
wavelengths forward destructive again
three wavelengths four would be
destructive again and so the integer
wavelengths this time are going to give
me destructive what about the half
integers let's see I'll go forward a
half a wavelength look at this perfectly
in phase it's going to be constructive
how about if I go three halves 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 if one source 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 from the other
speaker and remember these don't have to
be
speakers they could be any wave source
if one speaker is a PI phase shift from
the other speaker well 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 energy wavelengths give
you destructive the half 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 in some sort of
double slit experiment or light in a
thin-film experiment or sound with
speakers or water waves anytime 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