hey it's professor Dave let's talk about
interference and diffraction we know a
bit about wave mechanics now so it's
time to look at some wave related
phenomena like what can happen when two
waves overlap or when a wave runs into
some solid surface
these are very common occurrences as we
are frequently experiencing sound from
more than one location at once and sound
will bounce off of walls and other
surfaces so we need to understand what
happens to waves in these scenarios we
know that two solid objects like two
people can't occupy the same space at
the same time but mechanical waves are
not matter they are displacements of
matter that carry energy so two waves
can occupy the same space and when two
waves combine in this way it is called
superposition when there are two
disturbances near one another and
they're respected series of waves
overlap this is called an interference
pattern and we can see how the regions
where the waves intersect generate a
completely new pattern this is easy to
see with waves in the water but sound
and light waves also do this
there are a few different things that
can happen when interference occurs say
two individual wave pulses are traveling
towards each other and they have the
same amplitude when these meet the
amplitudes at each point will be added
together to produce the respective
points on the resultant wave so there
will be a moment where there is one wave
with twice the amplitude then the two
waves continue in the direction they
were moving in each wave maintains its
own characteristics before and after the
interference when a resultant wave has
greater amplitude than the individual
waves like this case this is called
constructive interference now let's say
the pulses are on opposite sides of the
equilibrium position
again according to the superposition
principle we will add the amplitudes to
get the resultant wave but in this case
the two amplitudes add to zero so the
resultant wave will be as though there
is no wave at all then the waves
continue along their trajectories this
kind of interference where the resultant
wave has a smaller amplitude than the
individual waves is called destructive
interference and if the resultant wave
has an amplitude of zero like this
example it is called complete
destructive interference
this concept applies to periodic waves
as well first we can consider two sine
waves that are precisely aligned they
are said to be exactly in phase we can
add the amplitudes at every single point
and the result is a similar-looking wave
with twice the amplitude due to
constructive interference because the
crests aligned with the crests and the
troughs aligned with the trough but then
if we shift one of these by half its
wavelength
now the crests of one aligned with the
troughs of another and at every single
point on the x-axis these waves will add
up to zero
they are said to be exactly out of phase
and this will be an example of complete
destructive interference this is what
noise cancellation headphones do small
microphones detect background noise and
process the Associated signal and then
reproduce this noise in a way that is
precisely out of phase with signal the
resulting destructive interference
results in zero or at least dramatically
reduced sound waves reaching your ears
in reality interference patterns are
often much more complicated than these
two extremes but in every case the
superposition principle is still
applicable we also want to understand
what happens when waves hit a boundary
of some kind if a boundary is free to
move waves will be reflected bouncing
back in the opposite direction but
maintaining the same amplitude if
instead this boundary is fixed waves
will be both reflected
and inverted bouncing back in the
opposite direction but now with
amplitude of the opposite sign let's say
instead of arriving at a solid boundary
a wave arrives at a boundary with a
small gap in it when waves reach an
opening like this they will Bend around
the edges producing a phenomenon called
diffraction a diffraction pattern is
another kind of interference pattern
because of the series of maxima and
minima that result and waves of all
types will exhibit this behavior
it was the diffraction of light that
provided some of the strangest data we
have collected in physics contributing
to the development of quantum theory but
that will have to wait until the modern
physics course for now let's check
comprehension thanks for watching guys
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