This lecture is about standing wave patterns in physics. So far all of the
waves that we've talked about have actually been traveling waves. A
traveling wave is a wave where the maxima and minima move continuously
through the material they're in. So if you look at any one point in the
material of the wave, that one point is going to be oscillated completely by the
wave as the wave moves through it. There's no part of the material that
doesn't oscillate as the wave moves through it, and the wave moves
continuously through the material. The new pattern we're talking about in this
video is a standing wave where the maxima and minima stand still in place
and do not move. The wave oscillates by flattening out and then achieves the
maxima and minima again, so you can see in the animation on the right that is an
example of a standing wave, and you can see how it's different from the
traveling wave. Its maxima and minima oscillate up and down, but there are also
certain points on the wave that actually do not oscillate at all. They just stay
in place. This seems like a pretty subtle difference, but standing waves are really
key to understanding a ton of stuff that happens in physics. Standing waves are
actually the result of the superposition of two traveling waves with the same
wavelength and frequency moving through each other.
As their amplitudes add together, following the rules of superposition
they produce a single standing wave. Here the blue and red traveling waves are
moving through each other and adding to produce the black standing wave
oscillating up and down. This pattern is going to be essential to understanding
everything else that happens in this series on standing waves. You have to
understand that a standing wave is really just the superposition of two
traveling waves moving through each other like this.
So I would honestly take just another second to observe the pattern that
you're seeing here and make sure you understand how that standing wave is
forming. It's just the sum of the amplitudes of the two waves moving
through each other following the rules of superposition.
All standing waves share certain properties. Nodes are point on the
standing wave that do not move at all. this is where destructive interference
is always occurring between the two traveling waves making the standing wave.
So at every node, that's the exact point where the two waves are cancelling each
other out to produce a total amplitude of zero. So those nodes do not oscillate
at all. The material in the nodes of a standing wave does not oscillate up or
down at all, it just stays in place. Anti-nodes are the points on the wave that
move the most, so the places where it reaches its maximum and minimum
displacement are the anti nodes of the wave. The wavelength and amplitude of a
standing wave followed the same pattern as a traveling wave. Sometimes students
can get a little confused by the wavelength and assume that the length is
just the distance between two nodes, but it's still the length of one complete
wave pattern going all the way up and then all the way down, and then back to
where it started. So that purple line shows the full wavelength of this
standing wave, and the amplitude is just from the center point to the maximum
point, not from one extreme to the other extreme so not from the very minimum
bottom of the wave to the very top of the wave. The period of a standing wave
is the amount of time an anti-node takes to go from one extreme to the other and
back. The frequency is the number of these repetitions completed every second.
This is another really central fact about a standing wave, it has the same
wavelength and frequency as the two traveling waves that make it up. So if
you observe how many complete traveling waves pass by a certain point in 1
second, that's exactly equal to how many oscillations the standing wave makes in
one second. So the period and frequency of the two traveling waves are equal to
the period and frequency of the standing wave. If I count the total period for the
standing wave, the time it takes to oscillate from the top to the bottom and
back, I can count 1 2 3 4, so this seems to have a period of about
4 seconds, and if I watch at any one point that the traveling wave is moving
through and count 1 2 3 4 that's the time the traveling wave takes
to complete one full motion through that point. Because a standing wave has both a
wavelength and frequency, we can also talk about it having a velocity in
quotes, because the velocity of a wave is equal to wavelength times frequency. And
when we talk about the velocity of a standing wave we really mean the
velocity of the traveling waves that make the standing wave up. We can use
these interchangeably because the traveling waves have the same
wavelength and frequency as the standing wave.
So because the standing wave is standing, obviously it's not actually moving at
say 3 meters per second, but it can still have a velocity because when we talk
about velocity we can really be referring to the travelling waves that
make it up. So as an example problem, we can ask if
the period of this standing wave is 4 seconds, what is its velocity? I can see
that because this total length is 8 meters, the wavelength is going to be 4
meters. Because that total length is 2 complete wavelengths, the period is 4
seconds, which means that the frequency which is always 1 over period is equal
to 0.25 Hertz. So the velocity is wavelength times frequency, which is
equal to 1 meter per second, so even though the standing wave is not actually
moving from left to right we can still describe it as having a velocity of 1
meter per second because it has a wavelength and a frequency. So that's
the intro information that you need to know about standing waves.