Hi. It’s Mr. Andersen. And this AP Physics essentials video 115. It is on standing waves.
Standing waves are like they sound. They are waves that appear to stand still. And so an
example of a sound standing wave is the waves found inside a vuvuzela. And so you blow on
it. You get that sound. You blow it with a higher frequency and then you could even try
to pierce your lips a little bit more and get an even higher frequency. But what is
happening is you have these specific standing waves that sit within the chamber, the chamber
of the vuvuzela. Now a wine glass works the same way. If you rub your finger with a little
bit of water around the surface of it, what you can do is generate these standing waves
inside the wine glass. What you are doing is vibrating the sides and as you do that
you are vibrating the air. And since you have a standing wave inside there it makes this
pitch. Add water to it and you are going to have a slightly different pitch. And so waves
can either be traveling or standing waves. Traveling waves will move from one place to
another. And standing waves will appear to stand still. Now when you look at it it is
kind of an illusion. They are standing still but the traveling waves are bouncing back
and forth. In other words they are being reflected off of the boundaries and then there is interference
to create these standing waves. And so if we look at this animation the dark wave is
going to be the standing wave but in the background you can see the blue and the red waves that
are bouncing back and forth and back and forth. And it is the summation of them that creates
the standing wave. Now if you notice that standing wave is going to have areas where
it is not moving at all. And that is due to destructive interference where the waves are
canceling each other out. And we call those in physics nodes, areas where it is not moving.
And then we are going to have total constructive interference in certain areas, and we call
those antinodes. That is where it is moving the maximum amount back and forth and back
and forth. And so an example of this could be found in instruments for example. So a
string instrument is going to be fixed at either end. And this animation is a good example
of that. It is fixed on either end and as the waves bounce back and forth and back and
forth you create these standing waves. If we shorten that, like on a guitar, then we
can get different pitches. A tube is going to be the same way. A tube could be open on
both ends, like a flute or it could be closed on one end like a vuvuzela. And that is going
to create these standing waves as well. So let’s starting with traveling versus standing
waves. And so the PHET simulation, I am generating some waves. Those waves, and this is just
kind of theoretical, are moving out the door and then they moved on forever. But if we
add a boundary on the other side, in other words if we add a fixed boundary you can see
now there is reflection back. So those waves did not just keep going. They will bounce
back. And now they are going to bounce back again. And as that wave goes back and forth
and back and forth you can see that we are starting to generate these standing waves.
And you can even see those nodes and those antinodes. In other words, those areas where
it is not moving and those ares where it is moving quite a bit. So this is an animation
of standing waves. And so what we are doing is as the blue wave moves to the right, becomes
the red wave which moves back to the left and it just keeps going and going and going,
we are getting destructive interference, that is causing these nodes where they cancel each
other out. And then we have constructive interference and that is creating these antinodes where
those two waves add together to make a much bigger wave. Now an example of this, if you
have ever played baseball before, when you hit the ball sometimes you will hit it and
the bat will kind of buzz in your hands. In other words it vibrates quite a bit. And the
reason why is that you are hitting the ball on antinode, an area where the wave is going
up and down the bat are actually constructively interfering to create a huge vibration in
there. And we refer to it as the sweet spot, the spot on a bat where the node is, is where
you do not have much vibration, that you hit the ball and you do not feel really any vibration
at all. And so let’s go through experimentation. So this is a simbucket simulation. What we
are doing is looking at standing waves. The first one we are going to look at is when
you have two fixed ends. So an example of this could be a guitar. And so what you do
is you have a string. You hold it on one side and then you pluck it and you are going to
have vibration. So what do you get? Waves going back and forth and back and forth. What
is the standing wave then? The standing wave is going to be that green wave in this simulation.
It is that wave that is the addition of the other waves. What is interesting in a guitar
is that you do not only have one, what we call harmonic or one standing wave, but you
can have multiple standing waves. Now in all of these standing waves what makes them the
same is that we have a node on either side. In other words there is not net movement on
either side of that string. If we look at an instrument like a tuba or a vuvuzela, what
is the characteristic of that? Well, we are vibrating it but you can see that on the left
side we have a node. It is not vibrating. But we have an antinode at the right side.
So in each of these harmonics the left side is going to be a node. It is not going to
move at all, but the right side is going to be an antinode. And so we still have those
traveling waves going back and forth and back and forth. It is just that one of those ends
is free to create an antinode. And then we just have reflection off of that end. These
are all of the different harmonics. What keeps them all in common is the node on the left,
antinode on the right. If we then look at something that has two open ends, like a flute.
A flute you do not blow in one end, you are blowing on the top to create a vibration or
a pan flute would be an example of that. And so what is going to create the standing wave
here? Well in this first harmonic we have the node in the middle and then we have antinodes
on either side. Now we have two nodes near the middle and antinodes on the side. So what
is the characteristic of a standing wave in a chamber that has two open ends? It is always
going to be an antinode on either side. But depending on the frequency we can get difference
pitches as we blow through. Rubens tube is a really cool example of that. And a Rubens
tube what you do is you fill up a chamber with gas, a gas that is flammable. And so
this guy is lighting the chamber, so we have flames coming out of the top. But on a Rubens
tube you put a speaker on the side. And what that speaker does is create these longitudinal
waves. Those longitudinal waves, as they move through will create areas where there is a
lot of compression. And an area where there is a lot of compression or antipodes, then
the gas really cannot make its way out. And so it will be really low there, but at the
nodes it will actually come out quite a bit. And so did you learn to predict the properties
of standing waves. They result from reflection of these traveling waves. Could you collect
data? Again I used simbucket simulation to do that. And then finally could you describe
examples of when this occurs, standing waves. Musical instruments are good. Baseball bats are great.
And I hope that was helpful.