Hi. It’s Mr. Andersen. And this is AP Physics essentials video 113. It is on wave superposition.
What does that mean? When waves interact with each other they can either build each other
up or tear each other down. And so let’s watch this wave right here. We are sending
two waves, these are transverse waves, towards each other. And so what is going to happen
when they meet? What is going to happen at that point where the slinkies are connected?
Well there will be superposition. They will come together and we are going to add the
values that they had before. And so watch what happens when they come together. We get
one giant wave. Now it is hard to watch that and figure out did the waves hit each other
and bounce off or did they go through each other? So this one might help a little bit.
We now have a wave coming from the left that is on the top and from the right that is on
the bottom. And so what is going to happen here? Well, you probably figured out that
they cancel each other out. And so if you watch that point in the middle it will not
move up or down very much at all. But watch what happens to those waves after they hit.
The one on the bottom continues to the left of the bottom. And the one on the top continues
to the right. And so when waves interact they do not bounce of each other, they will move
right through each other. But as they move through each other they will interfere with
one another. And that interference can be constructed. In other words when two waves
come at each other we build one giant wave. Or it can be destructive. In other words they
cancel each other out. But superposition is that idea that when they are together we add
those two values together. And we could do that through experimentation or we can make
sure that applies through experimentation. And so if we look at this, now we are adding
a transverse wave from the left and a longitudinal wave from the right. And so watch what happens.
They move right through each other. And so if I take a picture of right when they are
together, what we are doing is simply adding wave A plus wave B. It is very simple. It
is almost like algebra as a way to think about what happens to the waves. And so if we have
two waves that are in phase like this, and so let’s add numbers to it, let’s say
this wave here is 1 centimeter above equilibrium. And this is 1 centimeter above equilibrium,
then what is going to be the constructive wave of those two together? Well it is simply
going to be, let’s add them up, it is going to be 2 centimeters above. Or right here it
is at 0. At here it is 0. So here it is also going to be 0. Now we could also have destructive
interference. And that is when it cancels each other out. So let’s look at that. This
one, let’s say, is at 1 centimeter. This one right here is at negative 1 centimeter.
And so what is the destructive interference? It is at 0. In fact it is a 0 all the way
across. Now sometimes we will send waves back and forth and back and forth. And we can create
what is called a standing wave. And so the black wave that you are looking at right here
is a standing wave. It appears not to be moving. It is just moving up and down. But now let’s
concentrate on the blue wave. What is the blue wave doing? It is moving to the right.
You can see it is transferring its energy to the right. It is then reflecting back and
now it is the red wave that is moving back to the left. And so we have the blue going
to the right. We have the red going to the left. And what is that dark band or that standing
wave? It is the summation. It is the superposition of both of those waves together. So I can
just randomly stop this video right here. And so why is it really tall here? Well if
you think about it, they both are around 1 centimeter off the top. And so this is going
to be around 2 centimeters. Why is this one not moving at all? Well this one, we will
say is about 0.5 centimeter above and this is negative 0.5 centimeter. And so this one
is at 0. And so in fact, no matter where we go along the way, these areas right here,
we will talk about this in a future video called Nodes, is total destructive interference,
where it is not moving at all. And then if we look at these troughs right here, or these
antinodes, rather, those are going to be areas where we have total constructive interference.
It is coming together. And so did you learn to use representations of constructive interference
and then destructive interference? Could you come up with an experiment? The one I did
was let’s launch waves at each other and then video what is going on. And then could
you actually measure it? Could we measure how high is the displacement before that interaction.
And then during the interaction? I hope so. And I hope that was helpful.