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PROFESSOR: OK, today we are going
to do a very interesting experiment with this setup
here.
This is called a Bell Labs machine,
and it has many, many rods in this setup.
And they are connected to each other such
that it is essentially approximation to an infinitely
long coupled system.
Of course this is essentially not infinitely long in reality,
and in this demonstration, we were
wondering what will happen if I excite a propagating
pulse on this system and how these pulse will react
to the boundary where we can have
two different kinds of boundary conditions
which we discussed during the lecture.
The first one will be a closed-end situation,
and the other one will be an open-end situation.
At the edge of the rods, they are, for instance,
have paint such that it can actually light up--
brighten up, and you can see the green dot so that you increase
the visibility of the edge.
In the first part of the demo, what we are going to do
is the following.
I am going to fix one end with clips here such
that this point can now move.
And we were wondering what will happen
to the experimental result if I excite a propagating wave,
and how does that compare to the mathematical calculation?
So let's immediately do this experiment.
So now I am going to create a mountain.
This mountain will go in the approach to this boundary.
And you can see that the mountain got reflected.
And let's do this experiment again.
If we look at this mountain, it does change sign
after it passed a fixed end, as we
predicted from the mathematics during the class.
That is because if I create a mountain, at the edge
it has to be super--
it has to be a superposition of a mountain,
and the valley such that this side is actually not moving.
The sum of the mountain and valley
should be equal to zero such that this point never
move as a function with time.
Let's take a look at this demonstration again using
a valley.
So now we'll excite a valley, and you
can see that this valley becomes a mountain.
And interestingly when this valley
touch the other side, which is the open end,
it is actually refracted again, as you can see,
and it's still a valley.
Let's take a look at the result again.
A valley becomes a mountain, and a mountain then
becomes a valley.
You can see that when touching the open end,
the behavior is different.
It doesn't change sign.
To see this effect more clearly, what I am going to do
is that I'm going to remove this setup here very, very
carefully such that this side is also becoming an open end.
So now I have both ends open, so what is going to happen
is the following.
So if I excite a mountain, this mountain
will be a mountain again, mountain again,
mountain again, and going back and forth.
That is actually because when this mountain touch
the open end, you will not change sign.
As you can see from this demonstration,
this mountain is going back and forth.
The amplitude is decreasing because this
is a realistic system such that there
will be energy dissipation.
If I have no energy dissipation, like idealize the system,
what is going to happen is that this mountain will go back
and forth, back and forth, back and forth, back and forth
over and over again forever.
But in reality, you do see that the amplitude is decreasing
as a function of time.
Let's also do another version of this experiment
to excite the valley.
You can see this valley goes back and forth.
It's always a valley.
It doesn't change sign, as we predicted from the mathematics
during the class.