Video Transcript
The motion of a water wave on the
sea is shown in Figure one. The direction in which a particle
in the wave moves is also shown. Which of the following statements
is correct? Tick one box. The water wave is a transverse
wave. The water wave is a longitudinal
wave. The water wave is not purely a
transverse wave or purely a longitudinal wave.
Looking at Figure one, we see it
shows us a wave in the ocean moving left to right as well as a particle that moves
in the water, while the wave passes by. Interestingly, though the wave
moves left to right, the particle we see is moving in a circular path. And based on the information in
this figure, we want to figure out which of these three statements is correct.
The statements have to do with what
type of wave the water wave is: whether transverse, longitudinal, or not entirely
either one. To figure this out, let’s recall
what transverse and longitudinal waves are in the first place. When we think about waves, these
are the two broad categories we divide them into: transverse and longitudinal.
A transverse wave is one in which
the displacement of the wave is perpendicular to the wave’s direction. In other words, if our wave was
moving left to right, then in a transverse wave the wave displacement would be up
and down, perpendicular to the wave’s direction.
On the other hand, for a
longitudinal wave, the displacement of the wave is parallel to the wave’s
direction. For this kind of wave, if the wave
direction was left to right, then the wave displacement would be along that same
axis forward and backward.
Knowing all this, if we look back
at Figure one, we see that we have a wave, which is moving left to right. This means that if this wave was
purely transverse, we would expect our particle which is in the water to be moving
up and down or if this wave was longitudinal, we would expect the particle to be
moving left to right only.
But as we look at the path of the
particle’s motion, we see that it’s necessary for the particle to move in all these
directions at various times. Each one is required for the
particle to move in a circular arc. This indicates that the water wave
in the sea is some combination of transverse and longitudinal. It’s not purely either one.
And therefore, we tick the third
box. Based on the particle’s motion, the
water wave is not purely a transverse wave or purely a longitudinal wave.
Next, let’s consider how the
distance between a fixed point on our travelling wave and the particle varies over
time.
The peak of a wave is initially at
the position of the particle shown in Figure one. Describe how the distance between
the particle and the peak of the wave varies over time.
Looking again at Figure one, we see
that a peak of this travelling wave is colocated with the particle at this instant
in time we’re shown. We knew though that the wave is
moving left to right. So this particular point on the
wave will become more and more distant from the particle as time passes.
As we consider this distance and
how it changes over time, we see though that there’s a second dynamic at play. And that’s the fact that this
particle is moving in a circular arc. This tells us that sometimes the
particle is moving towards the point on the wave, sometimes it’s moving away, and at
other times it’s moving neither closer nor farther away.
We want to describe how the
distance between this particular wave peak and the particle changes with time. And since both the wave and the
particle are in motion, our description will involve both elements.
First, let’s describe what it means
that the wave is moving left to right, while the average position of our particle is
constant. Based on that, we can say that in
general the distance from this particular peak on the wave to the particle increases
over time. That makes sense since the wave is
in steady motion, while the average position of the particle doesn’t change.
But as we’ve seen, this isn’t the
only factor that affects the distance between the particle and the peak of the
wave. There is also this cyclical effect
of the particle’s motion, moving sometimes closer sometimes farther away from the
wave peak.
Even though the distance between
the peak and the particle is always increasing, the rate at which that increase
happens is not constant thanks to this cyclical motion. As a second part of our description
then, we can say this: we can say, “The rate at which the distance increases changes
cyclically.” It’s not constant, but it is
affected by the particle’s circular motion.
Taken together, these two
statements describe how the distance between the particle and the peak of the wave
changes with time. Finally, let’s consider how water
waves can help drive the motion not just of particles, but of power generators.
Figure two shows an electrical
generator that is powered by wave motion. Explain how the generator uses the
motion of water in waves to generate and distribute electrical power.
Looking at Figure two, we see it
starts off with a wave of water which comes in contact with a flat plate which is
part of this power generator. Connected to the flat plate is a
permanent magnet. And this magnet is wrapped around
with a conducting coil, which itself is connected by cables to the national grid
where everyone commercially and residentially gets their power.
Our task is to explain just how
this generator actually works — in other words, just how is it that waves may be in
the ocean help to generate and distribute electrical power through this
generator. For our explanation, we’ll simply
walk step by step through just how it is that this generator operates.
If we begin at the beginning, we
see that there are water waves, which push down on this flat metal plate. So let’s write that out as step
one. Having written that out, we might
wonder just how do we know that the waves actually do push down on the plate. What if the wave is a longitudinal
wave and it only pushes objects left to right?
It’s a good question and let’s
consider it this way. Let’s assume that the waves in this
diagram are moving either left or right; that is, like virtually all waves we
experience on a large body of water, these waves are moving horizontally. So that means the wave direction is
horizontal. But we see from this diagram that
the wave displacement — at least a component of it — is vertical.
This is the hallmark of a
transverse wave. This tells us that our water wave
has at least some transverse wave element to it. And for a transverse wave, the wave
displacement is perpendicular to the wave’s direction. That tells us that this water wave
indeed will at times press downward under this flat plate.
Okay, so after the plate is pushed
down, what happens next? Looking at our diagram, we see that
the plate is connected to this permanent cylindrical magnet. And since they’re connected, the
two must move together. That means that when the plate
moves down, so does the magnet.
We’ll write that out. We’ll say that when the plate moves
down, the magnet also moves down since after all the two are connected. We see from our diagram that our
permanent cylindrical magnet is surrounded by this conducting coil. And the coil is called a rigid
conducting coil.
That tells us that the coil and the
magnet move independently or specifically that the coil is fixed in one place. We can say then that because the
coil is fixed in place, the magnet moves past the coil. That may not seem particularly
profound, but it actually makes a big difference for the power generation in this
generator.
Here’s where the process gets very
interesting. When we think about this permanent
magnet that’s part of our generator, we know that a magnet will create magnetic
field lines between its north and its south poles. It will look a little bit like this
if we draw those field lines in.
As the water wave pushes down on
the flat plate and causes the centre or south pole of this permanent magnet to drop,
that magnet will be put in motion, which will change the magnetic field. The rigid coil which we’re told
does not move will be exposed then to a changing magnetic field due to the moving
permanent magnet. This tells us that the loops in
this coil will be exposed to a changing magnetic flux.
And what happens when a loop of
conducting coil has a changing magnetic flux through it? We know from Faraday’s law that
what will happen is an EMF will be induced across this rigid conducting coil, which
will cause the motion of current. If we put this in writing, we’d say
that when the magnet moves past the coil, this induces a current in the coil. This is the critical step in the
process where electricity is actually generated. It’s through the induction of
current in this rigid conducting coil.
Now that we’ve generated
electricity, we move on to the question of how we will distribute this electrical
power. Looking again at our diagram, we
see that our rigid conducting coil, which at this point has induced current running
through it, is connected by cables to the national electrical grid. This is the means by which the
induced current is spread out or distributed.
Writing out this step, we could say
that the current induced in the coil is transmitted to the national grid by
cables. At this point, we’ve covered
electrical generation and distribution. The only question is “How does the
system actually reset itself so we can do all this over and over and over
again?” This is where we get to the last
step in the process. And it involves this spring, as
shown in the bottom of Figure two.
We know the water wave is capable
of pushing down on the flat plate, but it’s not capable of pulling the plate back
up. That’s where the spring comes
in. The spring’s job is to lift this
whole magnetic apparatus back up so that another wave can come along and press it
back down, creating an up and down motion which continuously generates
electricity.
These six steps in this order
explain just how it is that this generator both generates and distributes electrical
power.
