Lesson video

Hello, my name is Mr. Fairhurst.

This lesson is called Transverse Waves and it's from the unit Measuring Waves.

So in this topic, we're going to be using some important keywords that you need to be familiar with and you really need to know how to use them accurately in your descriptions of things.

You've probably seen some of these words before in your earlier work.

You may have used the words crest and trough to describe the shape of a wave.

You may have used the word wavelength and amplitude to describe waves.

We're going to use all of these words very specifically in relation to transverse waves today.

And in particular, we're going to focus on what we mean by this word displacement.

It's got a very particular meaning when it comes to thinking about transverse waves.

At the end of this lesson, you should be able to label all the parts of a transverse wave using those key terms accurately that I've just mentioned.

And you should also be able to interpret and sketch scale drawings of transverse waves.

And when I say scale drawings, what I really mean is displacement distance graphs, graphs that are drawn off the waves, but to scale.

Now the lesson's split into four parts.

The first couple of parts are going to be about labelling and describing transverse waves accurately and carefully.

And much of this we will be reviewing what ideas and understanding that you may already know and be familiar with.

But here we really need to make absolutely certain we've got a strong foundation of our understanding in order to take those ideas further.

And then the second part of the lesson is going to pick out what we mean by displacement, what we mean by amplitude and how we can represent transverse waves on displacement distance graphs.

So let's make a start by looking at how we're going to label a transverse wave.

When we think about waves, it's always important to remember that there are two types of wave.

We've got longitudinal waves and we've got transverse waves.

And I'm going to guess that the longitudinal wave that you are most familiar with is a sound wave.

But for now, let's focus our attention on transverse waves.

I'm gonna start by thinking very much about water waves.

Water waves are transverse waves and it's a really good example of a transverse wave because we can actually physically see what's going on.

We can examine how the water moves as the wave flows or moves across the surface of the water.

And rope waves are another sort of wave which you can see what is physically happening.

When I'm talking about a rope-wave, I'm sort of imagining two people holding either end of a long piece of rope and one of them shaking it side to side vigorously or up and down and sending a wave along the rope.

We can physically see what's happening to the rope as the wave moves along that.

Other types of transverse waves you might be familiar with are light waves, radio waves and S waves in earthquakes that shake you up and down or side to side as the earthquake passes by.

Now, as I said, water waves is a really good example of transverse waves 'cause we can see what's going on.

In a water wave, what's happening is that each little piece of water, each that little block of water, if you like, moving up and down.

It's oscillating or vibrating up and down, up and down, up and down, about a rest position as the wave passes forwards across the surface of the water.

And what we can do, we can imagine a rest position.

This is the level that the water would be at if it was completely still and flat.

And when there's a wave, the water's either moved up or down to create the shape of the wave.

So once the wave's moving forward, something is going forward with the wave, but it's not the water.

What's actually moving forward with the wave is energy.

Energy's being transferred by the wave.

I'll come back to that in just a moment.

Let's have a think about that by thinking about this little paper boat bobbing up and down on the wave.

As the wave moves past it, the boat would just bob up and down.

You've probably experienced this at the seaside when you've been out swimming and you stood in the waves and as the waves goes past, they push you up and down.

They don't throw you onto the beach.

And if you stood on the beach, the beach doesn't fill up with water.

What happens on the beach is that the waves start moving the sand or the pebbles where they hit the beach and the energy that they're transferring will be used to make those pebbles and stones and things move about on the beach.

So in essence, what we're saying here is that waves transfer energy forwards, but without transferring matter.

The way water wave will transfer energy forwards, but the water won't move with the wave.

Let's have a little check of what you've understood.

So have a look at this question here.

Which of the following is not an example of a transverse wave? Just pause the video for a moment to make your decision and then start it again when you are ready.

Okay, so I'm guessing that you've probably got the right answer, which is sound waves.

Sound waves are actually a form of longitudinal waves.

Water waves and light waves are both transverse waves.

What about this question? Again, just pause the video if you need to or as you think about your answer.

What is it that a wave transfers forward? Okay, what did you say? The correct answer is energy, but not matter.

A wave will transfer energy forwards, but the parts of the wave that are vibrating won't travel forwards with the wave.

We're going to now have a look at how we can describe waves and the parts of a wave.

So here's a pitch for wave and the rest position I've marked on as a faint dotted line in the middle.

The highest point on that wave is called a crest, or sometimes it's called the peak of the wave and the lowest part of the the wave is called a trough.

And on this diagram there are three crests and three troughs.

Here's a picture of a rope-wave.

And on this rope-wave, we've marked on the amplitude of the wave.

That is the maximum distance, the biggest distance that each part of the rope will move from its rest position as the wave goes past.

And as you can see, it's not the whole height of the wave, it's just the distance from where the rope would be if there was no wave on it.

So let's check you've understood that.

Again, pause the video if you need to.

But which arrow shows the amplitude of this wave? Okay, hopefully you got the right answer, which is B.

It's the distance the rope is with the maximum distance the rope has moved from where it would be if there was no wave at that point.

Here's another question for you.

Which arrow or arrows show the amplitude of this wave? And the answer is A, the distance it's moved from its rest position, but it's also answer D 'cause the the amplitude could be measured in whichever direction the part of the wave has moved away from its rest position.

Here's another thing that we can label on the wave and this is the wavelength.

The wavelength is the distance between two crests, the length, if you like, of the wave between two different crests.

And it can also be the distance between two troughs or between any two identical points.

If you look closer, each of these arrows that I've drawn, they're all the same length.

So any point on a wave measured lengthways to the same point on the next wave gives you the wavelength.

So let's check you've understood that then.

Which of these arrows shows the wavelength of this wave? And the answer here is B.

It's not drawn from a crest or a trough, but it's drawn from the same point on one wave to the same point on the other way or the next wave there.

So that's the wavelength.

Which arrow or arrows on this diagram show the wavelength of the wave? And here the answer is all three.

They are all the same length.

They all measure the same wavelength.

So here's some practise for you.

You might like to use the worksheet if you have that to hand.

On the wave below, what I'd like you to do is to label a crest, a trough and the rest position, label the wavelength in three different places, so three different wavelengths and also label the amplitude twice into different places.

Make your labels nice and clear and use a ruler for all straight lines.

Just pause the video whilst you're doing that.

How did you get on? Let's have a look at the answers and then you can compare your answers with these ones.

The crest and the trough, well, there's three crests aren't there, all along each of the tops of the wave could be labelled.

So it doesn't matter which one you've chosen.

And the same can be said for the troughs.

The wavelengths can be from crest to crest, from trough to trough or from any point on one wave to the same point on the next one.

And again, I've just drawn three wavelengths.

So you can draw any number of different positions as long as you've got the same length each time.

Then the amplitude of each wave can be shown from the rest position to a crest or the rest position to a trough.

And there are several different positions you can draw those on this diagram.

So well done if you've got all of those accurately drawn and also if you've used a ruler and a sharp pencil.

We're now moving on to part two of the lesson in which we describe a transverse wave in more detail.

How exactly is this wave being produced? The person is moving that end of the rope up and down quickly to generate this up and down movement of the rope and then the wave is moving forwards along the rope towards the wall.

Now we're going to just be a bit careful here.

We're not going to keep going forever.

We'll just imagine the wave moving from the person to the wall to this point and not bouncing off the wall or reflecting off that 'cause that will complicate matters.

So the wave moves forwards.

In a transverse wave, the oscillations you'll have noticed are at right angles, at 90 degrees, or the (indistinct) is perpendicular to the direction in which the wave travels.

That's the direction of the wave going forwards and the vibrations are at 90 degrees to that.

It doesn't matter whether it's up and down or side to side, it's just 90 degrees from the direction of the wave.

And the vibrations as I mentioned, they're not always up and down.

They could be left and right or in any direction as long as it's at right angles to the direction that the wave is moving in.

So have you understood that? Which of the following correctly shows the relationship between the wave vibrations and the direction the wave is travelling in? You can pick all of these that are correct.

So again, pause the video if you need time to look at these and then start it again when you are ready.

Okay.

The first one, that's correct because the vibrations are up and down and the wave is travelling at 90 degrees.

In this case, it's travelling backwards to what we've seen waves travel so far, but that's fine.

Wave C is also correct.

The vibrations are up and down and the wave is travelling forward.

But in B, the vibrations shown are forwards and backwards in the same direction.

So that is not a transverse wave.

And what about this question? For transverse waves, the vibrations are what at right angles to the direction of wave travel? That's right.

They're always in the right angles to the direction of the travel.

The vibrations happen at 90 degrees to the direction that the wave is moving in.

Okay, have a little go at this task to practise what we've just been talking about.

Describe the properties of the rope-wave that make it a transverse wave and put as much detail in that as you can sensibly do so, but use nice, short, descriptive sentences.

And once you've done that on each of the waves, draw an arrow to show the direction the vibration is and another to show the direction that the wave is travelling in.

Just pause the video whilst you're doing that.

Okay, how have you got on? First of all, you were asked to describe the properties of the rope-wave that make it a transverse wave.

The rope-wave is moving forward, but each bit of the rope is moving up and down at right angles to the direction of transverse vibration at the right angles of travel.

And if you draw those vibrations onto these waves, the vibrations are at 90 degrees to the direction that the wave is travelling in each case.

So there's the vibration and there's the direction.

Okay.

You could of course have drawn the waves travelling the opposite direction and the vibration at the opposite end.

So now we've come to part three of the lesson in which we describe in much more detail what we mean by displacement.

Displacement when it's linked to a transverse wave is precise, specifically the distance that each part of the wave moves from its rest position as the wave passes.

And it's equal to zero as each of these points marked.

You can see the rest position drawn by a faint horizontal dotted line.

Under each of these points, the rope is actually in the same position that it was before the wave passed by.

So it's zero at these points.

However, at other points of the wave, the displacement is very different.

And these arrows show the displacement of the wave from its rest position at different points along its length.

These arrows, let's just go back a slide and look at the other ones.

These arrows that remain, these are the amplitudes, which is the maximum distance that each part of the wave moves from its rest position.

In other words, the amplitude is the maximum displacement.

So just a reminder, any distance that the wave has moved or part of the wave has moved from its rest position is a displacement and the maximum displacement is the amplitude.

So let's just check you've understood that.

Where is the displacement of this wave equal to zero? Because many of these letters as you think is appropriate and just pause the video if you need a little bit of extra time.

And the answer is A because the rope is in the same position as it was at rest and also D, in fact D, it's not even started to move yet.

What about this question? This is a different question.

Where is the amplitude of this wave equal to zero? And the answer is that it's not equal to zero anywhere.

This was a little bit of a trick question.

If you had in your mind the displacement, the displacement is zero at A and D, but the amplitude remember is the maximum displacement of the wave.

So the amplitude can never be equal to zero unless there is no wave whatsoever.

Let's have a go at this task then.

And again, just pause the video whilst you do the task and then start again when you finished.

Okay, how did you get on? On part A, on the wave below, you are asked to add a line to show the same route with no wave.

Here is the dotted blue line.

Whoops.

Let's go back again.

Here it's the dotted blue line, the rest position.

That will be the rope when it's pulled nice and tight and there's no wave moving along it.

And the blue arrows represent all of the different amplitudes that you could have.

So any two of those, the maximum displacement are the amplitudes.

And then for part B, you are asked what you think a common mistake made when measuring the amplitude might be.

And the most common one is to measure the whole height of the wave right from the top of one crest down to the bottom of a trough.

That's not right.

The amplitude is the height of the wave or the distance the wave has moved or part of the wave has moved away from its rest position.

The maximum distance part of the rope has moved away from its rest position.

And part C, why is the amplitude often difficult to measure? It's because it's not always clear where the rest position is.

However, one little trick that you might like to use is that the amplitude is equal to half the distance between the trough and the peak.

So if you measure the whole height of the wave from the bottom of the trough to top of the peak, the rest position is always halfway between those.

So the amplitude is half of that peak to trough distance.

So that might be a little shortcut that you can use when you're answering these questions in an exam perhaps.

That brings us onto the final section of this lesson, displacement distance graphs.

Here's a picture of a water wave, transverse wave with the water vibrating or oscillating up and down as the wave moves forwards, perhaps from left to right in this case.

There we go.

There's the arrow to show that that's what I meant in the first place.

The displacement of the water is the distance part if the water's moved from its rest position.

So we've added the rest position for the still water with no wave in the dash line there.

And the displacement distance graph is an accurate representation of the wave.

That's an accurate representation, but this is not a picture of the wave.

There's a graph with the wave that it represents.

So you've got a water wave which is quite a shallow wave with quite a long wavelength.

Can only just about make out that there's a wave on that water, but the graph shows very clearly the same wave.

The reason it's a different shape is because the scale of the displacement and the scale for distance are both different and they've been changed to make the wave nice and clear to see.

So the graph is not a photograph of the wave, it's a representation.

It shows the wave, but it's not the same shape.

So this is a little check for you.

A student makes a wave with a rope.

And you can see the student making the wave there by vibrating the rope up and down.

And his friends have drawn this graph to represent the wave.

It's a displacement distance graph.

How is the graph related to the rope-wave? There's three statements.

I want you to pause the video in a moment and then for each statement decide whether you are sure it's right, you are sure it's wrong, or if you're not completely sure.

If you think it's more likely to be right, if not, you can tick the second box along.

And if you think it's more likely to be wrong than not, you can tick the third box slot.

And I want you to tick three boxes, one for each row.

So just pause the video and do that.

How did you get on? Well, the first statement, the graph shows the position of all the rope and the wave in one instant.

Yes, that's right because the graph shows the distance along the whole rope on the horizontal axis and each point it shows where the rope is.

Statement B is the graph in the exact shape of the rope.

Now, of course, it's not because it's been (indistinct) the scale of the displacement is much bigger than the scale of the distance, which makes the graph of the wave seem a lot taller than the actual wave.

And you can see that if you compare the two diagrams. What about statement C? The displacement is the distance of the rope above the ground.

Now that's wrong again.

It's the displacement is the distance the rope has moved from its rest position.

So that's not the ground.

It's not been, didn't start resting on the ground.

Let's have a look at this example.

Then let's have a look at a graph of the wave and see if we can interpret the graph to take some measurements of the wave 'cause that's really why we draw these graphs, so we can actually examine the wave in much more detail.

So in this question, what is the wavelength of the wave? The way we do that is we mark on a wavelength, we draw dash lines or use a clear ruler to go down to the horizontal scale and take our measurements.

So one wavelength is between five metres and one metre and that gives us a wavelength of four metres.

So what I'd like you to do is pause the video, have a look at this graph and measure its wavelength.

So how did you get on? Let's have a look at second graph and do the same thing that we did last time.

So first of all, let's put on the wavelength and measure from crest to crest and see what the measurements are.

So there's that wavelength and if you draw the dotted lines down or use a clear ruler, you should be able to read the scale on the horizontal axis, which is 25 centimetres and five centimetres.

It's a bit more of a difficult scale than the first one, but there we go.

The one thing to note here is that the scale measurements have changed.

So it's now measured in centimetres rather than in metres and 25 take away 5 'cause it's a wavelength of 20 centimetres.

We can do the same thing for measuring amplitude of the wave.

So there's a wave, what's its amplitude? Or we can first of all draw on an amplitude and use a clear ruler or draw a line to the vertical scale and read off the distance, the amplitude which is simply three centimetres or more formally 3 takeaway 0, which is 3.

And you'll notice straight away that there's an error in this answer.

The displacement given up the side is in centimetres and the distance along the wave is in metres.

But this answer's been given in metres, which is wrong.

It should really have been put into centimetres.

So that's something to be very careful about with these graphs is that the scales on each axis could be different.

Have a go at this one yourself.

Make a note of the scales and measure the amplitude of this wave.

Just pause the video whilst you do so.

Okay, so how did you get on with that one? Let's draw the amplitude in.

It can be anywhere for any of the amplitudes.

There we go.

And reading across the horizontal scale, the amplitude is 35 and it's measured in centimetres.

So this time 35 centimetres with the correct units.

And finally, we can measure the displacement, the displacement at nine and a half metres along the wave.

So to do that we have to measure nine and a half metres along the wave and draw a line up to meet the wave and to meet the graph and to draw a horizontal line to the scale from there or simply use a clear ruler.

And here we find that the scale, if you look really closely, you can see that it's 2.

1.

And again, the scale here is in metres.

It should be centimetres and the answer should be 2.

1 centimetres.

This is me doing the slides quickly and making a silly mistake.

It's always worth double checking your answers after you've written them.

So again, pause the video and measure for yourself the displacement of this graph at a distance of five metres along it.

Okay, hopefully you've done that.

Now let's have a little look at five metres.

The displacement is three centimetres.

Again, I put the wrong units.

Hopefully you got the right units going up in centimetres.

So that's three centimetres for the displacement.

Here's a final practise task for you to have a go at this lesson.

Again, just read the task and pause the video whilst you do that.

Okay, so how did you get on? Let's take these one at a time.

So first of all, the wavelength.

I've drawn the wavelength here from the points where the wave has crossed the axis at zero.

So that's gone from zero to two metres.

This time I've got the units right, so that's two metres.

The amplitude is the maximum displacement of the wave at any point.

So we could draw it in there.

And if we measure across that comes to be seven centimetres for the displacement.

Make sure you get those correct units.

And then the displacement at different points along the wave at 2 metres is actually crossing the line, so it's displaying something.

It's going to be equal to zero.

At 4.

1 metres, that's little bit fiddly to do.

And you've got to be quite careful with your scales here.

But at 4.

1 metres, if you've got this correct, it comes back at 1.

6 centimetres.

On the scale there, there's eight small squares out of 10 to reach the two centimetre mark on the scale.

So 2 centimetres divided by 10 makes each tiny division equal to naught 0.

2 centimetres and eight of those gives you 1.

6 centimetres.

And at 5.

5 metres, we can draw the displacement on the graph and read off the scale.

And the reading off the scale here tells us that it's minus seven centimetres.

Now we often use negative displacement to indicate that the displacement is in the opposite direction.

So here what we've sort of said is that the displacement upwards is positive and the displacement downwards is negative.

And that brings us to the end of the lesson.

Apart from just to double check with a summary what it is that we've learned today.

So there's a picture of a transverse wave and the dotted line in the middle indicates the rest position, which is the position of the wave if there were no vibrations, in fact if there was no wave.

The top of the wave is called the crest.

The bottom of the wave is called a trough.

And the amplitude is a distance between the rest position and either a crest or a trough of the wave.

It's also equal to the maximum displacement of the wave.

And the wavelength is the distance between one wave trough or crest and the next, or in fact any point on the wave and the same point on the next wave.

In a transverse wave, we've seen that the oscillations or the vibrations are always at right angles to the direction in which the wave travels.

And we've seen that the displacement is the distance that any one part of the wave has moved away from its rest position.

Displacement is positive in one direction and it's negative in the other direction.

And the wave can be represented by a displacement distance graph that looks like this one in which we might exaggerate or increase the scale in one direction so we can see the wave more clearly.

So I hope you've enjoyed the lesson and you've learned sufficient to form a good foundation for the rest of this unit.