Video: Comparing Transverse and Longitudinal Waves

In this video, we will learn how to identify the differences and similarities between transverse and longitudinal waves in terms of amplitude, wavelength, and frequency.

16:18

Video Transcript

In this video, we will be looking at two different types of wave and learning about the similarities and differences between them. Now, we might have a very abstract idea of what a wave actually is. Maybe we think about it as a wobbly thing that moves in a certain direction, perhaps a way of transferring energy from one place to another. But in order to understand transverse and longitudinal waves, we first need to understand the general definition of a wave. Now, the key idea is that a wave is some sort of disturbance, maybe some sort of oscillations, that transfers energy from one point to another. But importantly, this is done without any net transfer of matter or of the stuff that the wave is travelling through.

Now, to understand this more clearly, let’s imagine we’ve got two people, Gary and Mindy, holding the two ends of a skipping rope. Now, they’re holding this rope taut. And Gary is going to send a wave along this rope. He does this by flicking the end of the rope that he’s holding upwards first and then downwards. Now, what Gary has just done is to provide some energy to the skipping rope. He’s also caused a disturbance in the rope because although, originally, the rope was stationary, he’s now caused a chunk of it to move upward and another chunk downward. In other words then, he is passing a wave along the length of this rope. And we see that as time progresses, this wave moves along the length of the rope. So it goes towards Mindy. And the wave itself, like we said earlier, is a transfer of energy from Gary down the rope towards Mindy. And Mindy will be able to feel this energy when the wave finally reaches her.

However, before we think about the wave actually reaching Mindy, let’s consider a certain chunk of the rope, let’s say this chunk of rope here. And let’s see what happens to that chunk of rope as the wave passes by it. Well, we see at this point in time, the chunk of rope is exactly where it was before when Gary hadn’t flicked the rope yet. In other words then, it’s in the same position as earlier. But as soon as the wave starts getting closer to it, we see that this chunk of rope is going to start moving. As the wave finally reaches that chunk of rope, we see that it moves upwards first, then back down to its original position where it was earlier. Then, it moves below its original position and then finally returns to its original position as the wave has passed it. And so what we’ve seen here is that as the wave moves in this direction, our green chunk of rope moves up and down about its original position.

So although our green chunk of rope does move around, there is no net motion of our green chunk of rope. It first moves up then returns to its original position, then moves down, and then returns to its original position again. So it just oscillates about its original position. And after the entire wave has passed, guess what? It’s back at its original position again. And so that’s how we see a transfer of energy from left to right without any net transfer of matter, where in this case matter is the stuff making up the rope. The rope itself is not moving from left to right. But there’s energy being transferred from left to right along the rope. So now that we understand this general property of waves, let’s look at different classifications of waves.

The two classifications of wave that we’re going to be looking at are called transverse waves and longitudinal waves. Now, both of these types of wave do transfer energy. But the key difference between transverse and longitudinal waves is the direction of oscillation of the medium or the stuff that the wave is travelling in, compared with the direction of the wave’s motion. Now, that sounds a little bit complicated. So let’s break it down.

Let’s start with transverse waves. Now, we’ve seen an example of a transverse wave already. The wave moving along our skipping rope from left to right is an example of a transverse wave. And the reason that it’s called a transverse wave is because as the wave itself moves from left to right, each little chunk of the skipping rope moves up or down about its original position. And if we were to have a continuous wave moving along this rope rather than just a single pulse, we would see that each little chunk of rope continues to move up and down and up and down and up and down. In other words then, the direction of oscillation of each chunk of the rope, of the medium that the wave is travelling in, is perpendicular to the direction in which the wave itself is travelling. Now, in this case, the wave is travelling left to right. And the direction of oscillation of each little chunk of the rope is up and down. Both of these directions are perpendicular to or at right angles to the direction in which the wave is travelling, which is left to right as we said earlier.

And so we can say that our definition of a transverse wave is that the direction of oscillation, so that’s the direction in which each little segment of our rope moves in this case, is perpendicular to or at right angles to the direction of motion of the wave itself. A good example of a transverse wave is light or any other form of electromagnetic radiation. This kind of radiation is created by the transverse motion, up and down motion in this case as we’ve drawn it, of electric and magnetic fields. So the energy can propagate either left to right or right to left as we’ve drawn it.

So from looking at light waves, let’s now consider sound waves. Sound waves are a kind of longitudinal wave. In this kind of medium, if the wave is travelling toward the right, then the oscillations of the medium are actually back and forth, parallel to the direction in which the wave is travelling, unlike a transverse wave where the oscillations are perpendicular to the direction of the wave’s travel.

Now, sound waves are oscillations of air particles or of course oscillations of the medium that they’re travelling in. But most commonly, we think about sound waves travelling in air. So let’s imagine that all of these are particles of air. Now, when a sound wave passes through this region, what we see are regions of high air particle concentration, known as compressions, and regions of low particle density, known as rarefactions. And as the wave propagates from left to right, each compression region and rarefaction region moves towards the right as well. However, if we were to focus on one particular particle out of these air particles, then we would see that as the wave moves left to right, the particle itself only oscillates back and forth, left to right and right to left. And once again, it oscillates about its original position, just like this chunk of rope did when we were considering transverse waves.

And so coming back to longitudinal waves, what we see is that every particle oscillates backwards and forwards, left to right and right to left, about its original position whilst the wave itself moves left to right as we’ve drawn it. And so we can say, for longitudinal waves, that the direction of oscillation is parallel to the direction of motion of the wave. And so at this point, we’ve seen the difference between transverse and longitudinal waves. In transverse waves, the direction of oscillation is perpendicular to the waves’ direction of motion whereas, for longitudinal waves, it’s parallel to the waves’ direction of motion.

Now, we’ve already seen that, for longitudinal waves, the areas of high concentration are known as compressions. And the areas of low concentration are known as rarefactions. Well, we can also remember that, for transverse waves, if we draw in a dotted line to represent the medium’s original position before the wave even came along, then we can say that the medium’s maximum displacement, away from this original equilibrium position in the positive direction or the upper direction as we’ve drawn it, is known as a peak or a crest whereas the maximum displacement in the opposite direction, so in the negative direction. Well, that region of the wave is known as a trough. And so we can use the words peak or crest and trough to describe transverse waves. And we can also use compressions and rarefactions to describe longitudinal waves. However, there’re some more general terms that can be used to describe both kinds of waves, for example, words such as wavelength.

Now, the wavelength of a wave, whether transverse or longitudinal, is defined as the distance covered by one full cycle of the wave. So for a transverse wave, a full cycle could, for example, start here and then go all the way up, come back to zero, and then go all the way back down and return to this position here. In other words, this point here and this point here are two exactly equivalent points, because both of these points are at the equilibrium position of the wave. And as we move towards the right from both points, the displacement of the wave is increasing. And so between this point and this point, the wave has completed one full cycle. Therefore, the wavelength, which we can call 𝜆, is the shortest distance between these two points. And so that’s how we work out the wavelength of a transverse wave.

Conversely, we could say that the wavelength of a transverse wave is the distance between two adjacent peaks or two adjacent troughs, in other words, maybe the distance from here to here, because, remember, the wavelength is the distance covered by one full cycle of the wave. And that distance from here to here happens to be the same as this distance that we’ve labelled here. So this distance is also the wavelength.

And then, for a longitudinal wave, a full cycle of the wave contains one compression and one rarefaction. So we could define the wavelength of a longitudinal wave as the distance between the start of one compression region and the start of the next compression region, because then that region contains one compression and one rarefaction. Or conversely, an easier way to measure this is the distance between the center of one compression region and the center of the next, because that distance is the same as the one we’ve labelled here. And both of the orange distances are 𝜆, the wavelength of a longitudinal wave. So we can use the word wavelength to describe something about both transverse and longitudinal waves.

Now, let’s look at another word that we can use to describe certain properties of both kinds of wave. That word is amplitude. Well, the amplitude of a wave is the maximum possible displacement of the medium that it’s oscillating in. So for the transverse case, if we’re considering a wave on a string, then the medium that’s oscillating is the string itself. And the maximum possible displacement that this medium can have is the maximum possible distance between its equilibrium position, the position it was at before the wave came along, and the position it gets to, whilst oscillating. In other words then, the distance between the equilibrium position or its original position and a peak or the distance between the equilibrium position and a trough, both of which are the same distances, are known as the amplitude, which we will call 𝐴. So once again, the amplitude is the maximum possible displacement of the oscillating medium.

Now, for a longitudinal wave, it becomes a little bit trickier, because, remember, the oscillations of the medium are back and forth, parallel to the direction in which the wave is moving. So let’s say that the particle that we’ve labelled is currently in the position that it started out at before the wave came along. Well then, in that case, the amplitude of the longitudinal wave is the maximum possible displacement of that particle in one direction, in other words, the distance between its original position and its maximum possible displacement, which is here, or equally the distance between its equilibrium position and the maximum possible displacement in the other direction. Both of these distances are the same. And they are known as the amplitude of the longitudinal wave. And we can see some parallels between transverse and longitudinal waves here. We can see that the amplitude is measured as the distance between the positions of the particles or the medium before the wave came along or when the wave wasn’t even there and the point at which the medium goes to when it’s at its maximum displacement. So now, we’ve looked at a second word that can be used to describe properties of both transverse and longitudinal waves.

Now, there is one more word that we’re going to look at. And that word is frequency. Now, the frequency of a wave is defined as the number of full wave cycles passing a point per unit time, for example, per second. In other words, we know that, in both cases, the way that we’ve drawn these waves here, they’re moving from left to right. And so for the transverse wave, for example, at one moment in time the wave is here. But after a certain amount of time, every bit of the wave has moved slightly towards the right. It is propagating towards the right. In other words then, this peak has moved from here to here. And this midpoint has moved from here to here and so on and so forth. And so if we were to place an observer, for example, here, there’s the eyeball looking down at the wave, and they were to count at this position in space, the number of full cycles of the wave passing per second or per minute, for example, then they would be able to calculate the frequency of the wave.

Now, one easy way to do this would be to count the number of peaks passing per second or equivalently the number of troughs passing per second or, of course, the number of any particular point along the cycle passing per second. But it’s most easily done with peaks or troughs. And similarly, for longitudinal waves, we could place an observer here. And they could count the number of compressions passing by that point every second or every minute. And this would also tell them the frequency of the longitudinal wave. And so at this point, we’ve looked at three different words to describe the properties of transverse and longitudinal waves, the wavelength of a wave, the amplitude of a wave, and the frequency of a wave. As well as this, we’ve looked at similarities and differences between transverse and longitudinal waves as well as their main properties, which define what they actually are. So with all of that being said, let’s take a look at an example question.

A transverse wave consists of individual particles that might possibly move in the directions A, B, C, and D shown in the diagram. Which of the following directions can the yellow particle move in as the wave travels to the right?

Okay, so in this diagram, we can see that we’ve got a bunch of blue particles that are all oscillating as a wave travels from left to right. Now, in this question, we’re focusing on this yellow particle in the middle. We’ve been asked to find which of the directions, A, B, C, or D, the yellow particle can move in as the wave moves from left to right. And importantly, we’ve been told that this wave is a transverse wave.

Now, we can recall that, for a transverse wave, the direction of oscillation is perpendicular to the direction of wave propagation, where in this case the direction of oscillation is referring to the direction in which all of these blue dots can move. And the direction of wave propagation is the direction in which the wave moves, in this case from left to right. So if the wave can move left to right and the direction of oscillation of each one of these dots is perpendicular to this or, in other words, at right angles to this, then each one of these dots can move in either the upward direction or the downward direction, because both the upward direction and the downward direction are perpendicular to, at right angles to, the direction at which the wave is moving. And so we can see that the yellow particle in question can move in the direction A or the direction C.

Now, we can see that this diagram is basically a snapshot of the wave moving through space. However, if we were to look at the same wave a little time later, then we would see that the wave has moved forward a little bit. And the reason that this has happened is because say, for example, this particle has moved down. This particle has also moved down. This one has move down. This one has moved down a bit. This one has moved up slightly. This one has moved up and so on and so forth. So we can see how particles oscillate up and down in order for the wave to move from left to right. And so that just confirms the answer that we arrived at earlier. The direction that the yellow particle can move in as the wave travels to the right is direction A and direction C. Okay, so now that we’ve looked at a question about transverse waves, let’s take a look at a question about longitudinal waves.

A longitudinal wave consists of individual particles that might possibly move in the directions A, B, C, and D shown in the diagram. Which of the following directions can the yellow particle shown in the diagram move in as the wave travels to the right?

Okay, so in this question, we’ve got these blue particles that make up some medium. And this medium is carrying along a longitudinal wave travelling from the left to right. Additionally, we’ve been asked to consider this yellow particle in particular. We need to work out which of the directions A, B, C, and D can this yellow particle move in. Now, to answer this question, we need to recall that, for longitudinal waves, the direction of oscillation is parallel to the direction of wave propagation, where the direction of oscillation is referring to the direction in which these particles can move as the wave passes through the medium made up by these particular particles. And the direction of wave propagation is simply the direction in which the wave is moving, in this case left to right.

So if the wave is moving left to right and the particles can move in any direction parallel to this, then the particles themselves could move left to right or right to left. In other words then, they can move in the direction B or in the direction D. Now, an easy way to remember that for longitudinal waves, those are the possible directions of oscillation, is to remember that, in a longitudinal wave, the particles move along the same direction as the wave itself. And hence, we’ve found the answer to our question. The directions in which the yellow particle can move as the wave travels to the right is direction B and direction D. Okay, so now that we’ve had a look at a couple of example questions, let’s summarise what we’ve talked about in this lesson.

We firstly saw that waves transfer energy from one region to another, without any net transfer of matter or the medium through which they are travelling. We also saw that, in transverse waves, the direction of oscillation of the medium, that is, the medium through which the waves are travelling, is perpendicular to the direction of the wave motion, whereas for longitudinal waves, the direction of oscillation of the medium is parallel to the direction of wave motion. And finally, we saw that properties that could be found for both kinds of waves were their wavelength, amplitude, and frequency.

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