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 question we’ve been given a transverse wave. The diagram also shows the particles that move in order to make up this wave. We’re asked to find out which of the directions the yellow particle can move in, 𝐴, 𝐵, 𝐶, or 𝐷.
We’re also told that the wave travels to the right. So what we can do is to draw another diagram on top of the one that we’ve been given, showing what the wave looks like a few seconds later, basically when it’s moved a little bit to the right. So let’s say that this peak of the wave has moved a little bit to the right.
Let’s say that the peak now corresponds to this particle here. And so that particle has moved in this direction. So here, we’ve drawn a subset of the particles showing what the wave looks like a few seconds later. We can see that this peak as we said earlier has moved to the right and so has, for example, this trough.
And in general, the pink wave is the wave a few seconds later and it’s traveled to the right. However, as we can see from all the dotted lines, the particles actually haven’t moved left or right. They’ve only moved either up or down, because this particle has moved up now, so has this one, so has this one, so has this one.
This one’s moved down. That one’s moved down, and so on and so forth. We’ve been asked to find out what happens to the yellow particle. Now the yellow particle specifically is not special in any way in that it behaves in exactly the same way as all the other blue particles around it.
And as we’ve already, seen the blue particles only move up or down and so does the yellow one. In this diagram, we can see that it’s moved down. But as the wave continues to travel, it will move up as well. And hence, the only two directions that the yellow particle can move in is 𝐴 and 𝐶, upwards or downwards.
And this perfectly represents the behavior of a transverse wave. A transverse wave is called a transverse wave in the first place because the direction of the travel of the wave is transverse to the direction of motion of the particles that move.
Transverse basically means 90 degrees to. So if the wave is moving to the right, then the particles will move in the transverse direction, up or down. And so our final answer is that the yellow particle can move in the directions 𝐴 and 𝐶.