Video Transcript
The diagram shows a transverse wave and highlights the wave’s wave fronts. The wave fronts shown without the wave can represent the wave. How many wavelengths of the wave separate each wave front from its nearest neighboring wave front?
Let’s take a closer look at this diagram. This red curve represents the transverse wave in a very typical manner. It’s continuously oscillating, like a regular sinusoidal waveform does. We can see it form crests and troughs. And because this wave represents regular periodic or repeating motion, we could draw in a horizontal line to represent the wave’s equilibrium position.
Notice that the wave has constant amplitude. So the crests and troughs all show the same magnitude of maximum displacement. However, these features aren’t immediately obvious when we look at the part of the diagram that only uses these vertical lines to represent the wave fronts. One way to think about these representations is that the red curve shows the wave as viewed from the side and the vertical lines show the wave as viewed from above.
We can get a better idea of how this works when we look at the middle part of the diagram, which shows the wave fronts along with the red continuous waveform that we’re so used to seeing. Notice that each wave front corresponds to or lines up with a single crest on the waveform.
Now, this question is asking us, how many wavelengths separate each wave front from the next one? To answer this, it will be helpful to recall that a wavelength is the distance covered by one full wave cycle. Wavelength is perhaps most commonly measured from trough to trough or crest to crest. In this diagram, because the wave fronts line up perfectly with the wave’s crests and because the distance between each successive crest constitutes a wavelength, we know that the wave is completing a full cycle between each wave front. There’s one wave front for every full cycle, so we know each wave front is separated by one wavelength. This is our answer.
It’s worth mentioning that, whether they line up with the wave’s crests, troughs, or any other feature, wave fronts should always be separated by only one wavelength. Thus, we know that one wavelength of the wave separates each wave front from the next.
