A transverse wave is shown in the diagram. What is the wavelength of the wave?
To begin, let’s recall that the wavelength of a wave is the distance covered by one full cycle. We can think of the wavelength as the distance between consecutive troughs or crests. Really, we can measure wavelength using any two successive points on the waveform, so long as the wave has completed a full cycle between those points.
Looking at the wave in the diagram, we see its displacement plotted as a function of distance. So we can use the vertical axis to identify successive points in the wave cycle and the horizontal axis to measure the distance between those points. There are several different features on the waveform that could help us easily find the wavelength. For instance, we could measure from crest to crest. And finding the difference between these two points on the horizontal axis means subtracting one meter from five meters.
Alternatively, we could measure from trough to trough. And finding the difference between these points on the horizontal axis means we’ll be subtracting three meters from seven meters. Because this is a regular sinusoidal wave with a constant wavelength, any method that we use is going to give us the same result, which comes out to four meters. Therefore, we’ve determined that the wavelength of the transverse wave shown in the diagram is four meters.