A transverse wave is shown in the diagram. What is the period of the wave?
To begin, let’s recall that the period of a wave is the time it takes to complete a cycle. This time period can be measured between consecutive features of the wave, like from trough to trough or crest to crest. We have to be careful though if we use the equilibrium position to measure a wave’s period, because if we measure from one equilibrium point to the very next, the wave has only had time to complete one-half of a cycle. Remember, the period measures the time taken to complete an entire cycle. So the wave needs time to oscillate in both directions before we call it a period.
Now, looking at this wave in the diagram, we see displacement graphed as a function of time. This means we’ll be using the horizontal axis to take a measurement of the wave’s period. Notice that at the vertical axis, which marks a time of zero seconds, the wave has zero displacement. Then, as time goes on, the wave oscillates in the positive direction before it reaches the equilibrium position again. But like we mentioned before, this only marks a half of one cycle.
To measure a complete period, the wave needs time to oscillate in both directions. The waveform, as we’ve drawn in orange here, has had time to oscillate in the positive and negative directions before returning back to the equilibrium position at a time of 10 seconds. Therefore, it takes 10 seconds for the wave to complete a full cycle. So the period of the transverse wave shown in the diagram is 10 seconds.