Video Transcript
What is the frequency of the wave shown in the diagram?
Let’s begin by recalling that the frequency of a wave is the number of cycles it completes in one second. We can also recall that frequency is measured in units of hertz, which is equivalent to an inverse second because we’re telling how many times something happens per second. Now let’s take a closer look at this diagram. On the vertical axis, we have the displacement of a wave measured in meters, and the horizontal axis represents time in units of seconds. This diagram shows us the displacement of a wave over a time interval of one second. So if we count its number of full cycles over that one second, we’ll be able to tell its frequency.
We can start at the origin because at zero seconds the wave has no displacement. It’s in its equilibrium position. As time goes on, we see the wave rise to a crest, fall down to a trough, and then rise back to the equilibrium position. What we’ve highlighted here in pink constitutes one full cycle of the wave’s motion, and it happened over a time period of a half a second. And now, as we look at what happens in the remaining half a second, the wave completes one more full cycle. This makes for a total of two cycles per second. And because hertz is equivalent to per second, we can just say that the frequency of the wave shown in the diagram is two hertz.
