Video: Calculating Wave Frequency from Distance–Time Graph

What is the frequency of the wave shown in the diagram?

01:42

Video Transcript

What is the frequency of the wave shown in the diagram?

We see in this diagram this displacement in meters measured against time in seconds. And we see that that displacement follows a wave like pattern. It goes up then down, then back up to its original point. And at this point, the cycle begins again and the wave again moves up and then all the way down and then back up to its original displacement. Based on this information, we want to know what is the frequency of the wave.

To figure this out, we can recall the definition of frequency, that it’s the number of cycles that wave completes in a time of one second. Looking at our graph, there are a couple of different ways we can solve for this wave’s frequency. One method involves figuring out the amount of time it takes for the wave to go through one cycle, on our graph that looks to be 0.5 seconds, and then calculating frequency based on that.

But another method is to simply count the number of wave cycles that elapse in one second of time. And we see that that’s equal to two complete wave cycles. Where here, at the far-right edge of our horizontal axis, we have one second of time elapsed. So, this wave goes through two complete cycles in one second of time. In other words, two complete movements from the wave moving up and then down past its original starting point then back up to that original displacement. That’s one wave of cycle.

Knowing that this wave finishes two cycles every one second of time, we can now recall that the unit cycles per second can be written another way. A cycle per second is equal to what’s called a hertz, abbreviated Hz. So, the frequency of this wave, we’ll call it 𝑓, is equal to two cycles per second, or two hertz. That’s the frequency of the wave shown in the diagram.

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