Video Transcript
What is the frequency of the wave shown in the diagram?
Let’s begin by recalling that the frequency of a wave measures the number of cycles that completes in one second. Now, in this diagram, we have a wave plotted on a displacement–time graph. So, at a given moment, we’re able to tell where the wave is in its cycle. But notice that if we check on the wave at a time of one second, it’s not even close to having completed a full cycle. Rather, the wave starts at equilibrium at a time of zero seconds. And by the time it actually completes a cycle, 10 seconds have passed. This is very useful information.
Recall that the time it takes for a wave to complete one cycle is known as its period, represented by 𝑝. So we know that for this wave, 𝑝 equals 10 seconds. Now, let’s also recall that we can relate the period of a wave to its frequency 𝑓 using the formula 𝑓 equals one divided by 𝑝. Since we already have a period value in SI units of seconds, let’s go ahead and substitute it into the formula, which gives 𝑓 equals one divided by 10 seconds.
At this point, it’s helpful to remember that the unit of frequency, hertz, has base SI units of inverse seconds. So another way to write our expression for frequency is one divided by 10 inverse seconds, or hertz. And finally, we can choose to write this value as a decimal rather than a fraction. So we have 0.1 hertz. This is the frequency of the wave shown in the diagram. And as a brief side note, we can refer back to this written definition of frequency and see that at a time of one second, the number of cycles the wave had completed is in fact one-tenth, since it has a period of 10 seconds.
