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.