The period is 1/5 second, and the frequency is 5 Hz.
Explanation:
Let's start by reviewing some definitions about waves:
- The period of a wave is the time taken for the wave to make one complete cycle. It is indicated with T and it is measured in seconds (s)
- The frequency of a wave is the number of complete cycles made by the wave in one second. It is indicated with f and it is measured in Hertz (Hz). It is equal to the reciprocal of the period:
![f=\frac{1}{T}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B1%7D%7BT%7D)
where f is the frequency and T is the period.
In this problem, we have a wave that passes a given point five time per second. This means that the number of oscillations per second is five, and so its frequency is:
![f=\frac{5 cycles}{1 sec}=5 Hz](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B5%20cycles%7D%7B1%20sec%7D%3D5%20Hz)
It follows than the period of the wave is:
![T=\frac{1}{f}=\frac{1}{5}s](https://tex.z-dn.net/?f=T%3D%5Cfrac%7B1%7D%7Bf%7D%3D%5Cfrac%7B1%7D%7B5%7Ds)
Therefore, the correct statement is
The period is 1/5 second, and the frequency is 5 Hz.
Learn more about waves, frequency and period:
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