Question

frequency and wavelength quick check 1 of 51 of 5 items question what is the period of a wave with a wavelength of 8 cm and a frequency of 0.5 hertz?

Answer 1

`2\; {\rm s}`.

Step-by-step explanation:

The frequency
`f` of a wave is the number of cycles completed in unit time.

In this question, it is given that the frequency of the wave is
`f = 0.5\; {\rm Hz} = 0.5\; {\rm s^(-1)}`. Thus, on average,
`0.5` cycles of this wave are completed in every second.

The period
`T` of a wave is the time it takes to complete one cycle of the wave.

For example, if
`(\text{number of cycles})` of cycles are completed in a certain
`(\text{duration})`, the time it takes to complete each cycle would be:

`\displaystyle T = \frac{(\text{duration})}{(\text{number of cycles})}`.

From the frequency of this wave,
`0.5` cycles are completed on average in
`1\; {\rm s}`. Thus,
`(\text{duration}) = 1\; {\rm s}` while
`(\text{number of cycles}) = 0.5`. The time it takes to complete each cycle would be:

`\begin{aligned}T &= \frac{(\text{duration})}{(\text{number of cycles})} \\ &= \frac{1\; {\rm s}}{0.5} \\ &= 2\; {\rm s}\end{aligned}`.

In general, the period of a wave is the reciprocal of frequency:

`\begin{aligned} T = (1)/(f)\end{aligned}`.

For the wave in this question:

`\begin{aligned} T &= (1)/(f) \\ &= \frac{1}{0.5\; {\rm Hz}} \\ &= \frac{1}{0.5\; {\rm s^(-1)}} \\ &= 2\; {\rm s}\end{aligned}`.