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8.6 Period and frequency (ESACP)

Imagine you are sitting next to a pond and you watch the waves going past you. First one crest arrives, then a trough, and then another crest. Suppose you measure the time taken between one crest arriving and then the next. This time will be the same for any two successive crests passing you. We call this time the period, and it is a characteristic of the wave.

The symbol $$T$$ is used to represent the period. The period is measured in seconds (s).

Period

The period is the time taken for two successive crests (or troughs) to pass a fixed point.

Quantity: Period ($$T$$)         Unit name: second         Unit symbol: s

Imagine the pond again. Just as a crest passes you, you start your stopwatch and count each crest going past. After 1 second you stop the clock and stop counting. The number of crests that you have counted in the 1 second is the frequency of the wave.

Frequency

The frequency is the number of successive crests (or troughs) passing a given point in 1 second.

Quantity: Frequency ($$f$$)         Unit name: hertz         Unit symbol: Hz

The frequency and the period are related to each other. As the period is the time taken for 1 crest to pass, then the number of crests passing the point in 1 second is $$\frac{1}{T}$$. But this is the frequency. So

$f = \frac{1}{T}$

or alternatively,

$T = \frac{1}{f}$

For example, if the time between two consecutive crests passing a fixed point is $$\frac{1}{2}\text{ s}$$, then the period of the wave is $$\frac{1}{2}\text{ s}$$. Therefore, the frequency of the wave is:

\begin{align*} f & = \frac{1}{T} \\ & = \frac{1}{\frac{1}{2}\text{ s}} \\ & = \text{2}\text{ s$^{-1}$} \end{align*}

The unit of frequency is the Hertz ($$\text{Hz}$$) or $$\text{s^{-1}}$$.

Worked example 3: Period and frequency

What is the period of a wave of frequency $$\text{10}$$ $$\text{Hz}$$?

Determine what is given and what is required

We are required to calculate the period of a $$\text{10}$$ $$\text{Hz}$$ wave.

Determine how to approach the problem

We know that:

$T = \frac{1}{f}$

Solve the problem

\begin{align*} T & = \frac{1}{f} \\ & = \frac{1}{\text{10}\text{ Hz}} \\ & = \text{0,1}\text{ s} \end{align*}

The period of a $$\text{10}$$ $$\text{Hz}$$ wave is $$\text{0,1}$$ $$\text{s}$$.