Wave period

The period of a wave is the time it takes for one complete wave to pass a given point.

Essentially, it’s another way of measuring how often waves pass a point (the frequency), but instead of counting how many waves pass in one second, we measure how long it takes for one wave to pass.

Notation

We usually use the letter T to represent the period of a wave.

Why? Because, uh… it’s the first letter of “time”. Sure.

Units

The period is measured in seconds (s).

Calculating period

The period can be calculated using the formula:

\text{Period} = \frac{1}{\text{Frequency}}

Or, using symbols:

T = \frac{1}{f}

Where:

• T is the period (in seconds, s)
• f is the frequency of the wave (in hertz, Hz)

This, of course, relies on us knowing the frequency of the wave. If we don’t, we can calculate it using the formulae covered in the wave-frequency and wave-speed chapters.

Find the period of a wave with a frequency of 5 Hz.

• T=\frac{1}{f} (write our formula)
• T=\frac{1}{5} (substitute in the values)
• T=0.2 s (calculate)
• Answer: 0.2 seconds.

Find the frequency of a wave with a period of 0.1 seconds.

• T=\frac{1}{f} (write our formula)
• f=\frac{1}{T} (rearrange it)
• f=\frac{1}{0.1} (substitute in the values)
• f=10 Hz (calculate)
• Answer: 10 hertz.

Find the frequency of a wave that takes 2 seconds for 4 complete waves to pass a point.

• T=\frac{\text{Total time}}{\text{Number of waves}} (write our formula)
• T=\frac{2}{4} (substitute in the values)
• T=0.5 s (calculate period)
• f=\frac{1}{T} (write frequency formula)
• f=\frac{1}{0.5} (substitute in the values)
• f=2 Hz (calculate)
• Answer: 2 hertz.

Find the frequency of a wave that has a period of 25 milliseconds.

• 25 ms = 0.025 s (convert period to seconds)
• f=\frac{1}{T} (write our formula)
• f=\frac{1}{0.025} (substitute in the values)
• f=40 Hz (calculate)
• Answer: 40 hertz.

Relationship with frequency

The period is inversely proportional to the frequency of the wave - that means that, as frequency increases, period decreases.

For example, a wave with a frequency of 2 Hz has a period of 0.5 seconds (1/2), while a wave with a frequency of 4 Hz has a period of 0.25 seconds (1/4) - half.