How to calculate period and frequency
The period of a wave is the time for one complete wave to pass a point. Frequency is the number of waves each second. They are reciprocals of each other:
period = 1 ÷ frequency
- T is the period in seconds (s)
- f is frequency in hertz (Hz)
UK mains electricity has a frequency of 50 Hz, so its period is 1 ÷ 50 = 0.020 s. Going the other way, a wave with a period of 0.25 s has a frequency of 1 ÷ 0.25 = 4.0 Hz.
On an oscilloscope trace, the period is the time across one complete cycle. Read it from the time axis, then use f = 1 ÷ T. Periods are often given in milliseconds: 2.0 ms is 0.0020 s.
Common mistakes that cost marks
- Not converting milliseconds. 2.0 ms is 0.0020 s.
- Mixing up period and frequency. A long period means a low frequency.
- Writing the unit of frequency as s. Frequency is in hertz (Hz); period is in seconds.
Practice questions
Try each one on paper first, then reveal the worked answer.
Q1UK mains electricity has a frequency of 50 Hz. Calculate its period.[2 marks]
- T = 1 ÷ f
- T = 1 ÷ 50
- T = 0.020 s
Q2A wave has a period of 0.25 s. Calculate its frequency.[2 marks]
- f = 1 ÷ T
- f = 1 ÷ 0.25
- f = 4.0 Hz
Q3An oscilloscope shows a wave with a period of 2.0 ms. Calculate its frequency.[3 marks]
- Convert: T = 2.0 ÷ 1000 = 0.0020 s
- f = 1 ÷ 0.0020
- f = 500 Hz
Endless practice
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Frequently asked questions
What is the equation for period?
Period = 1 ÷ frequency (T = 1/f). Period is in seconds (s) and frequency in hertz (Hz).
What is the period of a wave?
The time it takes for one complete wave to pass a point.
How do I find frequency from an oscilloscope trace?
Measure the time for one complete cycle (the period) using the time axis, then calculate f = 1 ÷ T.