AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Properties of waves: period = 1 / frequency
The period T of a wave is the time taken for one complete wave cycle to pass a fixed point, measured in seconds (s).
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 5 of 18
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The period T of a wave is the time taken for one complete wave cycle to pass a fixed point, measured in seconds (s). Frequency f is the number of complete cycles passing a point each second, measured in hertz (Hz). Because period and frequency describe the same repeating event from opposite viewpoints, they are reciprocals: T = 1 / f, and rearranging gives f = 1 / T. For example, a wave of frequency 4 Hz repeats four times each second, so each cycle lasts 1 ÷ 4 = 0.25 s. A ripple with period 0.02 s has frequency 1 ÷ 0.02 = 50 Hz. Always convert milliseconds to seconds before substituting, and check that the answer is sensible: a high frequency means a short period.
What earns the marks
- State that period is the time for one complete wave cycle and is measured in seconds (s).
- State that frequency is the number of complete cycles per second and is measured in hertz (Hz).
- Select and apply T = 1 / f, or its rearrangement f = 1 / T, to calculate the unknown quantity.
- Substitute values with correct units, converting ms to s where needed, and give the answer with the correct unit.
- Interpret a numerical answer, for example recognising that 0.25 s corresponds to 4 Hz and that a shorter period means a higher frequency.
Common mistakes and how to put them right
Writing T = f or multiplying frequency by period.
Put it right by remembering the reciprocal relationship T = 1 / f.
Forgetting to convert milliseconds to seconds, for example using 20 instead of 0.020 s.
Put it right by dividing ms by 1000 before substituting.
Giving frequency in seconds or period in hertz.
Put it right by attaching s to period and Hz to frequency and checking the unit against the quantity.
Exam tips
- Write the equation, then rearrange it before substituting numbers so the calculation is clear and less error-prone.
- Show the substitution line, including units, because method marks are often available even if the final arithmetic slips.
- Sanity-check the answer: if frequency is large, the period must be a small fraction of a second, and vice versa.
Try the lesson
The start of the Properties of waves: period = 1 / frequency lesson, made from checked teaching notes for this specification point.
Have a go first
A sound wave has a frequency of 20 Hz. Use the equation period = 1 / frequency to calculate the period of the wave in seconds.
Listen
The period T of a wave is the time taken for one complete wave cycle to pass a fixed point, measured in seconds (s). Frequency f is the number of complete cycles passing a point each second, measured in hertz (Hz). Because period and frequency describe the same repeating event from opposite viewpoints, they are reciprocals: T = 1 / f, and rearranging gives f = 1 / T. For example, a wave of frequency 4 Hz repeats four times each second, so each cycle lasts 1 ÷ 4 = 0.25 s. A ripple with period 0.02 s has frequency 1 ÷ 0.02 = 50 Hz. Always convert milliseconds to seconds before substituting, and check that the answer is sensible: a high frequency means a short period. A strong answer earns marks for these points. State that period is the time for one complete wave cycle and is measured in seconds (s). State that frequency is the number of complete cycles per second and is measured in hertz (Hz). Select and apply T = 1 / f, or its rearrangement f = 1 / T, to calculate the unknown quantity. Substitute values with correct units, converting ms to s where needed, and give the answer with the correct unit. A common slip: Writing T = f or multiplying frequency by period. Instead, remembering the reciprocal relationship T = 1 / f. Exam tip: Write the equation, then rearrange it before substituting numbers so the calculation is clear and less error-prone.
See it
Key words
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period
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frequency
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reciprocal relationship
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unit conversion
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See every definition
- period
- The time taken for one complete wave cycle to pass a fixed point, measured in seconds (s).
- frequency
- The number of complete cycles passing a point each second, measured in hertz (Hz).
- reciprocal relationship
- Period and frequency describe the same repeating event from opposite viewpoints, so T = 1 / f and rearranging gives f = 1 / T.
- unit conversion
- Always convert milliseconds to seconds before substituting, dividing ms by 1000 before substituting.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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