The frequency of a wave is the number of waves passing a point each second.

The idea

Frequency counts how many complete waves pass a fixed point every second. One complete wave is one full cycle, such as crest to crest or compression to compression. The unit is the hertz, Hz, where 1 Hz means one wave per second. If 30 waves pass a point in 6 s, the frequency is 30 ÷ 6 = 5 Hz. Frequency is linked to time period by f = 1 ÷ T, where T is the time for one complete wave in seconds. It also links to wavelength and wave speed through v = f λ. Frequency depends on the source of the wave, not on the speed of travel, so a wave keeps the same frequency when it enters a new medium even if its speed and wavelength change. On a displacement–time graph, frequency is the number of complete cycles each second.

What earns the marks

• Frequency is the number of complete waves passing a fixed point each second.
• The unit of frequency is the hertz, Hz, where 1 Hz equals one wave per second.
• Frequency can be calculated by dividing the number of waves counted by the time taken in seconds.
• Frequency is the reciprocal of the time period: f = 1 ÷ T, with T in seconds.
• Frequency is related to wave speed and wavelength by v = f λ.
• When a wave crosses into a new medium, its frequency stays the same because it is set by the source.

Common mistakes and how to put them right

• Counting part of a wave as a whole wave.

  Put it right: Count only complete cycles, for example crest to crest, and correct by marking one full cycle before counting.

• Using the time for one wave as the frequency.

  Put it right: The time for one wave is the period T, so the correction is to use f = 1 ÷ T.

• Forgetting to convert milliseconds or minutes to seconds.

  Put it right: Divide or multiply as needed so that time is in seconds before calculating frequency.

Exam tips

• Write down the number of waves and the time in seconds separately before dividing, so the calculation is clear.
• Check whether the question gives the time period; if it does, use f = 1 ÷ T rather than counting waves.
• Give the unit Hz with your answer, and use standard form for very large or very small frequencies.