Properties of waves: period, T, in seconds, s

The idea

The period, T, is the time taken for one complete wave cycle to pass a fixed point, or for one point on the wave to complete one full oscillation. It is measured in seconds, s. For example, if a wave crest passes a marker every 0.25 s, then T = 0.25 s. The period links to frequency by T = 1 ÷ f, so a wave with f = 4 Hz has T = 1 ÷ 4 = 0.25 s. On a displacement–time graph, T is the horizontal distance between two identical points on consecutive cycles, such as crest to crest. On a displacement–distance graph, the horizontal distance between identical points gives wavelength, not period, so always check the axis label before reading T.

What earns the marks

• States that the period is the time for one complete wave cycle or one full oscillation.
• Gives the unit of period as seconds, s, and uses it correctly in calculations.
• Reads T from a displacement–time graph as the time between identical points on consecutive cycles.
• Uses the relationship T = 1 ÷ f correctly, including choosing the appropriate rearrangement.
• Distinguishes period from wavelength by checking whether the horizontal axis is time or distance.

Common mistakes and how to put them right

• Confusing period with wavelength.

  Put it right: Period is a time in seconds, while wavelength is a distance in metres.

• Using T = f instead of T = 1 ÷ f.

  Put it right: Period and frequency are reciprocals, so T = 1 ÷ f.

• Counting from a crest to the next trough as one cycle.

  Put it right: Measure between identical points, such as crest to crest or trough to trough.

Exam tips

• Check the horizontal axis label first: if it is time in s, the repeat distance is the period; if it is distance in m, it is the wavelength.
• When using T = 1 ÷ f, write the rearranged equation before substituting numbers so the reciprocal is clear.
• Give the unit s with every period value, and check that a calculated period is smaller than 1 s when the frequency is greater than 1 Hz.