Properties of waves: All waves obey the wave equation:

The idea

The wave equation links wave speed, frequency and wavelength: v = f λ. Wave speed v is measured in metres per second (m/s), frequency f in hertz (Hz) and wavelength λ in metres (m). Frequency is the number of complete waves passing a point each second, while wavelength is the distance between two identical points on adjacent waves, such as crest to crest. For example, a wave with frequency 50 Hz and wavelength 2 m has speed v = 50 × 2 = 100 m/s. The equation applies to all waves, including sound, water and electromagnetic waves. Rearranged forms are f = v ÷ λ and λ = v ÷ f, which are useful when speed is known and either frequency or wavelength must be found.

What earns the marks

• Recall and write the wave equation as v = f λ, identifying each symbol and its unit.
• Substitute numerical values correctly into v = f λ, converting units such as cm to m or kHz to Hz where needed.
• Rearrange the equation to find frequency (f = v ÷ λ) or wavelength (λ = v ÷ f).
• Apply the equation to a range of waves, including sound, water ripples and electromagnetic waves.
• Interpret a wave graph or measurement to obtain frequency and wavelength before calculating speed.

Common mistakes and how to put them right

• Mixing up frequency and wavelength in the equation.

  Put it right by remembering f is the number of waves per second and λ is the length of one wave.

• Forgetting to convert units, for example using 500 Hz with 20 cm.

  Put it right by converting 20 cm to 0.20 m before multiplying.

• Writing the equation as v = f ÷ λ.

  Put it right by checking that multiplying frequency by wavelength gives a sensible speed in m/s.

Exam tips

• Always write the equation first, then substitute values, so method marks can be awarded even if the final answer is wrong.
• Check that your answer has the correct unit: speed in m/s, frequency in Hz, wavelength in m.
• For rearrangement questions, use a formula triangle or rearrange step by step to avoid errors.