Wave motion: (d) the wave equation v = fλ

The idea

The wave equation links the speed of a wave to its frequency and wavelength: v = fλ. Speed v is in metres per second (m s⁻¹), frequency f in hertz (Hz), and wavelength λ in metres (m). Frequency is the number of complete oscillations per second, so f = 1/T where T is the period in seconds. Wavelength is the distance between two successive points in phase, such as crest to crest. For a sound wave of frequency 440 Hz travelling at 330 m s⁻¹, λ = v/f = 330/440 = 0.75 m. Rearranging gives f = v/λ and λ = v/f. When a wave crosses into a new medium its speed and wavelength change, but frequency stays constant because it is set by the source.

What earns the marks

• States the wave equation as v = fλ and identifies v as wave speed in m s⁻¹, f as frequency in Hz and λ as wavelength in m.
• Uses f = 1/T to convert between frequency and period before substituting into v = fλ.
• Rearranges correctly to f = v/λ or λ = v/f and substitutes consistent SI values.
• Explains that when a wave enters a new medium, frequency is unchanged while speed and wavelength change together so that v = fλ still holds.

Common mistakes and how to put them right

• Confusing wavelength with amplitude.

  Put it right: Wavelength is the crest-to-crest distance in metres, while amplitude is the maximum displacement from the rest position.

• Using frequency in kHz or wavelength in cm without converting.

  Put it right: Convert all quantities to SI units (Hz and m) before substituting.

• Assuming frequency changes when a wave refracts into a new medium.

  Put it right: The source fixes the frequency, so speed and wavelength change instead.

Exam tips

• Write the equation, rearrange symbolically, then substitute numbers with units to reduce arithmetic slips.
• Check that the calculated wavelength is sensible: for audible sound in air it is typically centimetres to metres.
• If a question gives the period rather than frequency, calculate f = 1/T first and show that step.