The wavelength of a wave is the distance from a point on one wave to the…

The idea

Wavelength measures the repeat distance of a wave. Choose any point on one wave, such as a crest, then move to the same point on the next wave; the straight-line distance between them is the wavelength. On a displacement–distance graph, read the horizontal separation between successive crests or successive troughs. For a transverse wave, crest-to-crest or trough-to-trough both work; for a longitudinal wave, use the distance between successive compressions or successive rarefactions. Wavelength is a length, so it is measured in metres, often with prefixes such as cm, mm or nm. It is not the distance from a crest to the next trough, and it is not the amplitude, which measures displacement from the rest position. In the wave equation v = f λ, wavelength is the symbol λ and must be in metres when speed is in m/s and frequency is in Hz.

What earns the marks

• Wavelength is the distance between equivalent points on adjacent waves, for example crest to crest or trough to trough.
• Equivalent points must be at the same stage of the wave cycle, such as two successive compressions in a sound wave.
• Wavelength is a length, so the SI unit is the metre, with cm, mm and nm used for shorter waves.
• Wavelength is not the distance from a crest to a trough, and it is not the amplitude of the wave.
• On a displacement–distance graph, wavelength is the horizontal distance for one complete cycle.
• In v = f λ, λ is the wavelength in metres when v is in m/s and f is in Hz.

Common mistakes and how to put them right

• Measuring from a crest to the next trough.

  Put it right: This gives half a wavelength, so the correction is to measure between successive crests or successive troughs.

• Confusing wavelength with amplitude.

  Put it right: Amplitude is the maximum displacement from the rest position, whereas wavelength is a distance along the direction of travel.

• Using the wrong unit or mixing prefixes.

  Put it right: Convert cm, mm or nm to metres before substituting into v = f λ.

Exam tips

• Mark two equivalent points clearly on the diagram, such as two crests, before reading the scale.
• Check the axis label and unit on a graph; if the horizontal axis is in cm, convert your answer to metres when the question requires SI units.
• For a longitudinal wave, count compressions or rarefactions rather than crests, because crests are not visible on a compression wave.