Doppler effect

Physics · Wave behaviour. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

The Doppler effect is the change in the observed frequency of a wave when the source and the observer move relative to each other. Moving closer gives a higher frequency. Moving apart gives a lower frequency.

For sound, a moving source squashes the wavefronts in front of it, so the wavelength there is shorter, and stretches them behind. The speed of sound in the air does not change. A moving observer does not change the wavelength, but meets the wavefronts more or less often each second.

Light shows the same effect. A source moving away has its spectral lines shifted to longer wavelengths (redshift). A source moving towards us gives shorter wavelengths (blueshift).

Rules to remember

Common mistake

Students divide Δλ by the observed wavelength, or forget to say which way the source moves. Divide by the emitted (laboratory) wavelength, and state that a longer observed wavelength means the source is moving away.

Worked example

A spectral line has a laboratory wavelength of 400.0 nm. In the light from a galaxy it is observed at 402.0 nm. What is the speed of the galaxy relative to Earth, and which way is it moving? (c = 3.0 × 108 m s−1)

  1. Δλ = 402.0 − 400.0 = 2.0 nm. The observed wavelength is longer, so this is a redshift.
  2. Δλ ÷ λ = 2.0 ÷ 400.0 = 0.0050.
  3. v = c × (Δλ ÷ λ) = 3.0 × 108 × 0.0050 = 1.5 × 106 m s−1.

Answer: 1.5 × 106 m s−1, moving away from Earth

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