When a source of waves moves relative to an observer, the observed wavelength and frequency change: the Doppler effect. If the source moves away, the waves are stretched out, so the observed wavelength increases and the frequency decreases. If it moves towards the observer, the wavelength decreases.For light, an increase in wavelength shifts spectral lines towards the red end of the spectrum: red shift. A decrease is a blue shift.Astronomers compare the absorption lines in a star's or galaxy's spectrum with the same lines measured in the laboratory. The pattern of lines is the same, but shifted.
The red shift z is defined, for speeds much less than c, byz = Δλ/λ ≈ Δf/f ≈ v/c where Δλ is the change in wavelength, λ the laboratory (emitted) wavelength, v the speed of the source away from us and c = 3.00 × 108 m s−1.Worked example: a hydrogen line with laboratory wavelength 656.3 nm is observed at 662.9 nm in a galaxy's spectrum.z = (662.9 − 656.3) ÷ 656.3 = 0.0101 v = zc = 0.0101 × 3.00 × 108 = 3.0 × 106 m s−1 away from us The approximation only holds for v much less than c. Almost all galaxies show red shift, which means they are moving away from us.
The red shift z is defined, for speeds much less than c, by