Which effect shifts light frequency because of relative motion in special relativity?

The relativistic Doppler effect shifts light frequency because of relative motion in special relativity.

It extends the familiar Doppler effect to situations where speeds are significant compared with the speed of light. An approaching source and observer measure a higher frequency, called a blueshift; a receding pair measure a lower frequency, called a redshift. Unlike the ordinary sound-wave Doppler effect, the calculation does not use a stationary medium as a reference.

The relativistic formula includes time dilation through the Lorentz factor, reflecting that moving clocks run differently relative to an observer. For motion directly along the line of sight, the frequency ratio involves the factor √((1−β)/(1+β)), where β is speed divided by the speed of light. At right angles, special relativity predicts the transverse Doppler effect, a shift associated with time dilation.

A common mix-up is confusing this effect with gravitational redshift or cosmological redshift. Those also change observed light frequency, but arise from gravity or the expansion of space rather than ordinary relative motion. Christian Doppler first described the classical effect in 1842; Einstein’s 1905 theory supplied the relativistic treatment.