Doppler Effect
The change in the observed frequency of a wave when the source and the observer move relative to each other.
The Doppler effect is the apparent change in frequency of a wave when the source and the observer move relative to one another. It was proposed by Christian Doppler in 1842 and applies to all waves — sound, light, and water. When the source approaches, the waves ahead are compressed, so the observer hears a higher pitch; when it recedes, the waves stretch and the pitch drops. This is why an ambulance siren is higher-pitched on approach and lower after it passes.
For sound, the observed frequency depends on the speeds of both source and observer relative to the medium: f′ = f(v ± v₀)/(v ∓ vₛ), where v is the speed of sound and the signs depend on the direction of motion. Because sound propagates through a medium, the effects of source motion and observer motion are not symmetric. The formula breaks down as the source approaches the speed of sound; at the speed of sound the waves pile up into a shock front — the sonic boom — which is the acoustic analogue of a wake.
For light and other electromagnetic waves, the effect is purely relativistic: only the relative motion matters, and the shift factor is √((1 + β)/(1 − β)) with β = v/c. Motion toward the observer blueshifts the light (higher frequency), motion away redshifts it. Astronomers measure the Doppler shift of spectral lines to find the line-of-sight velocity of stars, galaxies, and gas clouds: the rotation of galaxies, the orbits of binary stars, and the expansion of the universe — distant galaxies are redshifted, and the redshift grows with distance, the observation that led to the discovery of cosmic expansion. Special relativity also predicts a transverse Doppler effect from time dilation even when the motion is perpendicular to the line of sight.
Doppler technology is everywhere: police radar and speed guns measure the frequency shift of reflected radio waves; Doppler weather radar detects the motion of precipitation within storms; and Doppler ultrasound measures blood flow in medicine. In astronomy the effect remains the primary tool for measuring radial velocities — including the wobble of stars caused by orbiting planets.