doppler

The Doppler effect, named after Christian Doppler, describes the change in frequency or wavelength of waves as measured by an observer moving relative to the source. It applies to sound, light, and radio waves. The observed frequency increases when source and observer move toward each other and decreases when they separate, especially along the line of sight.

In acoustics, the medium provides a reference frame. If a source emits frequency f and an observer moves with speed vo toward the source, or the source moves with speed vs, the observed frequency f' depends on the wave speed v in the medium: f' = f (v ± vo)/(v ∓ vs), with signs indicating toward or away. This explains the pitch of a passing siren.

For light, there is no medium, so the relativistic Doppler effect applies. Relative motion along the line of sight with velocity v (β = v/c) yields f' = f sqrt((1+β)/(1−β)). Approaching motion causes blue shift; receding motion red shift. Time dilation contributes at high speeds.

Applications span science and technology. In astronomy, redshift and blueshift indicate motion and cosmic expansion. In radar and weather radar, Doppler shifts measure target velocity. In medicine, Doppler ultrasound assesses blood flow. The technique also underpins speed enforcement, sonar, and tests of relativity.

History: Christian Doppler proposed the concept; later experiments confirmed the acoustic effect, and the relativistic formulation generalized it to light.