Doppler effect

Lore & Background

Christian Doppler first proposed the effect in 1842 in his treatise 'Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels' (On the coloured light of the binary stars and some other stars of the heavens). The hypothesis was tested for sound waves by Buys Ballot in 1845, who confirmed that the pitch was higher when the source approached and lower when it receded. Hippolyte Fizeau independently discovered the same phenomenon on electromagnetic waves in 1848; in France, the effect is sometimes called 'effet Doppler-Fizeau', though that name was not adopted elsewhere. In Britain, John Scott Russell made an experimental study of the Doppler effect in 1848.

For waves propagating in a medium such as sound, the observed frequency depends on the velocities of the source and receiver relative to that medium. The relationship is given by a formula where the observed frequency changes based on whether the source and receiver are moving toward or away from each other. If the source approaches the observer at an angle, the observed frequency decreases monotonically from a higher pitch through equality when perpendicular to the motion, to a lower pitch as it recedes. When the observer is very close to the path, the transition is abrupt; when far, it is gradual.

If the source moves at or above the wave speed, the Doppler equation predicts an infinite or negative frequency and becomes inapplicable. For sound, a source moving faster than the speed of sound creates a shock wave and a sonic boom. Lord Rayleigh predicted that if an observer moved from a stationary source at twice the speed of sound, a musical piece would be heard in correct tempo and pitch but played backwards.

Reader's Guide

The Doppler effect has significant practical applications across multiple fields. In astronomy, it is used to measure the speed at which stars and galaxies approach or recede, producing blueshift or redshift. This allows detection of binary stars, measurement of rotational speeds, and discovery of exoplanets. The effect typically occurs on a very small scale, not noticeable to the unaided eye. Among nearby stars, the largest radial velocities relative to the Sun are +308 km/s (receding) and −260 km/s (approaching). The cosmological redshift of the expanding universe is considered separate from Doppler motion or gravitational redshifts.

In radar, the Doppler effect is used to measure the velocity of moving objects, such as cars detected by police radar guns. A radar beam fired at a moving target experiences a wavelength change: increasing when the target recedes, decreasing when it approaches. For example, a police radar operating at 24.15 GHz detecting a vehicle at 30 m/s measures a Doppler shift of about 4.83 kHz. The proximity fuze, developed during World War II, relies on Doppler radar to detonate explosives at the correct time.

A common everyday example is the siren of a passing emergency vehicle, which sounds higher in pitch when approaching and lower when receding. The pitch remains constant if the vehicle approaches directly, then jumps to a lower pitch upon passing. The radial speed varies with the angle between the line of sight and the vehicle's velocity.

Did You Know?

• Christian Doppler first proposed the effect in 1842 in a treatise on the coloured light of binary stars.
• Buys Ballot confirmed the Doppler effect for sound waves in 1845 using a moving sound source.
• Hippolyte Fizeau independently discovered the effect for electromagnetic waves in 1848.
• Lord Rayleigh predicted that an observer moving from a stationary source at twice the speed of sound would hear music played backwards.