The Doppler Effect and Shift

The Doppler effect, named after Christian Andreas Doppler, is the change in frequency and wavelength of a wave for an observer moving relative to the source of the waves. For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analysed separately. The Doppler Effect was first proposed on theoretical grounds in 1842 and is essentially defined in the following sentence

The frequency (and wavelength) of a wave, perceived by an observer, varies with the motion of the source of the wave relative to the observer

The Doppler Effect was observed for sound waves in 1845 (Buys Ballot and musicians on railway trains!) and for electromagnetic waves in 1848. The correct understanding of the Doppler effect for electromagnetic radiation requires use of the Special Theory of Relativity.

The Doppler Shift

Change in frequency = Doppler shift, fd

fd = -2 Vr/λ or fd = -2(Vr/c)f

where

  • Vr = radial velocity (away = +ve)
  • λ = wavelength emitted by radar
  • f = frequency emitted by radar

Example:

For S band radar

  • λ = 10 cm
  • f = 2 800 MHz

Vr = +10 m/s → fd= - 200 Hz

NB: 200 Hz << 2 800 MHz = 2 800 000 000 Hz

Frequency changes by about 1 x 10-5 % → Hard to measure!