The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source.Imagine you're standing on a platform and a train with a siren rushes past. When the train approaches, the siren sounds higher pitched, and when it moves away, lower. That is the Doppler effect! The frequency of sound changes due to the motion of the source. The same happens with light: if a star is moving toward us, its light 'blueshifts', and if it moves away, it 'reddens'. This is how scientists learn where distant galaxies are moving.
In 1842, Austrian physicist Christian Doppler theoretically described the dependence of frequency on the motion of the source and observer for sound and light in his work 'On the Color of Double Stars'. He mistakenly believed that all stars are white and their color is determined by motion. In 1845, Dutchman Buys Ballot experimentally confirmed the effect for sound using a locomotive and musicians. For light, the effect was first detected by William Huggins in 1868 by measuring a shift in the spectral lines of Sirius. The relativistic formula was derived by Albert Einstein in 1905 as a consequence of special relativity.
The effect arises because wave crests reach the receiver at different intervals during their mutual movement. In radar, a transmitted pulse reflects off a moving target — the speed is calculated from the frequency shift. In astrophysics, Doppler shift of spectral lines is the main method for measuring radial velocities. Limits of applicability: for sound — speeds much less than the speed of sound, otherwise shock waves occur; for light — the relativistic formula works at any speed up to the speed of light. At speeds close to the speed of light, transverse Doppler shift due to time dilation becomes significant.
The Doppler effect is used not only by astronomers but also by traffic police in radar guns! The device sends a radio wave, it reflects off the car, and by the change in frequency, they calculate the speed. If the frequency returns higher, you've exceeded the limit.
| z | variable | redshift parameter — redshift |
| v | variable | relative velocity between source and observer — velocity metre per second |
| θ | variable | angle between velocity vector and line of sight — angle radian |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| cos | operator | trigonometric cosine function — cosine |
| \nu_{\text{out}} | variable | Observed frequency of reflected light — frequency hertz |
| \nu_{\text{in}} | variable | Frequency of incident light in the source frame — frequency hertz |
| v | variable | Speed of the mirror relative to the source — velocity metre per second |
| c | constant | Universal constant, speed of light in vacuum — speed of light = 299792458 metre per second |
| \frac{1 - v/c}{1 + v | operator | Ratio of observed to emitted frequency for a receding source — doppler factor |
| \Delta\lambda | variable | Line broadening (full width at half maximum) — line width metre |
| \lambda | variable | Central wavelength of the spectral line — wavelength metre |
| T | variable | Temperature of the emitting/absorbing gas — temperature kelvin |
| m | variable | Mass of the emitting/absorbing particle — mass kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| k_B | constant | Relates thermal energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin |
| \sqrt{} | operator | Takes the square root of the argument — square root |
| v | variable | relative velocity of source and observer along the line of sight — velocity metre per second |
| Δλ | variable | observed wavelength shift (λ_observed - λ_0) — wavelength shift metre |
| λ_0 | variable | rest wavelength of the emitted light — wavelength metre |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| c | variable | cross-correlation value — cross correlation |
| v | variable | Doppler shift velocity — velocity metre per second |
| λ | variable | wavelength — wavelength metre |
| S1 | variable | first spectrum — spectrum |
| S2 | variable | second spectrum — spectrum |
| S̄1 | variable | mean of first spectrum over wavelength — mean spectrum |
| S̄2 | variable | mean of second spectrum over wavelength — mean spectrum |
| σ | variable | standard deviation of spectrum — standard deviation |
| ∑ | operator | sum over wavelength bins — summation |
| \delta | variable | Doppler factor — doppler factor |
| \Gamma | variable | Lorentz factor — lorentz factor |
| \beta | variable | velocity in units of c — velocity |
| \theta | variable | angle between source velocity and line of sight — angle radian |

























