effect

Doppler effect

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source.
9 related articles · 6 formulas · 5 who worked here

Description

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.

History

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.

How it works

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.

Fun fact

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.

Concept graph →

Formulas

$$1+z = rac{1}{ rac{ ext{v}}{c} ext{cos} heta ext{ sign} ext{ adjusted}}$$
Redshift due to relative motion between observer and source.
What is in the formula
zvariableredshift parameter — redshift
vvariablerelative velocity between source and observer — velocity metre per second
θvariableangle between velocity vector and line of sight — angle radian
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
cosoperatortrigonometric cosine function — cosine
1+z_{\odot}=\sqrt{\frac{1-β}{1+β}},\quadβ=\frac{v}{c}\cosθ · 2605.03004v1
$$\frac{\nu_{\text{out}}}{\nu_{\text{in}}} = \frac{1 - v/c}{1 + v/c}$$
Frequency shift for light reflected from a moving mirror.
What is in the formula
\nu_{\text{out}}variableObserved frequency of reflected light — frequency hertz
\nu_{\text{in}}variableFrequency of incident light in the source frame — frequency hertz
vvariableSpeed of the mirror relative to the source — velocity metre per second
cconstantUniversal constant, speed of light in vacuum — speed of light = 299792458 metre per second
\frac{1 - v/c}{1 + voperatorRatio of observed to emitted frequency for a receding source — doppler factor
\frac{ν_{{out}}}{ν_{{in}}}=\frac{1-v/c}{1+v/c} · 2606.04052v1
$$\Delta\lambda = \frac{\lambda}{c} \sqrt{\frac{2k_B T}{m}}$$
Thermal motion broadens spectral lines via the Doppler effect.
What is in the formula
\Delta\lambdavariableLine broadening (full width at half maximum) — line width metre
\lambdavariableCentral wavelength of the spectral line — wavelength metre
TvariableTemperature of the emitting/absorbing gas — temperature kelvin
mvariableMass of the emitting/absorbing particle — mass kilogram
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
k_BconstantRelates thermal energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin
\sqrt{}operatorTakes the square root of the argument — square root
t_d=\frac{mc^2}{2k_bλ^2}\frac{δλ^2_{{fit}}-δλ^2_{{inst}}}{4\ln2} · 2606.06577v1
$$v = c \frac{\Delta\lambda}{\lambda_0}$$
Velocity from wavelength shift in Doppler effect.
What is in the formula
vvariablerelative velocity of source and observer along the line of sight — velocity metre per second
Δλvariableobserved wavelength shift (λ_observed - λ_0) — wavelength shift metre
λ_0variablerest wavelength of the emitted light — wavelength metre
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
v=c*\frac{δλ}{λ_0} · 2606.25164
v=c\frac{λ_{{obs}}-λ_0}{λ_0} · 2607.21733v1
$$c(v) = \sum_{\lambda} \frac{ (S_1(\lambda,v) - \bar{S}_1(v)) (S_2(\lambda) - \bar{S}_2) }{ \sigma^2(\lambda) }$$
Measures similarity between two spectra at Doppler shift v.
What is in the formula
cvariablecross-correlation value — cross correlation
vvariableDoppler shift velocity — velocity metre per second
λvariablewavelength — wavelength metre
S1variablefirst spectrum — spectrum
S2variablesecond spectrum — spectrum
S̄1variablemean of first spectrum over wavelength — mean spectrum
S̄2variablemean of second spectrum over wavelength — mean spectrum
σvariablestandard deviation of spectrum — standard deviation
∑operatorsum over wavelength bins — summation
c(v)=\sum_{λ}\frac{(s_t(λ,v)-\bar{s}_t(v))(s_{{obs}}(λ)-\bar{s}_{{obs}})}{σ^2(λ)} · 2607.12017
$$\delta = \frac{1}{\Gamma (1 - \beta \cos\theta)}$$
Relativistic Doppler factor for a moving source.
What is in the formula
\deltavariableDoppler factor — doppler factor
\GammavariableLorentz factor — lorentz factor
\betavariablevelocity in units of c — velocity
\thetavariableangle between source velocity and line of sight — angle radian
δ=\frac{1}{\gamma(1-β\cosθ)} · 2607.16104v1

Related articles · 46

How the Width of the Breaking Zone Filters Infragravity Waves
A spotlight with an adjustable beam width sweeps along the shore. Its light is the long ocean waves that are born in the surf zone and spread in both directions: toward the beach and out to the open sea. Previously, this spotlight was considered a point source, but the actual breaking zone, where short waves break, has a finite width, and it changes as the wave front advances and retreats.
Optics2026-08-212 minarXiv:2608.21282express
Light Bounces Off a Mirror Flying Faster Than a Bullet
The mirror races along at nearly forty thousand kilometers per second. Light that strikes it bounces back, but changed, like a ball volleyed by a racket in mid-swing. That's exactly the kind of mirror scientists have built inside an ultra-thin glass thread filled with hydrogen. First, a powerful laser pulse is sent down the fiber.
General Relativity2026-07-292 minarXiv:2607.27343express
Gravity Overflows Its Banks
A cloud of waves collapses under its own gravity. While it's loose, everything goes by the book: the field oscillates gently in nearly flat space, and approximate formulas work perfectly. But add just a bit more energy, and the picture changes. Physicists used a numerical model to catch the moment when simple calculations stop describing reality.
Galaxies2026-07-282 minarXiv:2607.26269
Gas Curtain of 'Little Red Dots': Why It's So Common in the Early Universe
Forty reddish sparks frozen in the images from JWST. The telescope spotted them in the depths of space, at distances where the Universe was less than two billion years old. These objects are active galactic nuclei — very compact and unusually red. Their color earned them the nickname 'little red dots' (LRDs).
Stellar2026-07-273 minarXiv:2607.24141
14 Seconds to Weave a Star: Direct Synthesis Returns
14 seconds. That’s all it takes for a new code to weave the full spectrum of a star, from ultraviolet to near-infrared. This spectrum is not just a rainbow but a detailed tapestry of thousands of dark absorption lines, each left by a specific atom in the star's atmosphere.
Galaxies2026-07-272 minarXiv:2607.24929
Cosmic Cross-Pollination: How Galaxies Enrich Their Neighbors with Metals
In 1,433 pairs of galaxies scattered across the sky, astronomers noticed an unusual pattern. Neighbors located 'above' or 'below' a massive stellar system contain up to a quarter more oxygen than those lying in the plane of its disk.
Galaxies2026-07-253 minarXiv:2607.22966
A Chick in a Dust Shell: How a Red Quasar Emerges
In the deep field of JWST, among thousands of galaxies, astronomers zoomed in on the source JADES-GS 209777 – and saw a cosmic chick. Its "shell" is a thick cocoon of gas and cosmic dust that long hid the growing black hole at its center. But at a redshift of 3,711 (1,8 billion years after the Big Bang), the shell began to crack.
A Quieting Fountain: Evolution of Protoplanetary Disk Winds as Seen by JWST
Seventy-two protoplanetary disks, swirling cocoons of cosmic dust and gas, came under the gaze of the MIRI instrument on JWST. Most of them shoot outflows into space: dense conical structures and narrow, high-speed jets. They blast like fountains. This process is not accidental.
Cosmology2026-07-223 minarXiv:2607.19938
Echoes of Reionization: How Sound Waves Were Frozen into Quasar Light
Light from quasar J0744+2052 traveled to us for almost 12 billion years. Along the way, it bumped into hydrogen clouds that snatched individual lines from the spectrum — like a comb sifting through delicate frequencies. Astronomers call this pattern the Lyman-alpha forest in spectroscopy.
Galaxies2026-07-223 minarXiv:2607.20606
Galactic Exhalation: Neutral Gas Leaves Massive Galaxies in the Early Universe
The JWST spectrograph caught a barely perceptible dip in the spectrum of a distant galaxy — two lines, like shadows cast by cold gas. These are the sodium lines, the very yellow light of streetlamps. Here, at the edge of the visible Universe, they betray the slow exhalation of a galaxy returning matter to space.
A Symmetric Shadow in the Chaos of Tabby's Star
Tabby's Star, a beacon in the cosmic sea, has baffled astronomers since 2015. Its light flickered not in the rhythm of planets, but as if scattered by a storm — deep dips, sharp spikes. But amid this chaos, a smooth, nearly perfect dip was found. The eye of the storm.
Cosmic Pressure Cooker: Unraveling the Mystery of Little Red Dots
Ten billion years ago, the universe was speckled with strange crimson sparks. The JWST spotted them in images at distant redshifts — compact sources blazing like entire galaxies yet no larger than a tiny central region. Astronomers nicknamed them “little red dots.” Their nature long defied explanation.
Stellar2026-07-193 minarXiv:2607.17348
SpecFANN: Lightning-Fast Sketch of a Star's Spectrum
An artist makes a quick charcoal sketch, and the face in the portrait is already recognizable. Astrophysicists face a similar challenge: the spectrum of a star is its individual portrait, revealing temperature, composition, and gravity.
Galaxies2026-07-173 minarXiv:2607.15515
Star Chefs of the Early Universe: Nitrogen Excess
For thirteen billion years, light battled through cosmic emptiness. It bent around massive galaxy clusters that, as Einstein predicted, acted as giant lenses — amplifying and distorting the distant glow. In 2023, the NIRSpec instrument on the James Webb Space Telescope captured this light and spread it into spectra.
Galaxies2026-07-173 minarXiv:2607.16104
Stellar2026-07-163 minarXiv:2607.15017
The Milky Way Symphony: Why Star Clocks Tick at Different Speeds
A star's age is the key to the galaxy's history. But prying that key from nature is no simple task: unlike a tree, a star doesn't grow annual rings. Yet, its atmosphere holds a chemical code — the ratio of elements that slowly shifted as generations of stars died and new ones were born.
Signal Processing2026-07-161 minarXiv:2607.15127express
Lightweight AI for Space Communications: More Accurate and Efficient
Communicating with a satellite is like trying to hear a whisper in a storm: the signal drowns in noise. Engineers have created an AI algorithm that runs directly on the satellite and, with minimal power consumption, detects distortions more accurately than previous methods.
Icy Origins: Most Hot Jupiters Come from the Cold
Among the scorching exoplanets that circle perilously close to their stars lies the secret of their birth. Nearly three decades ago, Michel Mayor and Didier Queloz discovered the first such world, and since then astronomers have been tormented by the question: how does a gas giant end up pressed against…
Molecular Melodies: How ELT/ANDES Will Tune Into the Breath of Exoplanets
The light of a distant star carries within it the silent hum of the atmospheres of planets orbiting it. For a long time, capturing it was like trying to make out a whisper over a roaring waterfall. But with the advent of the 39-meter Extremely Large Telescope (ELT) and the ANDES spectrograph with a resolution of 100,000, this task is no longer hopeless.
Music of the Spheres: How LISA Will Hear Dark Matter's Duet
Gravitational waves from merging black holes sound like bass chords, pulsars tap out a rhythm, and the cosmic microwave background carries echoes of the Big Bang. But there is a silent player — dark matter, whose presence is betrayed only by gravitational effects.
Galaxies2026-07-083 minarXiv:2607.07973
General Relativity2026-06-252 minarXiv:2606.27429express
How a Massive Field Alters the Dance of Stars Around a Black Hole
A tiny star spirals around a giant rotating black hole. Slowly, it moves closer in a spiral, and this dance lasts thousands of years. All the while, waves ripple through space, like ripples on water, but these are gravitational waves. They can be "heard" with special detectors.
Galaxies2026-06-232 minarXiv:2606.25022
Galaxies2026-06-232 minarXiv:2606.25164
Cosmic Sandblaster: How Dust Unveiled the Acceleration of Galactic Outflows
Massive gas outflows from active galactic nuclei are a key regulator of galactic evolution. They sweep out the interstellar medium, quench star formation, and dictate the growth of supermassive black holes.
Dance of Photons: When the Solar Sail Becomes Its Own Brake
Imagine a three-faced dancer on the crest of a light wave. One face is a catcher, absorbing incoming photons. The second is a perfect mirror, throwing light back. The third is frosted glass, scattering rays in all directions. As long as speed is low, the dance is harmonious. But at near-light speeds, the choreography breaks. This is like a surfer chasing a wave.
High Energy2026-05-251 minarXiv:2605.26387express
Magnetic Mirrors in Galaxy Clusters
A crowd is trapped in a narrow corridor between two rows of mirrors. Every now and then, someone shoves the wall hard, and a rumble rolls down the corridor — similarly, in the plasma of galaxy clusters, whistler waves and ion-cyclotron waves appear.
Quantum Physics2026-05-241 minarXiv:2605.27447express
Light under Control: One-Way Photons Without Magnets
Light loves symmetry: in an open channel, it flows equally both ways. To steer it one way, physicists often use magnets. A new approach does without, using rotation — just the speed of a vinyl record — and interference from two atoms. Rotation changes the “pitch” of light for different directions, just as a siren’s tone shifts when a car approaches or recedes.
Quantum Physics2026-05-201 minarXiv:2605.21206express
How Motion Teaches a Detector to Distinguish Directions
An ordinary photometry detector can't tell a left photon from a right one. But let it start moving, and everything changes. Imagine a rower moving between two flutists playing the same note. His ear is perfectly tuned to that note and ignores all others. As he moves, the pitch from the flutist ahead sounds higher, and from the one behind sounds lower.
General Relativity2026-05-202 minarXiv:2605.21584express
Gravitational Waves Through the Lens of Alternative Gravity
A stone drops into a pond, and ripples spread across the water. If a protruding branch blocks the ripples' path, part of the wave reflects, and part bends around the obstacle. Gravitational waves, ripples in spacetime itself, behave similarly when passing by galaxy clusters or black holes.
General Relativity2026-05-191 minarXiv:2605.20354express
A Vortex's Silent Patch Reveals Its Speed
In a water vortex swirling toward the drain, the flow speed near the center can exceed the speed of sound. Sound gets trapped: waves cannot escape back, forming a silent region — a sound shadow. Half a century ago, William Unruh realized that this is an exact copy of a black hole, but for sound instead of light.
Optics2026-05-152 minarXiv:2605.15632express
Light Flipped in Time
A pebble tossed into a pond sends ripples spreading in all directions. Now imagine the pond itself suddenly turning into jelly — instantly, faster than the wave can complete a single crest. Some ripples would keep spreading but change their spacing, while others would unexpectedly turn around and run back toward the point of impact, as if time were flowing backward for them.
Long-Throat Wormholes: How Doppler Notes Give Them Away
When a black hole steps into the lens, it leaves a perfect darkness in the image — a gravitational well where light falls forever.
Cosmology2026-05-043 minarXiv:2605.03004
Ocean of Currents: Why the Universe's Acceleration Varies with Direction
Cosmology holds that on large scales, the Universe is a calm ocean without storms or currents. This is the cosmological principle, the foundation of the standard ΛCDM cosmological model.
Optics2026-03-282 minarXiv:2603.27275express
Waves Frozen Beside a Moving Source
A swimmer cutting through water at the speed of the waves running on it finds themselves in a strange position: the waves they themselves generate can neither overtake them nor fall behind. They pile up at the swimmer's bow and freeze. A similar phenomenon occurs when a light source moves inside a medium at a speed matching the speed of energy transfer of the waves.
Stellar2026-03-181 minarXiv:2603.17241express
Waves on a Solar Streamer: Slow Eruptions Can Do It Too
Above the Sun's surface hang long ribbons of glowing gas — streamers. They look like giant harps stretched across the corona. When a wave runs along such a ribbon, it trembles and bends like a string after being plucked. For a long time, it was thought that only a very fast ejection of material, one traveling at more than 500 kilometers per second, could launch such a wave.