Doppler Effect Calculator

Quick Presets

Source Frequency f

Wave Speed v_wave

m/s

Moving Entity

Which is moving?

Velocity

Direction

Wave Type

Source Frequency f (Hz)

Wave Speed v_wave (m/s)

Source Velocity v_s (m/s)

Positive = moving toward observer

Observer Velocity v_o (m/s)

Positive = moving toward source

Fill in known values for instant frequency shift results.

What Is the Doppler Effect?

The Doppler effect, named after Austrian physicist Christian Doppler (1842), describes how a wave's perceived frequency changes when the source and observer are moving relative to each other. The classic example is an ambulance siren: as it approaches you, the pitch is higher; as it passes and recedes, the pitch drops.

Approaching (blueshift)

Wave crests arrive more frequently → perceived frequency increases → higher pitch / shorter wavelength.

Receding (redshift)

Wave crests arrive less frequently → perceived frequency decreases → lower pitch / longer wavelength.

The Doppler Formula and Sign Conventions

f' = f × (v_wave + v_o) / (v_wave − v_s)

v_o positive toward source; v_s positive toward observer

f — emitted (source) frequency in Hz
v_wave — speed of sound in the medium (343 m/s in air at 20°C)
v_o — observer velocity (+ve toward source, −ve away)
v_s — source velocity (+ve toward observer, −ve away)

Moving Source vs Moving Observer

Although the frequency shifts appear symmetric, the underlying physics differs. A moving source compresses or stretches the wave pattern in space, changing the wavelength. A moving observer intercepts more or fewer wavefronts per second without altering the wavelength.

Source moving, observer stationary

f' = f × v / (v ∓ v_s)

− if approaching, + if receding

Observer moving, source stationary

f' = f × (v ± v_o) / v

+ if approaching, − if receding

Relativistic Doppler and Redshift

For electromagnetic waves (light, radio, X-rays), the relativistic Doppler formula must be used because the speed of light is invariant:

Approaching

f' = f√((1+β)/(1−β))

Receding

f' = f√((1−β)/(1+β))

where β = v/c and c = 2.998 × 10⁸ m/s. The cosmological redshift z = (f_emit/f_obs) − 1 tells astronomers how fast galaxies recede.

Applications: Radar, Sonar, Medical Imaging

Police Speed Radar

Microwave signal reflects off vehicles. The frequency shift Δf = 2fv/c gives speed directly.

Weather Doppler Radar

Measures wind speed and precipitation motion by tracking the Doppler shift of reflected microwaves.

Doppler Ultrasound

2–15 MHz sound reflects off blood cells; frequency shift measures blood flow velocity and direction.

Astronomy

Stellar radial velocities and galaxy recession rates measured via spectral line redshift/blueshift.

Worked Examples

Example 1 — Ambulance Approaching

f = 700 Hz, v_s = 20 m/s, v_wave = 343 m/s

f' = 700 × 343 / (343 − 20)

f' ≈ 743.3 Hz

Example 2 — Train Receding

f = 400 Hz, v_s = 25 m/s, receding

f' = 400 × 343 / (343 + 25)

f' ≈ 372.8 Hz

Example 3 — Observer Moving Toward

f = 500 Hz, v_o = 30 m/s, v_wave = 343

f' = 500 × (343 + 30) / 343

f' ≈ 543.7 Hz

Example 4 — Relativistic Redshift

f = 6×10¹⁴ Hz, β = 0.1 (receding)

f' = f × √(0.9/1.1)

f' ≈ 5.39×10¹⁴ Hz

Frequently Asked Questions

The Doppler effect is the change in frequency (or wavelength) of a wave as perceived by an observer who is moving relative to the wave source. When a source approaches, waves compress and frequency rises (blueshift); when it recedes, waves stretch and frequency falls (redshift). It applies to sound, light, and all other wave types.

For sound, the observed frequency is f' = f × (v_wave + v_o) / (v_wave − v_s), where f is source frequency, v_wave is wave speed, v_o is observer velocity (positive toward source) and v_s is source velocity (positive toward observer). The sign convention ensures approaching motion raises frequency.

Classical Doppler applies to mechanical waves (sound) where the medium matters. Relativistic Doppler applies to electromagnetic waves (light) in a vacuum where there is no medium. The relativistic formula is f' = f × √((1+β)/(1−β)) for approach and f' = f × √((1−β)/(1+β)) for recession, where β = v/c. At low velocities both formulas agree.

Redshift is the Doppler shift toward lower frequencies (longer wavelengths) when a light source recedes from the observer. Astronomers use redshift z = (λ_obs − λ_emit)/λ_emit to measure how fast galaxies are moving away. The discovery that distant galaxies are redshifted led to the Big Bang theory of an expanding universe.

Police speed radar emits a microwave signal (typically 10–35 GHz) toward a vehicle. The reflected signal is Doppler-shifted by the vehicle's speed. The receiver measures the frequency difference Δf = 2 × f × v/c (factor 2 because both the emitted and reflected waves are shifted). Speed is computed from Δf. Modern LIDAR guns use light pulses instead.

Yes. Light exhibits a relativistic Doppler effect because it travels at a constant speed c regardless of the observer's or source's velocity. The formula differs from the classical sound formula because there is no medium. Approaching light sources appear blue-shifted; receding sources appear red-shifted. GPS satellites must correct for both special and general relativistic Doppler shifts.

In the standard formula f' = f(v + v_o)/(v − v_s): v_o is positive when the observer moves toward the source; v_s is positive when the source moves toward the observer. Moving toward each other raises the observed frequency; moving apart lowers it. Some textbooks use the opposite sign convention so always check the formula being referenced.

Doppler ultrasound uses sound waves at 2–15 MHz to measure blood flow velocity. The probe emits ultrasound; red blood cells reflect it with a Doppler shift proportional to their speed. Color Doppler imaging shows flow direction (red = toward probe, blue = away). Applications include echocardiography, fetal monitoring, and detecting DVT (deep vein thrombosis).

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