Doppler Effect Calculator
Compute the frequency shift of sound waves when the source or listener moves, find velocity from the observed frequency, and calculate light redshift (astronomy). All calculations run in your browser — no server, no data upload.
Sound Wave Doppler Effect
f′ = f · (v + vo) / (v − vs) — vo positive when the observer approaches the source, vs positive when the source approaches the observer.
- Change (Δf)
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- Relative change
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- Source velocity
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- Wave speed used
- 343 m/s (20 °C, standard)
Verified example
Verified example: a 1000 Hz source moving at 30 m/s toward a stationary observer (v = 343 m/s): f′ = 1000 × 343 / (343 − 30) = 1,095.85 Hz (up 9.58%).
Find Velocity from Observed Frequency
Given f and f′ plus one party’s velocity — compute the other party’s velocity. Useful e.g. for estimating an ambulance’s speed from the siren tone heard.
- In Mach
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Positive sign = approaching the other party; negative = moving away. Speed of sound 343 m/s (20 °C).
Light Doppler / Redshift
z = Δλ/λ — for astronomical spectrum lines. Non-relativistic (v = c·z) and full relativistic versions.
- Recession velocity (non-rel, v = c·z)
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- Recession velocity (relativistic)
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- Beta (v/c)
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Verified example
Verified example: H-alpha line, λ rest 656.28 nm observed at 700 nm → z = 0.066618; non-relativistic v = 19,971.55 km/s; relativistic v = 19,307.70 km/s.
Frequently Asked Questions
What is the Doppler effect?
The Doppler effect is the observed change in frequency (or wavelength) when the wave source and the observer move relative to each other. Everyday example: an ambulance siren sounds higher-pitched as it approaches and lower after it passes.
What is the Doppler effect formula for sound?
f′ = f × (v + v_o) / (v − v_s). Here v is the speed of sound (343 m/s at 20 °C), v_o the observer’s velocity (positive when approaching the source), and v_s the source’s velocity (positive when approaching the observer). This sign convention is used consistently throughout this calculator.
What is a worked calculation example?
A 1000 Hz source moving at 30 m/s toward a stationary observer, v = 343 m/s: f′ = 1000 × 343 / (343 − 30) = 1,095.85 Hz, up 9.58 percent.
When does this formula not apply?
When the source velocity reaches or exceeds the speed of sound (Mach 1 and above, the v − v_s denominator zero or negative), the classical formula breaks down because a shock wave (sonic boom) forms. This calculator rejects such input with an error message.
How does air temperature affect the speed of sound?
The speed of sound rises with temperature: v = 331.3 × sqrt(T/273.15) with T in Kelvin. At 20 °C (293.15 K) the result is 343.21 m/s; at exactly 0 °C it is 331.30 m/s. Enable the temperature correction option in Mode 1 to use this value.
How do you calculate light redshift?
z = (observed lambda − rest lambda) / rest lambda. Example H-alpha line (rest lambda 656.28 nm) observed at 700 nm: z = 0.066618. Non-relativistic recession velocity v = c × z = 19,971.55 km/s; relativistic version 19,307.70 km/s (beta = 0.064404 c). The non-relativistic formula is only accurate for z far below 1.
How does this tool differ from heart Doppler or speed-of-sound calculators?
This tool computes wave frequency shifts (wave physics: sound and light). Medical Doppler echocardiography, e.g. cardiac output of the heart, is a different clinical application. The speed-of-sound calculator computes sound speed in various media without Doppler shift, and the frequency converter only converts units. Each has its own tool.
Which units are supported?
Frequency: Hz and kHz. Velocity: m/s and km/h. Wavelength: nanometers (nm). Temperature: degrees Celsius for wave-speed correction. Redshift z is dimensionless and recession velocity is shown in km/s.
Related Tools
- Frequency & Wavelength Converter — convert Hz/kHz/MHz/GHz and frequency ↔ wavelength (not the Doppler effect).
- Speed of Sound Calculator — sound speed in air vs temperature/altitude/humidity and various media (no Doppler shift).
Scope note: medical Doppler tools (e.g. cardiac output computation from Doppler echocardiography) belong to a different health domain and are not covered here.
Free tool by NRTechStudio