Doppler Effect & Wave Calculator
Work out how motion changes the pitch of a sound. Solve the Doppler formula for the frequency heard, the frequency sent or the source’s speed, use v = fλ for any wave, and find the redshift of light from a moving source.
How to Use
- Pick what to find: the frequency heard, the frequency sent, the source’s speed, a wave’s v = fλ, or the redshift of light.
- For sound, enter the source frequency, the speed of sound (343 m/s in air at 20 °C) and how fast the source and listener move.
- Set each mover to “Towards” or “Away”. The calculator picks the plus and minus signs for you and lists them in Show Work.
- For v = fλ, choose which of speed, frequency and wavelength to find; for light, start from a speed or from a measured wavelength.
- Press a preset to load an example; the drawing shows the wavefronts bunching ahead of a moving source.
Worked Example
An ambulance siren at 700 Hz, driving at 30 m/s (108 km/h), in air at 343 m/s. Coming towards you, each wave is sent from 30 m/s closer than the last, so the waves are squeezed into 343 − 30 = 313 m of air per second: f′ = 700 × 343 ÷ 313 = 767.09 Hz.
The same siren going away. Now the waves are spread over 343 + 30 = 373 m: f′ = 700 × 343 ÷ 373 = 643.70 Hz. As it passes, the pitch falls by 123.39 Hz, about three semitones.
The common mistake: getting the sign backwards. Writing c + v_s for the approaching siren gives 700 × 343 ÷ 373 = 643.70 Hz, a lower pitch, which is the wrong way round. A quick check: anything coming towards you must sound higher, so the denominator must get smaller (343 − 30), giving 767.09 Hz.
Show Work
Formulas
From Trumpeters on a Train to Receding Galaxies
The Austrian physicist Christian Doppler proposed the effect in 1842, in a paper on the coloured light of double stars. In 1845 the Dutch scientist C. H. D. Buys Ballot tested it with sound: musicians played a steady note on an open railway carriage near Utrecht while trained listeners by the track judged the change in pitch as it went past. In 1848 Hippolyte Fizeau showed independently how the shift applies to light and spectral lines.
In 1912 Vesto Slipher measured the Andromeda galaxy approaching at about 300 km/s, and over the next decade found most galaxies receding. Edwin Hubble combined such redshifts with distances in 1929, the start of the evidence for an expanding universe. The same effect now runs police speed guns, weather radar and Doppler ultrasound. The speed of sound used here, 343 m/s, is for dry air at 20 °C; see the speed of sound calculator for other temperatures.
About This Calculator
This calculator solves the Doppler formula for sound with a moving source, a moving listener or both, for the frequency heard, the original frequency or the source’s speed, and reports the shift in hertz and in musical semitones. Towards and away switches replace the usual ± confusion, and Show Work states the signs it used. It also solves v = fλ for any wave, and gives the exact relativistic redshift of light next to the simple z ≈ v/c. The drawing shows the wavefronts crowding ahead of a moving source.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Speed of Sound Calculator, Frequency & Wavelength Calculator, and Snell’s Law & Refraction Calculator.
Frequently Asked Questions
What is the Doppler effect formula for sound?
f′ = f × (c ± v_o) ÷ (c ∓ v_s). Use the upper signs (+v_o, −v_s) when the listener or source moves towards the other, and the lower signs when moving away. A 700 Hz siren approaching at 30 m/s in air (c = 343 m/s) is heard at 700 × 343 ÷ 313 = 767.09 Hz.
How much does a siren drop in pitch as it passes?
At 30 m/s (108 km/h) the 700 Hz siren falls from 767.09 Hz to 643.70 Hz, a drop of 123.39 Hz. That is 3.04 semitones, about a minor third, which is the familiar “neee-owww”.
Is a moving listener the same as a moving source?
No. A listener moving at 30 m/s towards a still 700 Hz siren hears 700 × 373 ÷ 343 = 761.22 Hz, not 767.09 Hz. The source moving compresses the waves in the air; the listener moving only meets them faster. For light there is no air, and only the relative speed matters.
What is the relationship between speed, frequency and wavelength?
v = f × λ for any wave. Concert A (440 Hz) in air at 343 m/s has a wavelength of 343 ÷ 440 = 0.7795 m. A 100 MHz FM radio wave travels at the speed of light, 299,792,458 m/s, so its wavelength is 2.998 m.
What is redshift and when is z ≈ v/c good enough?
Redshift z = λ_observed ÷ λ_rest − 1. For speeds well below light, z ≈ v/c. At 3,000 km/s the exact relativistic value is 0.010057 against 0.010007 from v/c, 0.5% apart; at half the speed of light the exact value is 0.732, not 0.5. For distant galaxies most of the redshift comes from the expansion of space rather than motion through it.
How do I use the Doppler Effect & Wave Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Sirens and car horns
A horn at 440 Hz that sounds a semitone sharp (466.16 Hz) as it approaches is moving at 19.25 m/s, 69.3 km/h.
Music and acoustics
Concert A at 440 Hz has a wavelength of 77.95 cm in air but 3.37 m in fresh water at 20 °C, where sound travels at 1,481 m/s.
Radio and Wi-Fi
Wi-Fi at 2.4 GHz has a wavelength of 12.49 cm, which sets the size of the antennas inside a router.
Astronomy
The hydrogen-alpha line at 656.28 nm from a galaxy receding at 3,000 km/s arrives at 662.88 nm. Andromeda, approaching at about 300 km/s, shows it at 655.62 nm.
Physics homework
Both moving: a 500 Hz source at 20 m/s and a listener at 10 m/s heading towards each other give 500 × 353 ÷ 323 = 546.44 Hz.
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