What it does
When a source of waves moves towards you, its crests arrive bunched up and you hear a higher pitch; moving away, they are stretched and the pitch drops. This is the Doppler effect. The calculator covers four everyday cases:
- Sound from a moving source to a moving listener, with wind, plus the falling pitch curve as a siren or horn drives past, and the Mach number and Mach cone when the source outruns its sound.
- Echoes from a moving object, where the wave is shifted twice: a bat hunting a moth, a sonar, or a radar speed gun (choose radio waves).
- Light from a moving star or object, using special relativity: the redshift z and the wavelength you see.
- Beats between two close tones: how many times a second the sound swells and fades.
Each Doppler case can also run backwards: give the frequency or wavelength you measured and it finds the speed.
How to use it
- Choose the situation and the speed units (m/s, km/h, mph, knots or km/s).
- For sound and echoes, give the frequency sent out and what the waves travel through: air at a temperature, water, radio, or your own wave speed.
- Give the speeds and whether each is moving towards or away. Only the part of the motion along the line between them counts.
- Optionally give a measured frequency or wavelength to find the speed.
- Download the chart data as CSV, or the report as an image, PDF or Word file.
Worked example
The made-up example is a 700 Hz siren on a vehicle doing 25 m/s (90 km/h) towards a listener standing still, in air at 20 °C (sound at 343.21 m/s). The page shows Heard: 754.99 Hz (+54.99 Hz), 1.31 semitones high. As it passes, the pitch falls to 652.47 Hz, a drop of 2.53 semitones, and the chart shows how fast it falls when it passes 20 m away. Typing 754.99 as the measured frequency gives the speed back: 25 m/s towards.
For an echo, a bat calling at 40,000 Hz at a moth closing at 2 m/s hears 40,468.91 Hz, 468.91 Hz higher. For light, hydrogen’s 656.28 nm line from a star moving away at 3,000 km/s is seen at 662.881 nm, redshift z = 0.01006. For beats, 440 and 443 Hz give 3 beats per second, one every 0.3333 s, at a pitch of 441.5 Hz.
Tips
- Speed guns use the echo case with radio waves: a 10.5 GHz gun sees a shift of about 70 Hz for every m/s of the car’s speed.
- For the pass-by, the pitch changes fastest at the moment of closest approach; the closer you stand, the more sudden the drop.
- To tune two strings, play them together and adjust until the beats slow down and stop.
FAQ
Why is the shift different for a moving source and a moving listener at the same speed? The source moving squeezes the wavelength in the air, while a moving listener meets crests faster; the two only agree at low speeds.
Does this work for galaxies? For nearby objects, yes. For distant galaxies the stretching of space dominates; use the redshift calculator. For study and planning, not a substitute for professional judgement.
Where the numbers come from
- Doppler effect for sound with a moving source, listener and medium, f′ = f (c + u + v_o)/(c + u − v_s); two-way echo f (c + v)/(c − v); relativistic longitudinal Doppler f √((1 + β)/(1 − β)); Mach cone sin μ = 1/M; beats |f₁ − f₂|: standard physics.
- Speed of sound in air 331.3 √(1 + θ/273.15) m/s; in water about 1,480 m/s (rounded); speed of light 299,792,458 m/s (exact by definition).
- Checked against NumPy and SymPy, and the pass-by curve against an independent numerical solution (SciPy root finding for the emission time). The example siren and other values are made up.
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Last updated 2026-11-09.