Doppler Effect Calculator

Doppler effect: frequency shift due to motion

When a source and an observer move relative to one another, the frequency you actually hear or measure shifts. That is the Doppler effect. For sound it works out to f' = f · (v ± v_obs) / (v ∓ v_source), where v is the speed of sound (around 343 m/s in air at 20 °C). Coming closer raises the pitch, moving away lowers it. You hear this every time an ambulance siren screams past: high on the way in, dropping the moment it goes by. At 70 km/h that ambulance produces a Δf of roughly 5-6%, which is plenty to notice. Light behaves differently. In the relativistic regime the formula turns into f' = f·√((1+β)/(1-β)) with β = v/c. And on the cosmic scale, the redshift Hubble described in 1929 tells us that the more distant a galaxy is, the further its light slides toward red, which is how we know the universe is expanding.

Applications

Police speed traps run on microwave Doppler in their mobile units. Medical ultrasound uses it to map blood flow, which is what color Doppler shows you. Astronomers read stellar radial velocity from it and even spot exoplanets through the wobble they induce in their star. Weather services track tornadoes and storms with Doppler radar, and sonar relies on it too, both in submarines and in commercial fishing.

FAQ

Does the medium matter? For sound it does. The wave needs something to travel through, and v changes with temperature and with the gas itself. Light is a different story: it travels through vacuum, so the relativistic formula takes over.

What is the sign convention? When motion is toward, the observer speed adds in the numerator and the source speed subtracts in the denominator, which pushes f' above f. Flip both for motion away.

Why is the relativistic formula different? Light has no preferred reference frame. Time dilation comes into play, and what counts is only the relative velocity between source and observer.