Doppler Effect

How the Doppler effect works

The Doppler effect is the change in a wave's observed frequency when the source and the observer move relative to each other. As a source approaches, each successive wave crest is emitted from a slightly closer position, so the crests bunch up and reach you more often — a higher frequency. As the source recedes, the crests spread out and arrive less often — a lower frequency. The everyday example is a passing siren, which drops in pitch the instant it goes by.

The key is that the source's motion compresses the wavefronts ahead of it and stretches them behind. This simulator draws those expanding circular wavefronts directly, so you can watch them crowd together in front of a moving source and fan out behind it, with the observed frequency calculated at listener positions on each side.

Experiments to try in this simulation

1. Pitch shift: set a source frequency and start the source moving. The observer it approaches hears a higher frequency; the one it leaves behind hears a lower one — and the shift grows with the source's speed.

2. Break the sound barrier: push the source speed past Mach 1. The wavefronts can no longer outrun the source and pile up into a Mach cone — a sonic boom.

3. Redshift and blueshift: switch to spectrum mode and watch the hydrogen absorption lines slide toward red as a source recedes and toward blue as it approaches — exactly how astronomers measure the motion of stars and galaxies.

4. Beats: superimpose two nearby frequencies and see the slow throb of the beat envelope as they drift in and out of phase.

Key equations

For sound, the observed frequency is f′ = f·(v ± v_observer)/(v ∓ v_source), where v is the speed of sound and the signs depend on whether the motion is toward or away. When the source speed exceeds the wave speed, a Mach cone forms at a half-angle given by sin θ = 1/M, where M is the Mach number.

For light, the cosmological redshift is captured by the parameter z, the fractional stretch in wavelength. A positive z means a receding source, and the larger the z, the faster the recession — the relationship Edwin Hubble used to show that the universe is expanding.

Real-world applications

The Doppler effect runs a surprising amount of technology. Police radar and weather radar bounce waves off moving cars or raindrops and read the frequency shift to measure speed. Medical Doppler ultrasound images blood flow the same way. In astronomy, redshift is the primary tool for measuring how fast galaxies recede — and thus the expansion of the universe — while smaller shifts reveal orbiting exoplanets and binary stars. Even GPS must correct for the Doppler shift of fast-moving satellites to stay accurate.