This Doppler effect calculator computes the frequency you actually hear when a sound source and an observer move relative to each other — the ambulance-siren effect, in exact numbers.

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f′ = f × (v ± v_observer) ÷ (v ∓ v_source)

Signs follow one idea: motion toward compresses, motion away stretches. A source advancing into its own wavefronts shortens the wavelength in the medium (denominator v − v_s); an observer advancing into the wavefronts meets them faster (numerator v + v_o). Sound speed itself rides on temperature — v ≈ 331.3 + 0.606·T m/s in air. The wavelength those fronts carry: our Wavelength Calculator. Part of our Physics Calculators collection.

Worked Example (Verified)

  • 440 Hz source approaching at 20 m/s, 20 °C air (defaults): v = 343.4 m/s → f′ = 440 × 343.4 ÷ 323.4 = 467.2 Hz — about a semitone sharp (concert A becomes nearly A♯), matching every passing siren you’ve ever heard
  • The pass-by drop: the instant the same source passes and recedes, f′ falls to 440 × 343.4 ÷ 363.4 ≈ 415.7 Hz — a 51 Hz cliff, the most dramatic note-change in everyday physics
  • Observer symmetry check: observer approaching a static 440 Hz source at 20 m/s gives 440 × 363.4 ÷ 343.4 ≈ 465.6 Hz — close to but NOT equal to the moving-source figure, the asymmetry that proves the medium matters
  • At v_source → v, the denominator → 0: wavefronts pile into a shock cone (Mach 1) — the formula’s infinity is physics waving a red flag

Family of Dopplers

  • Medical ultrasound: blood-flow Doppler uses the double shift (moving red cells receive, then re-emit) at MHz frequencies.
  • Radar guns & weather radar: electromagnetic, relativistic-form, typically processed as a beat frequency.
  • Astronomy: redshift z = Δλ/λ — the universe’s expansion written in this same idea, with relativity’s transverse correction.
  • Bats and dolphins: echolocation is Doppler-corrected hearing with the gain staged.

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Frequently Asked Questions

How do you calculate the Doppler effect for sound?

f′ = f (v ± v_o)/(v ∓ v_s): add the observer’s speed to the sound speed in the numerator when they move toward the source; subtract the source’s speed in the denominator when it moves toward the observer. A 440 Hz source approaching at 20 m/s in 20 °C air is heard at 467.2 Hz.

Why do moving source and moving observer give different results?

Because sound travels through a medium with its own frame. A moving source physically changes the wavelength laid down in the air; a moving observer only changes the rate of crossing existing wavefronts. The numerical difference at 20 m/s is small (467.2 vs 465.6 Hz) but real — and it vanishes for light, where relativity removes the medium.

Does temperature change the Doppler shift?

Yes — sound speed rises ~0.6 m/s per °C, so the same motion in cold air (slower v) produces a larger fractional shift. This calculator takes temperature explicitly rather than assuming the textbook 343 m/s.

What happens at the speed of sound?

The classical formula’s denominator reaches zero as a source approaches Mach 1 toward you: wavefronts accumulate into a shock wave (sonic boom on passing) rather than an infinitely high pitch. Beyond that, the geometry is a Mach cone with sin θ = v/v_s.

Is this the same as redshift?

Same family, different equation: light obeys the relativistic Doppler formula (only relative motion matters, plus a transverse term), and astronomers quote z = (λ_observed − λ_emitted)/λ_emitted. At everyday speeds (stars’ radial velocities aside), the classical formula here approximates it well; at cosmic scales it does not.

Is this Doppler effect calculator free?

Yes — free, instant, no sign-up.