Doppler Effect Calculator

Observed frequency and shift when source, observer or both are moving.

Source frequency f₀ (Hz)

Wave speed v (m/s, e.g. 343 for air)

Source speed v_s (m/s)

Source direction

Observer speed v_o (m/s)

Observer direction

Results

Formula

f' = f₀ · (v ± v_o) / (v ∓ v_s)
Top signs: observer moving toward source / source moving toward observer (pitch rises).
Bottom signs: opposite case (pitch falls).

Physics behind the Doppler effect

If a source emits wavefronts at frequency f₀ and moves toward you, each successive crest is emitted from a slightly closer position, so crests arrive more frequently and the observed pitch rises. When the source recedes, crests are spread out and the pitch falls. A moving observer has a similar effect: moving into the waves encounters more crests per second, moving away encounters fewer. The classic example is an ambulance siren rising in pitch as it approaches and falling as it passes.

Worked example

f₀ = 500 Hz, v = 343 m/s (air), v_s = 30 m/s toward observer, v_o = 0

f' = 500 · 343 / (343 − 30) = 500 · 343/313 ≈ 548.0 Hz

Related tools

Wave Speed Snell's Law Wave Interference

FAQs

What is the Doppler effect?

The change in observed frequency when source and observer move relative to each other.

Speed of sound in air?

About 343 m/s at 20 °C.