Doppler Effect Calculator
Observed frequency and shift when source, observer or both are moving.
Formula
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), vs = 30 m/s toward observer, vo = 0
f' = 500 · 343 / (343 − 30) = 500 · 343/313 ≈ 548.0 Hz
Related tools
FAQs
How to calculate doppler effect frequency?
The classical sound Doppler formula is f' = f × (v ± v_o)/(v v_s), where v is the wave speed in the medium, v_o is the observer's velocity, and v_s is the source's velocity. Use the top signs when motion is toward the other party, bottom signs for moving away. So a 1000 Hz siren approaching at 30 m/s in still air (v ≈ 343 m/s) sounds like f' = 1000 × 343 / (343 − 30) ≈ 1096 Hz. Higher frequency on approach, lower on retreat — that's the pitch shift you hear from passing ambulances.
How do I use doppler effect formula moving source moving observer?
When both source and observer move, use the full formula: f' = f × (v ± v_o)/(v v_s). Sign convention is the trickiest part — pick toward as positive in the numerator and toward as negative in the denominator, both relative to the line joining them. If a 500 Hz source moves at 20 m/s toward an observer who's moving at 10 m/s toward the source, then f' = 500 × (343 + 10)/(343 − 20) ≈ 546 Hz. Always pause and sketch the velocities before substituting — the signs are where most marks are lost.
How do I use observed frequency calculator moving observer?
If only the observer moves and the source stays put, the formula simplifies to f' = f × (v ± v_o)/v. Plus sign for moving toward the source, minus for moving away. Example: a 440 Hz tuning fork heard by someone driving at 25 m/s straight toward it sounds like f' = 440 × (343 + 25)/343 ≈ 472 Hz. The observer essentially encounters wavefronts faster, so each wave reaches them sooner and frequency rises. Calculators take the guesswork out of the sign choice if you specify the direction correctly.
What happens to frequency when source moves toward observer?
Wave crests bunch up in the direction of source motion because each new wave is emitted from a position slightly closer than the last. The observer encounters those compressed wavefronts in less time, so the perceived frequency increases — pitch goes up. Behind the source, wavefronts spread out, and trailing observers hear a lower pitch. That's the classic ambulance-passing-by effect: rising pitch on approach, sudden drop after it passes. The actual frequency emitted by the siren never changes; only the rate at which wavefronts hit the listener does.
How do I use speed of sound for doppler effect calculator?
Most Doppler calculators default to the speed of sound in dry air at 20 °C, around 343 m/s. But sound speed depends on temperature: roughly v ≈ 331 + 0.6T m/s, where T is in Celsius. So at 0 °C it's 331 m/s, and at 35 °C it's about 352 m/s. In water it jumps to nearly 1480 m/s, in steel up around 5000 m/s. If your calculator lets you set the medium speed manually, use it — accuracy matters when the source or observer speed is a noticeable fraction of the wave speed.
How do I use doppler shift in Hz calculator?
Doppler shift is the difference Δf = f' − f, which tells you how much the frequency moves up or down compared to the rest frequency. Calculators that report Δf save you the subtraction. Positive Δf means approach, negative means recession. So a 1500 Hz source heard at 1620 Hz gives Δf = +120 Hz. This shift is what radar guns and astronomical redshift measurements rely on. Even a small shift in megahertz reveals motion — which is how police radar guns clock cars and how astronomers know galaxies are flying apart.
How do I use doppler effect sound vs light formula?
For sound, the formula depends on a medium and uses f' = f × (v ± v_o)/(v v_s). For light, there's no medium, and special relativity demands a different equation: f' = f × √((1 − β)/(1 + β)) for recession, with β = v/c. Light's formula is symmetric — only relative velocity matters, not whether source or observer moves. At low speeds, both formulas give nearly the same answer, but as v approaches c, the relativistic version diverges. That's why redshift in cosmology uses the light version, never the sound version.