Doppler Effect Calculator
The frequency you hear when a source or observer is moving — the reason a siren drops in pitch as it passes.
The observed frequency is f × (v + v_o) ÷ (v − v_s), where v is the speed of sound, v_o the observer's speed towards the source and v_s the source's speed towards the observer.
How the doppler effect calculator works
The observed frequency is f × (v + v_o) ÷ (v − v_s), where v is the speed of sound, v_o the observer's speed towards the source and v_s the source's speed towards the observer. Motion towards raises the pitch; motion away lowers it.
Source motion and observer motion are not symmetric, which surprises people. A source moving towards you at half the speed of sound doubles the frequency, but you moving towards a stationary source at the same speed raises it only by half. The reason is that a moving source compresses the wavelengths themselves, while a moving observer merely meets them faster.
Formula: f' = f × (v + v_observer) ÷ (v − v_source)
Worked examples
| Inputs | Observed frequency | Note |
|---|---|---|
| A 500 Hz siren approaching at 30 m/s | 547.923 Hz | 547.9 Hz, dropping to 459.8 as it passes |
| Standing still, nothing moving | 440 Hz | no shift |
| Driving towards a stationary bell | 543.732 Hz | 543.7 Hz — less shift than a moving source |
FAQFrequently asked questions
Why does a siren change pitch as it passes?
Approaching, the waves are compressed and the pitch rises; receding, they are stretched and it falls. The drop happens as it goes by.
Is a moving source the same as a moving listener?
No. A moving source compresses the wavelengths themselves; a moving listener merely meets them faster. The source effect is larger.
What is the speed of sound?
About 343 m/s in air at 20°C, rizing with temperature, and about 1,480 m/s in water.
What happens at the speed of sound?
The source catches its own waves and they pile into a shock wave — the sonic boom. The Doppler formula no longer applies.
Does this work for light?
The idea does, but light needs the relativistic formula. Redshift from receding galaxies is the same phenomenon.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.