Physics · Waves
Doppler effect calculator.
Enter the source frequency, the speed of sound and how fast the source and observer are moving to find the frequency that is heard.
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Doppler effect formula for sound
For sound in still air, the frequency heard is fo = fs × (v ± vo) ÷ (v ∓ vs). Here v is the speed of sound, vs the source speed and vo the observer speed. The upper signs are used when the observer moves toward the source (numerator) and when the source moves toward the observer (denominator); the lower signs when moving apart (OpenStax University Physics, equation 17.20).
Worked example (the OpenStax train). A 150 Hz horn on a train moving at 35 m/s with v = 340 m/s is heard by a stationary person at 167.2 Hz as it approaches and at 136 Hz as it recedes. A stationary 150 Hz source heard by an observer walking toward it at 20 m/s is heard at 158.8 Hz.
The formula assumes a source slower than sound, motion along the line joining them, and a still medium. Light and radio waves need the relativistic Doppler formula, which this page does not give. It is a classroom model and not for radar, medical ultrasound or traffic enforcement.
Frequently asked questions
What is the Doppler effect formula?
fo = fs × (v ± vo) ÷ (v ∓ vs) for sound. Use the upper signs when source and observer approach each other and the lower signs when they separate.
Why does a siren drop in pitch as it passes?
An approaching source crowds the waves into a shorter wavelength, raising the pitch. A receding source stretches them, lowering it (HyperPhysics).
What if the source is faster than sound?
The formula no longer applies; the source outruns its own waves and produces a shock wave instead, so the calculator shows an error.
Does it work for light?
Not this formula. Light needs the relativistic Doppler shift, because it does not need a medium and its speed does not depend on the observer.
What speed of sound should I use?
The temperature box sets 331.4 + 0.61 × T m/s. At 20 °C that is 343.6 m/s. The OpenStax example uses 340 m/s.
Sources
Checked
- OpenStax University Physics Volume 1, 17.7 The Doppler Effect
- HyperPhysics: The Doppler Effect for Sound
- HyperPhysics: Speed of Sound in Air
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Scope
Idealised textbook model for sound in still air. Not for radar, medical or traffic-enforcement use. Results are arithmetic from the formulas shown, for study and general interest, and not professional or engineering advice.