Doppler Sound Shift Calculator
The Doppler effect describes the change in perceived frequency of a sound when the source and observer are in relative motion. A passing ambulance is a classic example: the siren pitch drops noticeably as the vehicle passes. The effect is governed by f' = f x (c + v_o) / (c - v_s), where c is the speed of sound, v_o is the observer's speed (positive toward the source), and v_s is the source speed (positive toward the observer). Enter the source frequency and velocities in metres per second to find the observed frequency.
Doppler formula
f' = f × (c + vo) / (c - vs)
Where f is source frequency, c is the speed of sound, v_o is observer velocity (positive toward source), and v_s is source velocity (positive toward observer). The formula applies only when all velocities are below c (subsonic).
Practical notes
- An ambulance at 30 m/s emitting 700 Hz: approaching gives 764 Hz; receding gives 645 Hz.
- The pitch shift is asymmetric: the approaching shift is larger than the receding shift.
- Valid only for v_s < c. The denominator becomes zero at c (source at Mach 1).
Frequently asked questions
What is the Doppler effect for sound?
The Doppler effect is the change in observed frequency when a sound source and observer are moving relative to each other. A source approaching an observer produces a higher pitch; a receding source produces a lower pitch.
What is the Doppler formula for sound?
f_observed = f_source x (c + v_observer) / (c - v_source). Here c is the speed of sound (343 m/s in air at 20 degrees C), v_observer is positive when moving toward the source, and v_source is positive when moving toward the observer.
What sign conventions apply?
Observer velocity is positive when moving toward the source and negative when moving away. Source velocity is positive when moving toward the observer and negative when moving away. Both are magnitudes in this calculator using the sign convention built into the formula.
What happens when a source exceeds the speed of sound?
The classical Doppler formula breaks down at or above the speed of sound (Mach 1). A supersonic source creates a shock wave (sonic boom). This calculator is valid only for subsonic speeds.
Where is the Doppler effect used professionally?
Doppler radar in meteorology and aviation, police speed guns, medical ultrasound (blood flow measurement), and astronomical spectroscopy all rely on the Doppler effect. In audio production it creates the Leslie speaker 'vibrato' effect.
Official sources
- OpenStax University Physics Vol. 1, Chapter 17: Sound.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.