About the Doppler Effect Calculator
This Doppler effect calculator finds the frequency an observer actually hears when the source of a sound, the listener, or both are moving. Enter the emitted frequency, the speed of sound, and each speed with its direction, and it returns the observed frequency, the shift in hertz and percent, and the observed wavelength.
It explains why an ambulance siren sounds higher as it approaches and drops in pitch as it passes, and it is handy for physics homework, acoustics, radar and ultrasound intuition, and motorsport or train-spotting curiosity. The comparison table shows the pitch heard on approach and after passing for the same speeds.
The calculator uses the classical formula for sound in a still medium, with speeds measured along the line joining source and observer. It defaults to 343 m/s, the speed of sound in air at about 20 °C. For light at relativistic speeds a different formula applies.
With the default inputs, the observed frequency is 482.17 Hz. Change any value above to recalculate instantly.
How to use the doppler effect calculator
- 1Enter the frequency the source emits.
- 2Keep 343 m/s for air or enter the speed of sound for your medium.
- 3Enter the source speed and whether it moves toward or away from you.
- 4Enter the observer speed and direction (0 if standing still).
- 5Read the observed frequency, shift and the approach-vs-receding comparison.
Formula and method
The observed frequency depends on how the source and observer move relative to the air. A source moving toward you squeezes the wavefronts together, shortening the wavelength; an observer moving toward the source meets wavefronts more often. Both raise the pitch.
In the formula, v_o is positive when the observer moves toward the source and v_s is positive when the source moves toward the observer; motion away uses negative values. The calculator applies these signs from your direction choices. If the source reaches the speed of sound the denominator becomes zero and a shock wave forms instead.
- f'
- Observed frequency (Hz)
- f
- Emitted source frequency (Hz)
- c
- Speed of sound in the medium (m/s)
- v_o
- Observer speed, + toward the source
- v_s
- Source speed, + toward the observer
Worked examples
440 Hz horn approaching at 30 m/s
f' = 440 × 343 ÷ (343 − 30) = 482.2 Hz. A car horn tuned to A4 sounds about one and a half semitones sharp as the car (about 108 km/h) comes toward you.
700 Hz siren receding at 25 m/s
Moving away, the source speed is subtracted: f' = 700 × 343 ÷ (343 + 25) = 652.4 Hz, about 48 Hz lower than the siren actually emits.
Cyclist riding at 20 m/s toward a 500 Hz alarm
Only the observer moves: f' = 500 × (343 + 20) ÷ 343 = 529.2 Hz. Moving through the sound waves means meeting more of them each second.
Two trains closing at 15 m/s each, 1,000 Hz whistle
Both motions raise the pitch: f' = 1000 × (343 + 15) ÷ (343 − 15) = 1,091.5 Hz.
Frequently asked questions
What is the Doppler effect?+
The Doppler effect is the change in observed frequency of a wave when the source and observer move relative to each other. Approaching raises the frequency (higher pitch); separating lowers it.
What is the Doppler effect formula for sound?+
f' = f × (c + v_o) / (c − v_s), where c is the speed of sound, v_o is the observer’s speed toward the source and v_s is the source’s speed toward the observer. Use negative values for motion away.
Why does a siren change pitch as it passes?+
While approaching, each wave is emitted closer to you than the last, so waves arrive more often. After it passes, each wave starts farther away, so they arrive less often and the pitch drops.
Does the Doppler effect apply to light?+
Yes. Light from approaching stars is blueshifted and from receding galaxies redshifted. At high speeds you must use the relativistic formula, since light has no medium and moves at c for every observer.
Where is the Doppler effect used?+
Police radar speed guns, weather radar, medical ultrasound to measure blood flow, astronomy to measure how fast stars and galaxies move, and sonar all rely on measuring Doppler shifts.