Doppler effect calculator
Enter the sound and the speeds, get the frequency you hear.
What is the Doppler effect formula?
fₒ = fₛ × (v ± vₒ) ÷ (v ∓ vₛ), where v is the speed of sound, vₒ the observer’s speed and vₛ the source’s speed. Use the top signs when they move toward each other and the bottom signs when they move apart (OpenStax University Physics).
Example: a train horn
A 150 Hz horn on a train moving at 35 m/s, with sound at 340 m/s: approaching, you hear 150 × 340 ÷ 305 = 167 Hz; after it passes, 150 × 340 ÷ 375 = 136 Hz. Someone on the train hears 150 Hz.
What speed of sound should I use?
About 343 m/s in dry air at 20 °C (68 °F); it rises with temperature. The speed of sound calculator gives the value for your temperature.
Why does the pitch drop as the source passes?
Waves bunch up ahead of a moving source and spread out behind it, so you hear a higher frequency while it approaches and a lower one as it moves away.
What if the source moves faster than sound?
The formula breaks down when the source reaches the speed of sound toward you — the waves pile into a shock wave, the sonic boom.
Is the shift the same if the observer moves instead of the source?
Not exactly. For a 700 Hz siren and a relative speed of 30 m/s, a moving source gives 767.1 Hz approaching and 643.7 Hz receding, while a moving observer hears 761.2 Hz and 638.8 Hz. The formulas differ because the medium (the air) is the reference for the sound: a moving source changes the wavelength in the air, a moving observer changes only how quickly the wave crests are met.
Does the Doppler effect apply to light?
Yes, but light needs a different formula. It does not need a medium, so only the relative velocity of source and observer matters, and relativity enters at high speeds. The formula on this page is for sound in a medium such as air.
How the signs work
The calculator uses f = f₀ × (v + vₒ) ÷ (v − vₛ), with v the speed of sound in the medium, vₒ the observer's speed toward the source and vₛ the source's speed toward the observer. Both speeds are measured relative to the air. A source moving away has a negative vₛ and an observer moving away a negative vₒ. When both move toward each other the shift is the product of the two effects, so the frequency rises more than for either alone.
Worked example: a 700 Hz siren at 343 m/s
A siren sounding 700 Hz is on a vehicle moving at 30 m/s with sound at 343 m/s. A stationary listener hears 700 × 343 ÷ (343 − 30) = 767.1 Hz as it approaches and 700 × 343 ÷ (343 + 30) = 643.7 Hz as it recedes, a drop of 123.4 Hz at the moment it passes. If the source and the observer each approach the other at 20 m/s, the observed frequency is 786.7 Hz. The speed of sound itself matters: warmer air raises it, which slightly reduces the shift for the same vehicle speed.
Common mistakes
The most common error is a sign mistake: a source moving toward you puts a minus sign in the denominator, and an observer moving toward the source puts a plus sign in the numerator. Another is using the vehicle speed relative to the ground when there is wind, since the speeds must be relative to the air. A moving source does not change the frequency the source itself emits; the change is in what a listener receives. The formula also fails when the source speed reaches the speed of sound, where a shock wave forms.
Sources: OpenStax University Physics, Volume 1, section 17.7 (the Doppler effect for sound, Eq. 17.13 and the sign conventions). Related: speed of sound calculator, decibel calculator, standing wave calculator and speed calculator.