Doppler Effect Calculator
The frequency you hear from a moving source or while moving yourself, from the emitted frequency, the speed of sound and each speed and direction.
Result
Enter speed of the wave in the medium, v to see the result.
https://calcgallery.com/physics/doppler-effect-calculator/
Results come from the published equations applied to the values you enter. They are not electrical design, conductor sizing, laboratory safety or medical guidance. Weather indices describe a standard person in standard conditions and are not a forecast. Where codes apply, local rules vary and must be checked. Read the full disclaimer
How to use the Doppler Effect Calculator
- Enter the frequency the source gives out, such as a siren’s or a horn’s pitch.
- Enter the speed of sound in the air or other medium the sound travels through.
- Enter how fast the source and the listener move, and whether each is heading toward or away from the other, then read the frequency heard.
The formulas
f_o = f × (v + vₒ) ÷ (v − vₛ) both moving toward each otherf_o = f × (v − vₒ) ÷ (v + vₛ) both moving apartsource only: f_o = f × v ÷ (v ∓ vₛ)listener only: f_o = f × (v ± vₒ) ÷ vThe page flips the sign of vₒ or vₛ for whichever of the two moves away, and gives the pitch heard after they pass each other by reversing both. That pitch is shown only when the two are closing on each other: a source already moving away, or one a slower listener follows, is never passed.
Limits
The formula is for sound and other waves in a medium that is itself still, with both parties moving along the line between them. Wind, motion at an angle and echoes change the result. Light needs a different, relativistic formula, so this page is not for red shift or radar speed guns.
With your numbers
- f_o = f × (v + vₒ) ÷ (v − vₛ) = 700 Hz × (1,125 ft/s + 0 ft/s) ÷ (1,125 ft/s − 88 ft/s) = 759.4021 Hz
Quick reference
Sound in still air, with both moving along the line between them. Wind and motion at an angle change it.
| Example | Frequency heard |
|---|---|
| Train horn, 150 Hz at 35 m/s toward you, sound at 340 m/s | 167.2 Hz |
| The same train moving away | 136 Hz |
| Siren, 700 Hz at 60 mph, sound at 1,125 ft/s | 759.4 Hz |
| Driving at 20 m/s toward a 440 Hz source, sound at 343 m/s | 465.7 Hz |
| Both approaching, 500 Hz, 30 and 20 m/s | 579.9 Hz |
| 1,000 Hz source leaving at 20 m/s, listener following at 10 m/s | 972.5 Hz |
Common questions about the Doppler Effect Calculator
- What is the Doppler effect?
- The change in pitch when a source of sound and a listener move relative to each other. Coming closer, the waves are squeezed together and the pitch is higher; moving apart, they are stretched and it is lower. It is why a siren drops in pitch as it passes.
- What is the Doppler effect formula?
- f_o = f × (v ± vₒ) ÷ (v ∓ vₛ), where v is the speed of sound, vₒ the listener’s speed and vₛ the source’s. Use the top signs for motion toward each other. OpenStax University Physics section 17.7 works through a 150 Hz train horn at 35.0 m/s with sound at 340 m/s: about 167 Hz as it approaches and 136 Hz as it moves away.
- What speed of sound should I use?
- The one for your medium and temperature. OpenStax gives 343 m/s for air at 20 °C, and sound is faster in warmer air and much faster in water. The page does not assume a value because the answer depends on it.
- Why is moving source different from moving listener?
- A moving source squeezes the waves themselves, while a moving listener meets unchanged waves more or less often. So a source approaching at 20 m/s raises the pitch slightly more than a listener approaching at 20 m/s. The page takes both at once.
- What happens when the source reaches the speed of sound?
- The waves in front pile up into a shock wave, heard as a sonic boom, and the formula stops giving a steady pitch. The page says so rather than printing an infinite or negative frequency. It also refuses a listener moving away faster than the sound, who never hears it.