What Is the Doppler Effect and How Is It Calculated?
The Doppler effect is the change in the observed frequency of a wave when the source of the wave and the observer move relative to each other. Moving closer raises the frequency (higher pitch for sound); moving apart lowers it. It was first described by Austrian physicist Christian Doppler in 1842.
The classical Doppler effect formula for waves in a medium is: f′ = f × (v ± vₒ) ÷ (v ∓ vₛ), where f′ is the observed frequency, f is the emitted frequency, v is the speed of the wave in the medium, vₒ is the observer's speed and vₛ is the source's speed. Use + in the numerator when the observer moves toward the source, and − in the denominator when the source moves toward the observer. The observed wavelength is λ′ = v ÷ f′.
The effect was confirmed experimentally in 1845 by Dutch scientist C. H. D. Buys Ballot, who had trumpeters play a steady note on a moving train and musicians with perfect pitch record what they heard on the platform. According to standard physics references, the speed of sound in dry air at 20 °C is 343 m/s (1,235 km/h or 767 mph), rising about 0.6 m/s for every 1 °C increase.
How to Use This Doppler Effect Calculator
Fill in the fields and the observed frequency updates instantly:
- Source frequency (f): The pitch emitted, in hertz. Concert A is 440 Hz; an emergency siren is typically 600–1,500 Hz.
- Wave speed (v): 343 m/s for sound in air at 20 °C. Use about 1,480 m/s for sound in water, or adjust for temperature.
- Source speed and direction: How fast the source moves and whether it approaches or recedes from the observer.
- Observer speed and direction: The same for the listener. Leave at 0 for a stationary observer.
Choose m/s, km/h or mph for all speeds; values are shared through the URL. The formula is the same worldwide, but road speeds are quoted in km/h in most countries and mph in the US and UK, so the unit tabs convert for you.
Doppler Shift Examples: What Frequency Will You Hear?
The table shows observed frequencies for a stationary listener and a moving source in air at 20 °C, so you can sanity-check the calculator.
| Scenario | Approaching | Receding |
|---|---|---|
| 440 Hz source at 30 m/s (108 km/h) | 482.2 Hz | 404.6 Hz |
| 700 Hz siren at 90 km/h | 755.0 Hz | 652.5 Hz |
| 400 Hz train horn at 60 mph | 414.5 Hz | 386.5 Hz |
Doppler shifts underpin police speed radar, weather radar, medical Doppler ultrasound for measuring blood flow, and astronomers' redshift measurements of receding galaxies.
Frequently Asked Questions About the Doppler Effect
What is the Doppler effect formula?
The Doppler effect formula for sound is f′ = f × (v ± vₒ) ÷ (v ∓ vₛ), where f is the source frequency, v is the wave speed, vₒ is the observer speed and vₛ is the source speed. Use the upper signs when observer and source move toward each other.
Why does a siren sound higher as it approaches and lower as it passes?
As a source approaches, each wave crest is emitted closer to the previous one, shortening the wavelength and raising the frequency heard. After it passes, crests are emitted farther apart, lengthening the wavelength and lowering the pitch. A 700 Hz siren at 90 km/h shifts to about 755 Hz approaching and 652 Hz receding.
What is the difference between a moving source and a moving observer?
A moving source changes the wavelength of the wave in the medium, while a moving observer changes only the rate at which crests are encountered. For sound, the two cases give slightly different results at the same speed because the medium (air) is the fixed reference frame; for light, only relative speed matters.
Does the Doppler effect work for light?
Yes, but light needs the relativistic formula f′ = f × √((1 − β) ÷ (1 + β)), where β = v ÷ c for a receding source, because light has no medium. Edwin Hubble used the resulting redshift of galaxies in 1929 to show the universe is expanding. This calculator uses the classical formula, which is accurate when speeds are far below the speed of light.
How accurate is this Doppler effect calculator?
It applies the exact classical Doppler formula for waves in a stationary medium and is accurate for sound, water and ultrasound waves when the source speed stays below the wave speed. It assumes motion along the line between source and observer and does not model wind, temperature gradients or supersonic shock waves.