Doppler Effect Calculator
Inputs
| Source frequency | 1,000 Hz |
|---|---|
| Source speed | 20 m/s |
| Observer speed | 0 m/s |
| Speed of sound | 343 m/s |
Doppler Effect Calculator
Calculate the frequency a listener hears when a sound source or observer is moving, using the Doppler formula f = f₀·(v + vₒ)/(v − vₛ). Enter the source frequency, speed of sound, and the source and observer speeds.
Inputs
Constants
Results
Enter a value to see results.
There is no net motion along the line between them, so the observed frequency equals the source frequency.
Doppler Effect
The Doppler effect is the change in the frequency of a wave when its source and the observer are moving relative to each other. For sound, this is the familiar rise and fall in pitch of a passing siren. The observed frequency is given by , where is the frequency the source emits, is the speed of sound, and and are the speeds of the observer and source along the line between them. Christian Doppler described the effect in 1842, and it now underlies everything from radar speed guns to the measurement of the expanding universe.
This calculator returns the frequency an observer actually hears and the size of the shift, given the source frequency, the speed of sound, and the two speeds.
Why the pitch changes
The pitch you hear depends on how quickly wave crests arrive at your ear. When the source moves toward you, each successive crest is emitted a little closer than the last, so the crests bunch up and arrive more often — a higher frequency. When the source moves away, the crests are stretched out and arrive less often — a lower frequency. The observer's own motion does the same thing: moving toward the source, you run into the crests faster. The effect depends on motion along the line joining the two, not motion across it.
Formula
| Quantity | Symbol | Meaning |
|---|---|---|
| Source frequency | f₀ | Frequency emitted by the source |
| Speed of sound | v | Speed of sound in the medium (≈ 343 m/s in air) |
| Source speed | Positive when the source moves toward the observer | |
| Observer speed | Positive when the observer moves toward the source | |
| Observed frequency | What the observer hears, |
The sign rule is the only thing to get right: each speed counts as positive when that body is heading toward the other, and negative when heading away.
Worked example
An ambulance siren emits a 1000 Hz tone and drives toward a stationary listener at 20 m/s. The speed of sound is 343 m/s. The observer is at rest, so :
f=f0⋅v−vsv+vo=1000×343−20343+0=1000×323343=1061.9 HzThe pitch is raised by about 62 Hz while the ambulance approaches. The instant it passes and begins to recede, becomes −20 m/s and the heard frequency drops to Hz — a total swing of around 117 Hz, which is what makes the "nee-oww" of a passing siren so distinct.
Light and the wider Doppler effect
The same idea applies to light and other electromagnetic waves, though the exact formula differs because light needs no medium and relativity enters at high speeds. A receding light source is shifted toward longer, redder wavelengths (redshift) and an approaching one toward the blue. Astronomers measure the redshift of galaxies to find how fast they recede, the foundation of modern cosmology. Closer to home, Doppler radar uses the frequency shift of reflected microwaves to read the speed of cars and the motion of storm systems.
Limitations
This calculator covers the acoustic Doppler effect with the source and observer moving directly along the line between them. If they move at an angle, only the component of velocity along that line counts. The formula also assumes the source stays below the speed of sound; at or above it the denominator vanishes and a shock wave (a sonic boom) forms, which this simple model cannot describe.
Frequently Asked Questions (FAQ)
What is the Doppler effect formula?
For sound, the frequency heard by an observer is f = f₀·(v + vₒ)/(v − vₛ), where f₀ is the emitted frequency, v is the speed of sound, vₒ is the observer's speed and vₛ the source's speed. The speeds are taken as positive when each is moving toward the other. The same effect shifts the pitch up as a source approaches and down as it recedes.
How do the signs of the speeds work?
Each speed is measured along the line joining the source and observer. A positive source speed vₛ means the source moves toward the observer, which shrinks the denominator and raises the pitch. A positive observer speed vₒ means the observer moves toward the source, which enlarges the numerator and also raises the pitch. Reverse the sign of either when that body is moving away.
Where do I notice the Doppler effect?
The classic example is a passing ambulance or train: the siren or horn sounds higher-pitched as it approaches and noticeably lower as it passes and recedes. The pitch does not slide gradually — it is higher the whole time the vehicle approaches and lower the whole time it moves away, with the drop happening as it goes by. Racing cars and low-flying aircraft show the same effect.
Does the Doppler effect apply to light?
Yes, but with a different formula. Light has no medium, so only the relative velocity matters, and at high speeds relativity must be included. The optical Doppler effect shifts light toward the red end of the spectrum when a source recedes (redshift) and toward the blue when it approaches (blueshift). Astronomers use galactic redshifts to measure how fast distant galaxies are moving away, which is evidence for the expansion of the universe. This calculator covers the sound (acoustic) case.