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Doppler Effect Calculator

Calculate the observed frequency shift when a sound source moves toward a stationary observer.

Result

Observed Frequency
547.9 Hz
Frequency Shift
+47.9 Hz

This handles a source moving toward a stationary observer (positive speed = approaching, raising pitch; enter a negative speed for a source moving away, which lowers pitch).

About the Doppler Effect Calculator

This calculator finds the frequency a stationary listener actually hears when a sound source is moving toward or away from them, such as an approaching siren or passing train horn. It applies the acoustic Doppler shift formula to show both the observed frequency and how much it has shifted from the source's true frequency.

How It Works

You enter the source's true frequency, its speed (positive for approaching, negative for moving away), and the speed of sound in the medium. The calculator divides the speed of sound by the difference between the speed of sound and the source's speed, then multiplies that ratio by the source frequency to get the frequency the observer hears.

Observed frequency = Source frequency x (Speed of sound / (Speed of sound - Source speed)). Frequency shift = Observed frequency - Source frequency.

Formula & Methodology

By hand, first subtract the source speed from the speed of sound (using a negative source speed for a receding source). Divide the speed of sound by that result, then multiply by the source's original frequency. For a source at rest (speed = 0), the ratio equals 1 and the observed frequency exactly equals the source frequency, as expected.

Examples

An ambulance siren approaching at 30 m/s

With a 500 Hz siren, sound speed 343 m/s, and source speed 30 m/s, observed frequency = 500 x (343 / (343 - 30)) = 500 x (343/313), about 547.9 Hz, a shift of roughly +47.9 Hz.

The same siren moving away at 30 m/s

Entering -30 m/s for source speed gives observed frequency = 500 x (343 / (343 + 30)) = 500 x (343/373), about 459.8 Hz, a drop of about 40.2 Hz, illustrating the classic pitch drop as a vehicle passes.

Advantages

  • Lets you compare the pitch shift for both approaching and receding sources just by flipping the sign of the speed input.
  • Shows the numeric frequency shift alongside the observed frequency, making the size of the Doppler effect immediately clear.
  • Uses an adjustable speed of sound, so the same tool can model conditions other than standard sea-level air (343 m/s).

Common Mistakes

  • Entering a source speed at or above the speed of sound, which the calculator rejects since the underlying subsonic formula no longer applies.
  • Forgetting the sign convention and entering a positive speed for a source that is actually moving away, which produces the opposite pitch shift from what was expected.
  • Assuming the formula also handles a moving observer or a source moving off-axis, when it specifically models a stationary observer and straight-line source motion.

Edge Cases to Watch For

  • The calculator requires the source speed to be strictly less than the speed of sound; if speed of sound minus source speed is zero or negative, it returns an error since the standard subsonic formula breaks down at and beyond the sound barrier.
  • A negative source speed correctly models a source moving away, producing an observed frequency lower than the source frequency (a pitch drop).
  • This formula assumes a stationary observer and a source moving directly along the line connecting source and observer; it does not account for an observer that is also moving, or for motion at an angle.

Common Use Cases

  • Physics students verifying textbook Doppler effect problems involving sirens, horns, or other moving sound sources.
  • Audio and acoustics hobbyists exploring how vehicle speed translates into a perceptible pitch change.
  • Educators building demonstrations that connect the everyday experience of a passing siren to the underlying wave physics.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

Why does a siren's pitch drop as it passes you?

As the ambulance approaches, each successive sound wave is emitted from a slightly closer position, compressing the waves and raising the perceived frequency (higher pitch) - once it passes and moves away, each wave is emitted from farther away, stretching the waves out and lowering the perceived frequency, which is the classic Doppler effect pitch drop you hear.

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Conclusion

The Doppler effect explains why a moving sound source seems to change pitch as it passes a stationary listener, and this calculator turns that qualitative experience into an exact frequency shift. Adjust the source speed's sign and magnitude to see how approach versus recession changes what the observer actually hears.