Doppler Effect Calculator
Calculate the observed frequency when a sound source and observer are in relative motion using the Doppler effect equation.
About this calculator
This calculator applies the classical (non-relativistic) Doppler equation for sound, f_observed = f_source × (speed of sound + observer velocity) / (speed of sound + source velocity), to find how motion between a sound source and a listener shifts the perceived pitch. The sign convention is the trickiest part to get right: source velocity is positive when moving away from the observer (which lowers the ratio and drops the frequency) and observer velocity is positive when moving toward the source (which raises the observed frequency) — mixing these up is the most common way to get an answer with the wrong direction of shift.
From the observed frequency the calculator derives the absolute frequency shift, the percent shift, and the wavelengths at both the source and after the shift (using wavelength = speed / frequency), and it charts observed frequency across a sweep of source velocities so you can see the shift curve bend sharply as source speed approaches the speed of sound itself — the classic sonic-boom threshold. Because this uses the sound-wave Doppler formula rather than the relativistic Doppler effect for light, it only applies to waves traveling through a physical medium (air, water, etc.) at speeds well below that medium's own wave speed; for anything approaching or exceeding the speed of sound, or for electromagnetic waves, an entirely different set of equations is needed.
Inputs
Results
Observed Frequency
404.61 Hz
How to Use This Calculator
- Enter Source Frequency, Source Velocity, and Observer Velocity.
- Set Speed of Sound.
- Review the Observed Frequency (Hz) result.
- Use Frequency Shift (Hz) and Percent Shift (%) to inform your decision.
- Use the chart to visualize the results and explore different scenarios by adjusting inputs.
How the result changes with Source Frequency
| Source Frequency | Observed Frequency |
|---|---|
| 220 | 202.31 Hz |
| 330 | 303.46 Hz |
| 660 | 606.92 Hz |
| 1,100 | 1,011.53 Hz |
What each input means
- Source Frequency
- Frequency emitted by the source. Concert A = 440 Hz.
- Source Velocity
- Velocity of the source. Positive = moving away from the observer, negative = approaching.
- Observer Velocity
- Velocity of the observer. Positive = moving toward the source, negative = moving away.
- Speed of Sound
- Speed of sound in the medium. Air at 20°C ≈ 343 m/s, water ≈ 1480 m/s.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersSource Frequency = 440, Source Velocity = 30, Observer Velocity = 0, Speed of Sound = 343 = 4 input(s) provided
- Calculate Observed FrequencyObserved Frequency404.61 = 404.61
- Calculate Frequency ShiftFrequency Shift-35.39 = -35.39
- Calculate Percent ShiftPercent Shift-8.04 = -8.04
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Which direction of source or observer motion raises the observed frequency, and which lowers it?
Source velocity is positive when the source moves away from the observer, which increases the denominator (speed of sound + sourceVelocity) and lowers the observed frequency — the classic 'pitch drops as it passes and recedes' effect. Observer velocity is positive when the observer moves toward the source, which increases the numerator and raises the observed frequency. Getting either sign backwards will flip the direction of the shift.
How are the source and observed wavelengths calculated?
Both use the basic wave relationship wavelength = speed / frequency, applied to the speed of sound in the given medium. Source wavelength divides speed of sound by the emitted (source) frequency, while observed wavelength divides it by the Doppler-shifted observed frequency — so a frequency shift automatically produces a corresponding, inverse wavelength shift.
Why does the observed-frequency chart bend sharply as source velocity approaches the speed of sound?
The denominator in the Doppler formula is (speed of sound + source velocity), and as an approaching source's velocity magnitude gets close to negative the speed of sound, that denominator approaches zero — driving the observed frequency toward very large values. This is the mathematical signature of the sonic-boom threshold: the classical Doppler formula breaks down entirely once a source's speed reaches or exceeds the speed of sound.
Can this calculator be used for light or other electromagnetic waves instead of sound?
No — this implements the classical, non-relativistic Doppler formula for waves traveling through a physical medium like air or water, which requires a defined medium speed (speed of sound) that the wave travels through. Light doesn't need a medium and its Doppler shift follows the relativistic Doppler equation instead, which depends on the speed of light and Lorentz factors rather than a medium's wave speed.
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