Doppler Shift Calculator
The rising and falling pitch of a passing siren is the familiar part. The part worth understanding is that a moving source and a moving observer do not produce the same shift, even at the same relative speed — the source changes the wavelength that leaves it, while the observer changes how quickly waves arrive. Those are different mechanisms, and the formula treats them differently. This generates scenarios where that asymmetry is visible.
What this generator does
Generates a source frequency and speeds for both the source and the observer, then computes the frequency actually heard using the classical Doppler formula for sound. Positive speeds mean closing; negative mean separating.
How to use this tool
- Generate a scenario and read the source and observer speeds.
- Check whether the pitch should rise or fall before reading the answer.
- Compare a moving source with a moving observer at the same speed — the shifts differ.
- Notice how the shift grows sharply as the source approaches the speed of sound.
Understanding the controls
- Generate
- Produces a source between 100 and 2,000 Hz with source and observer speeds up to 60 and 30 metres per second in either direction.
- Seed
- Any word reproduces exactly the same scenario, so a problem can be set and marked later.
Common use cases
- Physics practice on the Doppler effect with checkable answers
- Teaching why source and observer motion are not interchangeable
- Generating problems for a lesson or a problem set
- Understanding radar and sonar principles at a basic level
- Setting the same scenario twice from a seed
How this generator works
The source's speed appears in the denominator and the observer's in the numerator, which is exactly why they are not interchangeable: as the source approaches the speed of sound the denominator approaches zero and the shift grows without limit, while no observer speed does anything so dramatic. The check confirms the arithmetic recomputes and that the direction of motion matches the direction of the shift.
Randomness and fairness
The frequency and both speeds are random; the observed frequency is then a deterministic calculation. A seed reproduces the same scenario exactly and is therefore explicitly not cryptographically secure. Without a seed the browser's cryptographically secure generator is used.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- The classical form for sound, using 343 m/s for dry air at 20°C — the speed of sound varies with temperature.
- Light needs the relativistic Doppler formula, where only relative velocity matters and this asymmetry disappears entirely.
- Motion is along the line between source and observer; the transverse case is not covered.
- Speeds at or above the speed of sound are excluded, where this form breaks down and a shock wave forms instead.
- Nothing is saved here — the seed is the only way back to the same numbers.
Privacy and your data
Every figure is computed in your browser. Nothing about the scenario or your seed is transmitted or kept.
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