Doppler Shift⚠ unverified
Physics / Acoustics · Observed frequency for a moving source and observer (speed of sound c = 343 m/s)
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| f0 | f0 | Hz | 440.0 | Source frequency |
| vs | vs | m/s | 30.0 | Source speed (toward observer +) |
| vo | vo | m/s | 0.0 | Observer speed (toward source +) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| f | f | Hz | Observed frequency |
The science & history
Understanding the Parameters
- $f_0$ — emitted frequency (siren, speaker, …).
- $v_s$ — moving source toward the listener raises $f$ (denominator shrinks). Require $|v_s| < c$.
- $v_o$ — observer moving toward the source also raises $f$.
- $c$ — speed of sound; the registry formula uses $c$ but may fix it internally (e.g. 343 m/s) if not listed as an input — check the live card.
Derivation (Approaching a Proof)
Wave crests: a moving source shortens/lengthens wavelength $\lambda' = (c \mp v_s)/f_0$. A moving observer changes the relative speed at which crests are met. Combining still-air cases yields
$$f = f_0\frac{c \pm v_o}{c \mp v_s}$$
with sign conventions as above. Wind and 3-D geometry need the full relative-velocity form.
History
Christian Doppler (1842) predicted the effect; Buys Ballot verified it with musicians on a train. It underpins radar, medical ultrasound, and astronomy (relativistic form for light).
Related Concepts: Speed of Sound in Air, Sound Pressure Level, Octave Band Center
Notes: Registry calculator doppler-shift (unverified). 1-D, still air. Confirm $c$ and sign
conventions on the live calculator.