The formula
f' = f · (v + v₀) / (v − vₛ)
| Symbol | Quantity | Unit |
|---|---|---|
| f' | Perceived frequency | Hz |
| f | Emitted frequency | Hz |
| v | Speed of sound | m/s |
| v₀ | Observer speed | m/s |
| vₛ | Source speed | m/s |
What it means
The Doppler effect does not change the sound the source emits: it changes how often the waves reach you. If the siren is approaching, each wave leaves from a slightly closer point than the last, so they arrive closer together and you hear them higher. Once it passes, the opposite happens and the pitch drops sharply. That jump between before and after is the characteristic wail.
How to work it out by hand
- Take the speed of sound in the medium: 343 m/s in air at 20 °C
- Make velocities positive when they close the gap and negative when they widen it
- Multiply the emitted frequency by (v + observer speed)
- Divide by (v − source speed)
What is worth knowing
The sign of the velocities is the only thing to keep straight, and the rule is simple: positive when the motion brings the two together, negative when it pulls them apart. The speed of sound is not a universal constant but a property of the medium and its temperature: 343 m/s in air at 20 °C, down to 331 at 0 °C, and up to around 1,480 in water. And the same phenomenon explains things far further away: the redshift of galaxies is Doppler applied to light, and that is where the evidence for an expanding universe came from.