Doppler Effect Formula
The Doppler effect formula calculates frequency shifts for moving sound and light sources.
Includes formulas for both approaching and receding.
The Formula (Sound)
The Doppler effect describes the change in frequency of a wave when the source or observer is moving. A siren sounds higher-pitched as it approaches you and lower-pitched as it moves away.
Variables (Sound)
| Symbol | Meaning |
|---|---|
| f' | Observed frequency (Hz) |
| f | Source frequency (Hz) |
| v | Speed of sound in the medium (343 m/s in air at 20°C) |
| v₀ | Speed of the observer (m/s) |
| vₛ | Speed of the source (m/s) |
Sign Convention
| Scenario | Formula |
|---|---|
| Source approaching stationary observer | f' = f × v / (v - vₛ) |
| Source receding from stationary observer | f' = f × v / (v + vₛ) |
| Observer approaching stationary source | f' = f × (v + v₀) / v |
| Observer receding from stationary source | f' = f × (v - v₀) / v |
The Formula (Light — Relativistic)
For light, the relativistic Doppler formula is used. Objects moving away show a redshift (lower frequency), while approaching objects show a blueshift (higher frequency).
Example 1
An ambulance siren emits a 700 Hz sound and approaches you at 30 m/s. What frequency do you hear?
Source approaching: f' = f × v / (v - vₛ)
f' = 700 × 343 / (343 - 30)
f' = 700 × 343 / 313
f' ≈ 767 Hz (noticeably higher pitch)
Example 2
The same ambulance passes you and drives away at 30 m/s. What frequency do you hear now?
Source receding: f' = f × v / (v + vₛ)
f' = 700 × 343 / (343 + 30)
f' = 700 × 343 / 373
f' ≈ 644 Hz (noticeably lower pitch)
When to Use It
Use the Doppler effect formula in wave and motion problems:
- Calculating pitch changes from moving vehicles (sirens, horns)
- Radar and speed guns used by police
- Medical ultrasound for measuring blood flow
- Astronomical redshift to determine if stars are approaching or receding