What is the Doppler Effect?
The Doppler effect (or Doppler shift) describes the change in frequency of a wave in relation to an observer moving relative to the wave source. When a source of sound approaches you, the sound waves are compressed, and you hear a higher pitch. As it moves away, the waves are stretched and the pitch drops. This phenomenon was first described by Austrian physicist Christian Doppler in 1842.
You experience it every day: the rising tone of an approaching ambulance siren that drops as it passes you — that is the Doppler effect in action.
Doppler Effect Equation
The observed frequency is calculated with the formula:
f = f₀ × (v + vr) / (v + vs)
Where:
- f — Observed frequency (Hz): what the listener actually hears.
- f₀ — Source frequency (Hz): the frequency emitted by the source.
- v — Speed of sound in the medium (m/s or ft/s). In air at 20 °C: 343.2 m/s (1125.33 ft/s).
- vr — Receiver velocity: positive if moving toward the source.
- vs — Source velocity: positive if moving away from the observer.
Sign Convention
| Movement | Sign | Effect on Frequency |
|---|---|---|
| Source moves toward observer | vs is negative | Frequency increases ↑ |
| Source moves away from observer | vs is positive | Frequency decreases ↓ |
| Receiver moves toward source | vr is positive | Frequency increases ↑ |
| Receiver moves away from source | vr is negative | Frequency decreases ↓ |
Step-by-Step Example: Ambulance & Bicycle
You are riding a bicycle along a road. An ambulance behind you is approaching. Both are heading in the same direction.
- Ambulance speed: 60 km/h = 16.67 m/s
- Bicycle speed: 15 km/h = 4.17 m/s
- Siren frequency (f₀): 700 Hz
- Speed of sound: 343.2 m/s
Before the ambulance passes you (ambulance approaching → vs = −16.67; bicycle moving away → vr = −4.17):
f = 700 × (343.2 + (−4.17)) / (343.2 + (−16.67)) = 700 × 339.03 / 326.53 ≈ 727 Hz
After the ambulance passes you (ambulance receding → vs = +16.67; bicycle moving toward source → vr = +4.17):
f = 700 × (343.2 + 4.17) / (343.2 + 16.67) = 700 × 347.37 / 359.87 ≈ 676 Hz
Frequency change: 727 − 676 = 51 Hz
Speed of Sound Reference
| Medium / Condition | Speed (m/s) | Speed (ft/s) |
|---|---|---|
| Air at 20 °C (68 °F) — standard | 343.2 | 1125.3 |
| Air at 0 °C (32 °F) | 331.3 | 1087.0 |
| Air at 35 °C (95 °F) | 351.9 | 1154.2 |
| Water (20 °C) | 1482 | 4862 |
| Steel | 5960 | 19 554 |
Unit Systems Supported
This calculator supports both the metric system (m/s for velocities, default speed of sound 343.2 m/s) and the American/Imperial system (ft/s, default 1125.33 ft/s). The source frequency is always entered in Hertz (Hz) regardless of the unit system.
Applications of the Doppler Effect
- Medicine — Doppler ultrasound measures blood flow velocity in arteries and veins.
- Meteorology — Doppler radar detects wind speed and storm rotation.
- Astronomy — Redshift/blueshift reveals the recessional velocity of distant galaxies.
- Traffic control — Speed radar guns use the Doppler principle to measure vehicle speed.
- Sonar — Submarines and ships use Doppler sonar for navigation and target tracking.