Doppler Effect Frequency Calculator
Calculate the observed frequency shift due to the Doppler effect.
Works for sound, light, and radar applications with source or observer motion.
The Doppler effect (or Doppler shift) is the change in frequency of a wave as its source or observer moves relative to each other. Named after Austrian physicist Christian Doppler (1803–1853), who described it in 1842, this effect is heard every day when an ambulance siren rises in pitch as it approaches and drops as it passes.
The Formula
f_observed = f_source × (v_wave + v_observer) / (v_wave − v_source)
Where:
- f_observed = Frequency heard by the observer (Hz)
- f_source = Frequency emitted by the source (Hz)
- v_wave = Speed of sound (or light) in the medium
- v_observer = Speed of the observer (positive if moving toward source)
- v_source = Speed of the source (positive if moving toward observer)
Sign Convention
- Observer moving TOWARD source → v_observer is POSITIVE
- Observer moving AWAY from source → v_observer is NEGATIVE
- Source moving TOWARD observer → v_source is POSITIVE
- Source moving AWAY from observer → v_source is NEGATIVE
Speed of Sound by Medium
| Medium | Speed of Sound |
|---|---|
| Air (20°C / 68°F) | 343 m/s / 1,125 ft/s |
| Air (0°C / 32°F) | 331 m/s |
| Fresh water (25°C) | 1,497 m/s |
| Seawater | 1,531 m/s |
| Steel | 5,120 m/s |
Real-World Examples
- Ambulance: Siren at 700 Hz sounds higher as it approaches, lower after it passes
- Weather radar: Meteorologists use Doppler radar to detect wind velocity inside storms
- Astronomy: The red shift (Doppler shift of light toward longer wavelengths) reveals that distant galaxies are moving away from us, which is evidence for the expanding universe
- Speed guns: Police radar guns use Doppler shift in reflected radio waves to measure vehicle speed
- Ultrasound: Medical Doppler ultrasound measures blood flow velocity by detecting frequency shifts in reflected sound waves
Redshift and Blueshift
When a light source moves away, its light shifts toward the red end of the spectrum (redshift, longer wavelengths, lower frequency). When it moves toward you, light shifts toward blue (blueshift, shorter wavelengths, higher frequency). Edwin Hubble observed in 1929 that distant galaxies are all redshifted — the universe is expanding.