Doppler Effect Calculator — Frequency Shift with Motion
Calculate observed frequency due to the Doppler effect. Covers moving sources and observers, sound and light, redshift, radar speed guns, and medical ultrasound.
The rising pitch of an approaching ambulance siren, the falling pitch as it passes — that's the Doppler effect in your everyday experience. The siren's frequency hasn't changed, but your perception of it has shifted because of relative motion. Police radar guns, medical ultrasound, and the discovery that the universe is expanding all use this same principle.
The CalcHub Doppler effect calculator calculates observed frequency for moving sources and/or moving observers.
The Formula
f_observed = f_source × (v_wave + v_observer) / (v_wave + v_source)Sign conventions:
- v_observer: positive when moving toward the source
- v_source: negative when moving toward the observer
(Different textbooks use different sign conventions — the calculator handles this automatically.)
For a moving source approaching a stationary observer:
f_obs = f_source × v_wave / (v_wave − v_source)
For a moving source receding from a stationary observer:
f_obs = f_source × v_wave / (v_wave + v_source)
Effect on Perceived Frequency
| Scenario | Effect on pitch |
|---|---|
| Source approaching | Frequency increases (pitch rises) |
| Source receding | Frequency decreases (pitch falls) |
| Observer approaching source | Frequency increases |
| Observer moving away | Frequency decreases |
| Both moving toward each other | Larger frequency increase |
Worked Example
An ambulance siren sounds at 700 Hz and approaches at 30 m/s. Speed of sound = 343 m/s.
f_obs = 700 × 343 / (343 − 30) = 700 × 343 / 313 = 767.1 Hz
As it passes and recedes:
f_obs = 700 × 343 / (343 + 30) = 700 × 343 / 373 = 643.7 Hz
That drop from 767 Hz to 644 Hz as the ambulance passes — about a minor third in musical terms — is the characteristic sound you hear on city streets.
How does a police radar gun use the Doppler effect?
The gun emits a radio wave at a known frequency. The wave reflects off your car and returns at a shifted frequency. The frequency shift is proportional to your car's speed. Doppler radar is accurate to within 1 km/h for speeds up to 300+ km/h.
What is redshift in astronomy?
Light from galaxies moving away from us is stretched to longer (redder) wavelengths — Doppler redshift. Edwin Hubble measured this shift for distant galaxies in 1929 and found they were all receding, faster at greater distances. This was the first strong evidence that the universe is expanding.
How is Doppler ultrasound used in medicine?
Medical ultrasound machines send sound waves into the body and detect the reflected waves. When reflected by moving blood cells, the frequency shifts according to the Doppler effect. This reveals blood flow speed and direction — useful for detecting blockages, valve problems, and monitoring fetal heart circulation.