Doppler Shift Calculator

The Doppler effect is the change in perceived frequency of a wave — sound, light, or any other — caused by relative motion between the source and the observer. It was first described by Austrian physicist Christian Doppler in 1842 and confirmed by direct experiment in 1845 using musicians on a moving train.

Sound wave formula:

f_observed = f_source × (v_sound + v_observer) / (v_sound + v_source)

Variable definitions:

• f_observed = frequency heard by the observer (Hz)
• f_source = frequency emitted by the source (Hz)
• v_sound = speed of sound in the medium (343 m/s at 20°C sea level; 1,125 ft/s)
• v_observer = observer’s speed (positive when moving toward source; negative when moving away)
• v_source = source’s speed (positive when moving away from observer; negative when moving toward)

Sign convention: easy rule:

• Motion toward each other → higher pitch
• Motion away from each other → lower pitch

Worked example: ambulance siren: Siren frequency: 700 Hz Ambulance approaching at 30 m/s (67 mph), observer stationary.

f_approaching = 700 × (343 + 0) / (343 − 30) = 700 × 343/313 = 767 Hz

After the ambulance passes and is moving away:

f_receding = 700 × (343 + 0) / (343 + 30) = 700 × 343/373 = 644 Hz

The characteristic “neee-yaww” sound of a passing emergency vehicle is the Doppler shift from 767 Hz down to 644 Hz — a drop of 123 Hz happening as the vehicle passes.

Temperature affects sound speed: v_sound ≈ 331 + (0.6 × Temperature in °C) m/s

At 0°C: 331 m/s | At 20°C: 343 m/s | At 40°C: 355 m/s

Light and electromagnetic waves (relativistic Doppler): For light, the classical formula does not apply — special relativity governs.

f_observed = f_source × √[(1 + β) / (1 − β)]

Where β = v/c (velocity as a fraction of the speed of light).

• Moving toward observer → blueshift (higher frequency, shorter wavelength)
• Moving away → redshift (lower frequency, longer wavelength)

Real-world applications:

• Astronomy: Redshift reveals that distant galaxies are moving away, the evidence for the expanding universe and the Big Bang
• Radar guns: Police radar measures the Doppler shift of reflected radio waves to determine vehicle speed
• Medical ultrasound: Doppler ultrasound measures blood flow velocity in real time
• Weather radar: Doppler radar distinguishes wind direction and speed inside storm systems