Doppler Effect Calculator — Frequency Shift
Calculate the observed frequency change due to the Doppler effect for sound waves. Find the apparent frequency when a source or observer is moving.
Doppler Effect Guide
The Doppler Formula
f_observed = f_source × (v_sound + v_observer) / (v_sound + v_source). Sign conventions: v_observer positive when moving toward source, negative when moving away. v_source positive when moving away from observer, negative when approaching. Simplified for stationary observer and moving source: approaching: f_obs = f_s × v / (v - v_s). Receding: f_obs = f_s × v / (v + v_s). A 440 Hz source moving toward you at 30 m/s (v_sound = 343 m/s): f_obs = 440 × 343 / (343 - 30) = 440 × 1.096 = 482 Hz. Notic
Everyday Examples
Ambulance siren: a siren at 700 Hz moving at 50 km/h (13.9 m/s). Approaching: f = 700 × 343/(343-13.9) = 730 Hz. Receding: f = 700 × 343/(343+13.9) = 672 Hz. Total shift heard as it passes = 730-672 = 58 Hz — clearly audible. Racing cars: Formula 1 cars at ~80 m/s. Approaching pitch at ~1.30× source, receding at ~0.81×. The characteristic 'nyeow' sound as a car passes. Supersonic aircraft: when v_source = v_sound, the formula breaks down — a sonic boom is produced (shock wave) rather than a freq
Doppler in Astronomy — Redshift
For light, the relativistic Doppler formula applies: z = Δλ/λ = f_source/f_observed - 1. Recession velocity v ≈ z × c for v << c. Hubble's Law: galaxies are receding from us with velocity proportional to distance (v = H₀ × d). The cosmological redshift of distant galaxies provided the first evidence for the Big Bang. Edwin Hubble observed in 1929 that distant galaxies show redshift (light shifted to longer wavelengths) — implying the universe is expanding. The Cosmic Microwave Background is reds
Medical Applications of Doppler
Doppler ultrasound: ultrasound (2-18 MHz) reflects off moving red blood cells. The frequency shift of the reflected wave reveals blood flow speed and direction. Applications: measuring blood flow velocity in arteries and veins. Detecting deep vein thrombosis. Foetal heart monitoring. Echocardiography (heart valve function). Colour Doppler: blood flow toward the probe shown in red, away in blue. Doppler weather radar uses the same principle — the frequency shift of reflected microwave pulses from
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