Doppler Effect Frequency Calculator

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 to 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

Temperature matters more than most people expect, and there is a simple rule for air:

v ≈ 331 + (0.6 × temperature in °C) m/s

That is why the same siren shifts slightly differently on a winter morning than on a summer afternoon. All six of these are in the medium dropdown, so you can pick one instead of typing the number.

Worked example: the ambulance

A siren sounds at 700 Hz. The ambulance approaches you at 30 m/s (67 mph) through air at 20°C, and you are standing still.

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

Once it passes, the source is moving away, so the sign flips:

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

That drop from 767 to 644 Hz, 123 Hz in the second or two it takes to go past, is the “neee-yaww” everyone recognises. In musical terms it is about 3 semitones, roughly a minor third, which is why it sounds like a tune rather than a blur.

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, and the universe is expanding.

The relativistic Doppler formula (for light). The classical formula above works for sound and slow-moving sources, but light is different, because there is no medium for it to travel through, and at high speeds Einstein’s special relativity matters. The correct form for light is:

f’ = f × √((1 − v/c) / (1 + v/c)) (source receding at speed v) f’ = f × √((1 + v/c) / (1 − v/c)) (source approaching at speed v)

where c is the speed of light. For everyday speeds (v much less than c) this collapses to the same answer the classical formula gives, which is why we don’t usually notice the difference. But for cosmological redshifts of distant galaxies, where v can be a meaningful fraction of c, the relativistic version is the one that’s actually correct.