Doppler Effect Calculator: Observed Frequency Shift
The Doppler effect describes how the observed frequency of a wave changes when the source and observer move relative to each other. When they approach, sound waves compress and pitch rises. When they move apart, waves stretch and pitch drops. This principle, first described by Austrian physicist Christian Doppler in 1842, underpins a remarkable range of modern technology. Astronomers use the light-wave version to measure galactic recession speeds and map the expansion of the universe. Meteorologists deploy Doppler radar to track storm velocity and detect rotation inside thunderstorms. Cardiologists use Doppler ultrasound to visualise blood flow and detect blockages without surgery. Traffic radar measures vehicle speed in milliseconds. This calculator applies the classical acoustic Doppler formula, f_obs = f_source x (v_sound + v_observer) / (v_sound - v_source), using a sign convention where positive values indicate motion toward the other party and negative values indicate motion away. Enter your values below to compute observed frequency, frequency shift, and pitch change percentage instantly.
Observed frequency: -- Hz
JavaScript is required for live calculations.
The Doppler effect formula
For a moving source and moving observer in the same medium, the classical Doppler formula for sound is:
f_obs = f_source × (v_sound + v_observer) / (v_sound - v_source)
Sign convention used in this calculator: a positive source velocity means the source is moving toward the observer (which increases the observed frequency). A positive observer velocity means the observer is moving toward the source (also increases the observed frequency). Negative values indicate motion away from the other party.
Key relationships
- Source approaching observer: v_source is positive, denominator decreases, f_obs rises.
- Source receding: v_source is negative, denominator increases, f_obs falls.
- Observer approaching source: v_observer is positive, numerator increases, f_obs rises.
- Observer receding: v_observer is negative, numerator decreases, f_obs falls.
- If the source velocity equals or exceeds the speed of sound the formula breaks down (sonic boom territory).
Frequency shift and pitch change
Frequency shift = f_obs - f_source. Pitch change percentage = ((f_obs - f_source) / f_source) x 100. A positive shift means the pitch rises; a negative shift means the pitch falls. Human hearing can typically detect pitch changes of around 0.5% or more in musical contexts.
Speed of sound reference values
| Medium / condition | Speed of sound (m/s) |
|---|---|
| Dry air, 0 °C | 331.3 |
| Dry air, 20 °C | 343.2 |
| Dry air, 35 °C | 352.0 |
| Fresh water, 20 °C | 1,481 |
| Sea water, 20 °C | 1,522 |
| Steel | 5,960 |
Frequently asked questions
What is the Doppler effect?
The Doppler effect is the change in frequency of a wave (sound, light, or any wave) as the source and observer move relative to each other. When source and observer approach, the observed frequency is higher than the emitted frequency. When they move apart, the observed frequency is lower. Christian Doppler described this principle in 1842.
How does the Doppler effect apply to light and red shift?
For light, the Doppler effect produces a red shift (lower frequency, longer wavelength) when a source moves away from the observer, and a blue shift (higher frequency, shorter wavelength) when approaching. Astronomers use red shift to measure how fast distant galaxies are receding, confirming the expansion of the universe.
How is the Doppler effect used in medical ultrasound?
Doppler ultrasound detects blood flow by measuring the frequency shift of sound waves reflected off moving red blood cells. If blood flows toward the transducer the reflected frequency is higher; if it flows away, the frequency is lower. This allows clinicians to measure blood velocity without invasive procedures.
How does police radar use the Doppler effect?
Police radar guns emit a microwave signal that reflects off a moving vehicle. The reflected signal returns at a shifted frequency proportional to the vehicle's speed. The gun computes speed from the measured frequency difference using the Doppler formula. Modern LIDAR units use infrared light pulses instead, but the same Doppler principle applies.
Why does a passing ambulance siren seem to drop in pitch?
As an ambulance approaches, sound waves are compressed (shorter wavelength, higher frequency). The moment it passes and moves away, the waves stretch (longer wavelength, lower frequency). The actual siren pitch never changes; only the pitch perceived by a stationary observer shifts, which is the classic acoustic demonstration of the Doppler effect.