Doppler Effect Calculator
Compute the observed frequency shift when a sound or wave source and observer move relative to each other. Perfect for physics coursework, radar, sonar, and astrophysics applications.
About this calculator
The Doppler effect describes the change in perceived frequency when the source or observer of a wave is in motion. The general formula is: f_obs = f_s · (v_w + v_o) / (v_w − v_s), where f_s is source frequency, v_w is wave speed in the medium, v_o is observer velocity (positive when approaching), and v_s is source velocity (positive when approaching the observer). When the source approaches, the denominator shrinks and f_obs rises (blue-shift). When it recedes, the denominator grows and f_obs falls (red-shift). The same principle applies to light in astronomy and to radar/lidar speed guns. This calculator handles multiple motion-direction configurations through conditional sign logic.
How to use
An ambulance siren emits f_s = 700 Hz. The ambulance approaches at v_s = 30 m/s; the observer stands still (v_o = 0); sound speed v_w = 343 m/s. Step 1 – direction = 'approaching'. Step 2 – f_obs = 700 × (343 + 0) / (343 − 30) = 700 × 343 / 313. Step 3 – 700 × 1.0959 ≈ 767 Hz. As the ambulance passes and recedes at the same speed: f_obs = 700 × 343 / (343 + 30) = 700 × 343 / 373 ≈ 644 Hz. The pitch drop from 767 Hz to 644 Hz is the classic Doppler shift.
Frequently asked questions
How does the Doppler effect work for sound versus light?
For sound, the Doppler shift depends on both the source velocity and observer velocity relative to the medium (usually air), because sound requires a material medium to travel through. For light in a vacuum there is no medium, so only the relative velocity between source and observer matters, governed by the relativistic Doppler formula. At everyday speeds the classical and relativistic results are nearly identical, but at velocities approaching the speed of light the relativistic correction becomes significant, as seen in the red-shift of distant galaxies.
What happens to observed frequency when source and observer move away from each other?
When source and observer recede from each other, the wavelength of each successive wave crest is stretched over a longer distance before reaching the observer, lowering the observed frequency. This is called a red-shift in light (the frequency moves toward the lower, red end of the spectrum) or simply a pitch drop in sound. The effect is symmetric: a receding source lowers frequency by the same factor that an approaching source raises it when speeds are equal.
Why do police radar guns use the Doppler effect to measure speed?
Radar guns emit a microwave signal at a precisely known frequency and measure the frequency of the reflection returning from a moving vehicle. The shift between emitted and reflected frequency is directly proportional to the vehicle's velocity via the Doppler formula, allowing speed to be calculated in milliseconds with high accuracy. Modern LIDAR guns use the same principle with laser pulses. The technique is reliable because the relationship between frequency shift and velocity is mathematically exact and independent of the gun's own position.