Doppler Effect Calculator — Frequency Shift for Moving Sources
When an ambulance passes you at speed, its siren drops in pitch as it recedes. That pitch change is the Doppler effect — a shift in observed frequency caused by relative motion between a wave source and an observer. The free Doppler effect calculator on PublicSoftTools quantifies that shift precisely.
The Doppler Formula
The observed frequency is: f_obs = f₀ × (v ± v_obs) / (v ∓ v_src)
Where v is the wave speed, v_obs is the observer's speed (positive when moving toward the source), and v_src is the source's speed (positive when moving toward the observer). The sign convention: upper sign (+/−) when approaching, lower sign (−/+) when receding.
Worked Examples
| Scenario | f₀ | Source velocity | f_observed |
|---|---|---|---|
| Ambulance (approaching at 30 m/s) | 700 Hz | 30 m/s toward | 767 Hz (+9.6%) |
| Same ambulance (receding) | 700 Hz | 30 m/s away | 643 Hz (−8.1%) |
| Train whistle (100 km/h, approaching) | 440 Hz | 27.8 m/s toward | 483 Hz (+9.8%) |
| Bat echolocation (5 m/s) | 40,000 Hz | 5 m/s toward | 40,587 Hz (+1.5%) |
How to Use the Calculator
- Open the Doppler effect calculator.
- Enter the source frequency f₀ in Hz (e.g. 440 for the A note).
- Enter the speed of sound v (343 m/s in air at 20°C).
- Enter the source velocity and its direction relative to the observer.
- Enter the observer velocity (set to 0 for a stationary observer).
- Read the observed frequency, frequency shift, and shift percentage.
Real-World Applications
Radar speed guns
Police radar emits a microwave signal at a known frequency. The signal reflects off the moving vehicle and returns at a shifted frequency. The Doppler shift is proportional to the vehicle's radial velocity. Because radar uses microwaves (not sound), the wave speed is c = 3×10⁸ m/s — but the Doppler principle is identical.
Medical ultrasound (Doppler imaging)
Doppler ultrasound measures blood flow velocity. The transducer emits ~5 MHz ultrasound; reflections from moving red blood cells return at shifted frequencies. Doctors interpret the shift as blood flow direction and speed — red blood cells flowing toward the transducer produce a blue shift; those flowing away produce a red shift.
Astronomy
Every galaxy's spectral lines are shifted relative to laboratory measurements. Redshifted spectra (lower frequency) indicate recession; blueshifted spectra (higher frequency) indicate approach. Edwin Hubble used this in 1929 to show that distant galaxies recede faster, establishing the expansion of the universe.
Common Questions
Does the Doppler effect apply to light?
Yes, but at relativistic speeds the classical formula breaks down. For light, the relativistic Doppler formula includes a time dilation factor. At everyday velocities (much less than c), the classical formula is a good approximation.
What happens when the source moves faster than the wave speed?
When a source moves at or above the wave speed (Mach 1), the classical Doppler formula breaks down — the denominator approaches zero. Instead, a shock wave (sonic boom) forms. Supersonic aircraft produce continuous sonic booms because they continuously outrun their own sound.
Calculate Doppler Frequency Shift
Enter source frequency, wave speed, and velocities to find the observed frequency and pitch change.
Open Doppler Effect Calculator