Doppler Effect Calculator Formula
Understand the math behind the doppler effect calculator. Each variable explained with a worked example.
Formulas Used
Observed Frequency
observed_freq = source_freq * (sound_speed + observer_speed) / (sound_speed - source_speed)Frequency Shift
freq_shift = source_freq * (sound_speed + observer_speed) / (sound_speed - source_speed) - source_freqVariables
| Variable | Description | Default |
|---|---|---|
source_freq | Source Frequency(Hz) | 440 |
sound_speed | Speed of Sound(m/s) | 343 |
observer_speed | Observer Speed (toward source +)(m/s) | 0 |
source_speed | Source Speed (toward observer +)(m/s) | 30 |
How It Works
Doppler Effect
The Doppler effect is the change in observed frequency caused by relative motion between source and observer.
Formula
f_obs = f_source * (v_sound + v_observer) / (v_sound - v_source)
Sign convention: speeds are positive when source and observer move toward each other.
Worked Example
An ambulance siren at 440 Hz approaches a stationary observer at 30 m/s.
- 01f_obs = f_s * (v + v_o) / (v - v_s)
- 02f_obs = 440 * (343 + 0) / (343 - 30)
- 03f_obs = 440 * 343 / 313
- 04f_obs = 482.2 Hz
Frequently Asked Questions
Why does a siren sound higher-pitched as it approaches?
The sound waves are compressed in front of the moving source, shortening the wavelength and increasing the observed frequency.
Does the Doppler effect apply to light?
Yes, but the relativistic Doppler formula must be used for light since light speed is constant in all reference frames.
What happens when source speed equals the speed of sound?
The denominator becomes zero, meaning infinite observed frequency. This corresponds to a sonic boom (shock wave).
Learn More
Guide
Understanding Wave Properties
A comprehensive guide to wave properties including wavelength, frequency, amplitude, wave speed, interference, diffraction, and the difference between transverse and longitudinal waves.
Ready to run the numbers?
Open Doppler Effect Calculator