Doppler Frequency Calculator Formula
Understand the math behind the doppler frequency calculator. Each variable explained with a worked example.
Formulas Used
Observed Frequency
observed_freq = source_freq * (sound_speed + observer_velocity) / (sound_speed + source_velocity)Frequency Shift
freq_shift = source_freq * (sound_speed + observer_velocity) / (sound_speed + source_velocity) - source_freqVariables
| Variable | Description | Default |
|---|---|---|
source_freq | Source Frequency(Hz) | 440 |
sound_speed | Speed of Sound(m/s) | 343 |
observer_velocity | Observer Velocity (+ toward source)(m/s) | 0 |
source_velocity | Source Velocity (+ away from observer)(m/s) | 30 |
How It Works
Doppler Effect for Sound
The Doppler effect shifts the observed frequency when the source or observer is moving relative to the medium.
Formula
f_obs = f_s * (c + v_obs) / (c + v_src)
Sign convention: v_obs is positive when moving toward the source; v_src is positive when moving away from the observer.
Worked Example
A 440 Hz siren moves away at 30 m/s, observer stationary.
- 01f_obs = 440 * (343 + 0) / (343 + 30)
- 02f_obs = 440 * 343 / 373
- 03f_obs = 440 * 0.9196
- 04f_obs = 404.6 Hz (lower pitch)
Frequently Asked Questions
Why does an ambulance siren change pitch as it passes?
As it approaches, the sound waves are compressed (higher frequency). As it recedes, the waves are stretched (lower frequency). The transition happens as the vehicle passes.
Does the Doppler effect apply to light?
Yes, but the relativistic Doppler formula differs. For light, there is no medium, and time dilation must be accounted for.
What happens if the source moves faster than sound?
A shock wave (sonic boom) forms. The Doppler formula breaks down and Mach cone analysis is needed.
Ready to run the numbers?
Open Doppler Frequency Calculator