Doppler Frequency Calculator Formula

Understand the math behind the doppler frequency calculator. Each variable explained with a worked example.

Use the Doppler Frequency Calculator

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_freq

Variables

VariableDescriptionDefault
source_freqSource Frequency(Hz)440
sound_speedSpeed of Sound(m/s)343
observer_velocityObserver Velocity (+ toward source)(m/s)0
source_velocitySource 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.

  • Source approaching: lower denominator, higher f_obs
  • Source receding: higher denominator, lower f_obs

    • Worked Example

    A 440 Hz siren moves away at 30 m/s, observer stationary.

    source_freq = 440sound_speed = 343observer_velocity = 0source_velocity = 30
    1. 01f_obs = 440 * (343 + 0) / (343 + 30)
    2. 02f_obs = 440 * 343 / 373
    3. 03f_obs = 440 * 0.9196
    4. 04f_obs = 404.6 Hz (lower pitch)

    Ready to run the numbers?

    Open Doppler Frequency Calculator