Doppler Effect Calculator Formula

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

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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_freq

Variables

VariableDescriptionDefault
source_freqSource Frequency(Hz)440
sound_speedSpeed of Sound(m/s)343
observer_speedObserver Speed (toward source +)(m/s)0
source_speedSource 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.

source_freq = 440sound_speed = 343observer_speed = 0source_speed = 30
  1. 01f_obs = f_s * (v + v_o) / (v - v_s)
  2. 02f_obs = 440 * (343 + 0) / (343 - 30)
  3. 03f_obs = 440 * 343 / 313
  4. 04f_obs = 482.2 Hz

Ready to run the numbers?

Open Doppler Effect Calculator