Doppler Effect Calculator for Sound (Observed Frequency)
Enter the frequency, how fast the source and the listener move and in which direction. The speed of sound is worked out from the air temperature.
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Formula
- Speed of sound in air:
v = 331.3 × √(1 + T ÷ 273.15)m/s, T in °C. - Observed frequency:
f_obs = f_src × (v + v_o) ÷ (v − v_s). - Emitted frequency:
f_src = f_obs × (v − v_s) ÷ (v + v_o).
v_o is positive when the observer moves toward the source, v_s is positive when the source moves toward the observer. Use negative values (choose "away") for the opposite directions. Speeds in km/h and mph are converted to m/s first (1 mph = 0.44704 m/s).
Worked example
A 440 Hz siren moves toward a standing listener at 30 m/s on a 0 °C day, so v = 331.3 m/s.
f_obs = 440 × 331.3 ÷ (331.3 − 30) = 483.81 Hz, a rise of 43.81 Hz. Moving away instead: 440 × 331.3 ÷ (331.3 + 30) = 403.47 Hz.
Frequently asked questions
What is the Doppler effect formula for sound?
f_observed = f_source × (v + v_observer) ÷ (v − v_source), where v is the speed of sound, v_observer is positive when the listener moves toward the source and v_source is positive when the source moves toward the listener. A 440 Hz source approaching at 30 m/s at 0 °C (v = 331.3 m/s) is heard at 440 × 331.3 ÷ 301.3 = 483.8 Hz.
How does temperature change the speed of sound?
In air v ≈ 331.3 × √(1 + T ÷ 273.15) m/s with T in °C. That is 331.3 m/s at 0 °C and 343.2 m/s at 20 °C, so the same moving source gives a slightly smaller shift in warmer air.
Why is the pitch lower when the source moves away?
Each wave crest is emitted from farther away than the last, so the crests arrive less often. The same 440 Hz source receding at 30 m/s at 0 °C is heard at 440 × 331.3 ÷ 361.3 = 403.5 Hz.
Can I find the source frequency from what I hear?
Yes. Choose the source-frequency mode and enter the observed frequency. The formula is inverted: f_source = f_observed × (v − v_source) ÷ (v + v_observer).
What if the source is faster than sound?
The formula only holds below the speed of sound. At or above it the waves pile into a shock wave (a sonic boom) and there is no steady observed frequency, so the calculator reports an out-of-range error. The same goes for an observer moving away faster than sound.