Doppler Effect (Sound)Free online science calculator — instant results, no sign-up
Calculate the observed frequency when a sound source moves.
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About the Doppler Effect (Sound)
The Doppler Effect (Sound) calculator finds the frequency heard by a stationary observer when a sound source moves toward or away from them. Enter the source frequency and its speed to compare the approaching and receding frequencies, using a sound speed of 343 m/s for air at 20 °C.
- Source frequency (Hz)
- The frequency emitted by the sound source, measured in hertz (Hz), defaults to 500 Hz.
- Source speed toward observer (m/s)
- The source's speed directly toward the observer, measured in meters per second (m/s), defaults to 20 m/s and is also used as the speed magnitude for the receding comparison.
Formula and method
f_approaching = f_s × c / (c − v_s); f_receding = f_s × c / (c + v_s), with c = 343 m/s.
- f_sFrequency emitted by the source, in Hz.
- v_sNonnegative source speed along the source–observer line, relative to the air, in m/s.
- cSpeed of sound in the air, fixed at 343 m/s.
- f_approachingFrequency heard by the stationary observer when the source approaches, in Hz.
- f_recedingFrequency heard by the stationary observer when the source moves away, in Hz.
The calculator uses the moving-source Doppler equations with a stationary observer. It subtracts the source speed from the sound speed for approach and adds it for recession, then divides f_s × c by each denominator. With the default inputs, f_approaching = 500 × 343 / (343 − 20) = 530.96 Hz and f_receding = 500 × 343 / (343 + 20) = 472.45 Hz, rounded to two decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Source frequency500 Hz
- Source speed toward observer20 m/s
Results
- Approaching530.96 Hz
- Receding472.45 Hz
- Sound speed used343 m/s (air, 20 °C)
How to use the Doppler Effect (Sound)
- 1Enter the emitted sound frequency in Source frequency (Hz); leave it at 500 for the worked example.
- 2Enter the source speed in Source speed toward observer (m/s); leave it at 20 for the worked example.
- 3Use a positive source frequency and a nonnegative source speed below 343 m/s for this model.
- 4Read the Approaching and Receding results to compare the heard frequency for motion in either direction at the entered speed.
- 5Check the Sound speed used row: the worked example uses 343 m/s for air at 20 °C.
Reading your result
Approaching is the frequency heard as the source moves toward the observer: 530.96 Hz with the default inputs, higher than the emitted 500 Hz. Receding is the frequency heard as the source moves away at the same speed: 472.45 Hz, lower than the emitted frequency. Sound speed used identifies the assumed propagation speed: 343 m/s (air, 20 °C). These outputs describe frequency shifts, not changes in loudness.
Limitations
The model assumes a stationary observer, still air, a steady emitted frequency, and source motion directly toward or away from the observer. The sound speed is fixed rather than calculated from local temperature, humidity, or medium. It does not model moving observers, angled trajectories, wind, echoes, or acceleration over time. Use source speeds below 343 m/s: the approaching formula is undefined at that speed, and sonic or supersonic motion requires a different treatment.
Common questions
Why does the calculator show both approaching and receding frequencies from one speed input?+
It uses the entered speed as a magnitude and evaluates two separate directions of travel. At 20 m/s with a 500 Hz source, approach gives 530.96 Hz and recession gives 472.45 Hz.
Why are the upward and downward frequency shifts not equal?+
Source speed appears in the denominator: 343 − 20 for approach and 343 + 20 for recession. These reciprocal relationships make the increase above 500 Hz larger than the decrease below it.
Can I use this calculator if the observer is moving too?+
Not directly. These equations assume the observer is stationary relative to the air; a moving observer requires an additional observer-velocity term.
Does this calculator adjust the sound speed for outdoor conditions?+
No. It uses 343 m/s for air at 20 °C. Different air conditions or a different medium can change the sound speed and therefore the observed frequencies.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.