HesapHanem

Doppler Effect Calculator

Find the Doppler-shifted frequency.

How it is calculated

For sound in air the tool fixes the speed of sound at c = 343 m/s and computes f' = f × (c + vo) ÷ (c − vs). Here f is the source frequency in Hz, vs is the source speed and vo the observer speed, both in m/s. A positive vs means the source moves toward the observer, a positive vo means the observer moves toward the source; negative values mean moving away. The movement is assumed along the line joining them. If vs is 343 m/s or more (a supersonic source), or the observer recedes at 343 m/s or more (vo ≤ −343), no result is given. The answer is shown in Hz with two decimals. Another medium or temperature changes c.

Worked example

A 440 Hz siren moves toward a stationary listener at 30 m/s (vs = 30, vo = 0). Numerator: 343 + 0 = 343. Denominator: 343 − 30 = 313. The ratio is 343 ÷ 313 = 1.0958. Then 440 × 1.0958 = 482.17 Hz. The listener hears 482.17 Hz, a little higher than the true 440 Hz.

Try this example →

Common mistakes

  • Getting the sign wrong. Positive source speed means approaching; entering it as positive for a receding source gives a pitch that moves the wrong way.
  • Entering speeds in km/h. Both speeds must be in m/s; 108 km/h is 30 m/s.
  • Using this for light or radar. The constant 343 m/s is the speed of sound in air at about 20 °C, so it does not apply to electromagnetic waves, or to sound in water or at very different temperatures.
  • Entering a source speed at or above 343 m/s. That is supersonic motion, where this formula no longer describes what a listener hears, so the tool returns no result (as it does when the observer recedes at 343 m/s or more).

Sources

About this calculator

This calculator finds the observed frequency shift caused by the Doppler effect for sound, using f' = f × (v ± v_observer) / (v ∓ v_source), where v is the speed of sound in the medium. It shows how the frequency you hear changes depending on whether the source and observer are moving toward or away from each other.

Physics students use it to check homework on wave motion, and it's the same effect behind a passing ambulance siren changing pitch. Police radar guns rely on the related electromagnetic Doppler shift, which uses a different formula and is not calculated here.

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Comments (1)

  • Editorial team

    This tool uses sound in air with the speed fixed at 343 m/s, roughly room temperature, so it is not meant for water, hot exhaust or light. Source speed counts as positive when the source moves toward you, and observer speed counts as positive when you move toward the source. A siren passing by gives two readings: run it once approaching and once receding with a negative speed. Which situation do you want to work through? Post your numbers if the pitch change looks odd.

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