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Doppler Effect (Approaching Source)

Also known as siren pitch change

f′=fvv−vsf' = \frac{f v}{v - v_s}
sig figs

Worked example: 700 Hz siren at 40 m/s (v = 340) → f' = 793.33 Hz. Press Try an example to run it live, then adjust anything.

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Where Doppler Effect (Approaching Source) fits

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Wave Speed (v = fλ)Period-Frequency RelationAngular Frequency (ω = 2πf)

See also

Doppler Effect (Approaching Observer): Both use observed frequency and source frequency.Fundamental of a Closed Pipe: Both use speed of sound.Fundamental of an Open Pipe: Both use speed of sound.Speed of Sound in Air: Both use speed of sound.
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Doppler Effect (Approaching Source) explained

vsfvf′

As a source rushes toward you, each successive wavefront is emitted a little closer than the last, squeezing the waves together and raising the pitch you hear. An ambulance siren emitting 700 Hz while driving at 30 m/s through 343 m/s air reaches you at 700 × 343/(343 − 30) ≈ 767 Hz: about a semitone and a half sharp. The instant it passes, the geometry flips, the waves stretch, and the pitch drops: the classic "nee-naw... nyooow" every child imitates.

The denominator tells a dramatic story of its own. As vₛ approaches the speed of sound, the wavefronts pile up on top of each other and f′ grows without bound: the physical wall of compressed air that early jet pilots called the sound barrier. Cross it and the piled-up fronts trail behind as a shock cone: the sonic boom. Police radar and medical Doppler ultrasound run the same relation in reverse, converting a measured frequency shift into the speed of a car or of blood cells in an artery.

Doppler Effect (Approaching Source) formula

f′=fvv−vsf' = \frac{f v}{v - v_s}
Where
  • f′f'= Observed frequency (Hz)
  • ff= Source frequency (Hz)
  • vv= Speed of sound (m/s)
  • vsv_s= Source speed (m/s)
Revised 16 October 2026
Cite this page

formula.expert. (2026, October 16). Doppler Effect (Approaching Source) Formula & Calculator. https://formula.expert/solvers/doppler-moving-source

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