Science calculator

Doppler shift.

Calculate frequency shift for sound in a stationary medium or for longitudinal light motion. Positive motion is towards the other party.

Wave

Observed frequency fₒ

Source frequency fₛ

Wave speed c

Observer speed vₒ

Source speed vₛ

Observed frequency fₒSolved

—

positive speed means approach

Frequency factor fₒ/fₛ: —

Display precision

f_{o} = f_{s} \frac{c + v_{o}}{c - v_{s}}

f_{o} = f_{s} \sqrt{\frac{1 + β}{1 - β}}, β = \frac{v}{c}

fₒ observed frequency · fₛ emitted frequency · c wave speed · vₒ observer speed · vₛ source speed · v relative light speed

Assumptions

For sound, the medium is stationary and motion is along the source–observer line.
Sound speeds vₒ and vₛ are positive towards the other party and negative away; c + vₒ and c − vₛ must remain positive.
For light, source and observer have constant relative velocity along the line of sight in vacuum.
The light model is relativistic: positive v is approach (blue shift), negative v is recession (red shift), and |v| < c.

How it works

For sound, observer motion changes how quickly wavefronts arrive, while source motion changes their spacing in the medium. These are separate effects in the classical equation.

Light needs no medium, so only relative motion matters. Special relativity combines the ordinary arrival-rate change with time dilation.

Choose the appropriate model and leave one value blank. The explicit sign convention lets the same fields describe approach or recession without hidden direction choices.

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