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Modern Physics
Modern Physics

Relativistic Doppler Effect

f′=f1−v/c1+v/cf' = f\sqrt{\frac{1 - v/c}{1 + v/c}}

The relativistic formula for frequency shift due to relative motion. For approaching sources (v negative), frequency increases (blueshift). For receding sources (v positive), frequency decreases (redshift).

Variables

f'
Observed frequency
Allowed values: greater than 0
Hz
f
Source frequency
Allowed values: greater than 0
Hz
v
Relative velocity (positive = receding)
m/s
c
Speed of light
Allowed values: greater than 0
m/s

Derivation

Combines classical Doppler effect with time dilation from special relativity.

Your notes

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Constants in this formula

c
Speed of Light in Vacuum
299,792,458. Exact by definition.
m/s

Other modern physics formulas with the same quantities

Where this formula is listed

Common questions

What is the Relativistic Doppler Effect formula?

Relativistic Doppler Effect is written f′ = f√((1 − v/c)/(1 + v/c)). The relativistic formula for frequency shift due to relative motion. For approaching sources (v negative), frequency increases (blueshift). For receding sources (v positive), frequency decreases (redshift). It belongs to Modern Physics, under Special Relativity.

What are the units in f′ = f√((1 − v/c)/(1 + v/c))?

In SI units, f′ is observed frequency, measured in Hz; f is source frequency, measured in Hz; v is relative velocity (positive = receding), measured in m/s; c is speed of light, measured in m/s.

How is the Relativistic Doppler Effect formula derived?

Combines classical Doppler effect with time dilation from special relativity. The result is f′ = f√((1 − v/c)/(1 + v/c)).