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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
Hz
f
Source frequency
Hz
v
Relative velocity (positive = receding)
m/s
c
Speed of light
m/s

Derivation

Combines classical Doppler effect with time dilation from special relativity.

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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).