A microwave source at rest emits radiation at a frequency of 10 GHz. An observer moves directly toward the source at half the speed of light. What frequency does the moving observer measure? (c = 3 × 10⁸ m/s)

Question

Accepted Answer

17.3 GHz. Because v = 0.5c is relativistic, use the relativistic Doppler effect for an approaching observer: ν' = ν*sqrt((1+β)/(1-β)). With β = 0.5: ν' = 10*sqrt(1.5/0.5) = 10*sqrt(3) = 10 × 1.732 = 17.3 GHz.

A microwave source at rest emits radiation at a frequency of 10 GHz. An observer moves directly toward the source at half the speed of light. What frequency does the moving observer measure? (c = 3 × 10⁸ m/s)

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