A speeder tries to explain to the police that the yellow warning lights she was

Question

A speeder tries to explain to the police that the yellow warning lights she was approaching on the side of the road looked green to her because of the Doppler shift. How fast would she have been traveling if yellow light of wavelength 576.3 nm had been shifted to green with a wavelength of 562.0 nm? Note: For speeds less than 0.03c, the equation below will lead to a value for the observed frequency accurate to approximately two significant digits. (Accordingly, please enter your response to 2 significant digits. Use c = 3.00 108 m/s.)

Explanation / Answer

using F for frequency

L for wavelength

V is relative velocity

and

c for the speed of light in the medium is 3x10^8 m/s

Lt = yellow wavelength
Lr = green wavelength

dF = -V / Lt

but also

dF = Fr - Ft = c ( 1/Lr - 1/Lt)

so

c ( 1/Lr - 1/Lt) = -V / Lt

V = -c (Lt / Lr - 1) = -3e8 (576.3/562.0 - 1) = - 7633451.957 m/s

where the "-" sign indicates she is approaching the source, necessary for blue shift.

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