(8%) Problem 7: Slick Willy is in traffic court (again) contesting a $50.00 tick

Question

(8%) Problem 7: Slick Willy is in traffic court (again) contesting a $50.00 ticket for running a red light. "You see, your Honor, as I was approaching the light, it appeared yellow to me because of the Doppler effect. The red light from the traffic signal was shifteed up in frequency because I was traveling towards it, just like the pitch of an approaching car rises as it approaches you." Calculate how fast Slick Willy must have been driving, in meters per second, to observe the red light (wavelength of 683 nm) as yellow (wavelength of 575 nm). (Treat the traffic light as stationary, and assume the Doppler shift formula for sound works for light as well.) Grade Summary Deductions Potential 0% 100% cos0 cotan0 asin) acosO atan0 acotansinh0 cosh0 tanh) cotanh0 Submissions Attempts remaining: 10 (1% per attempt) detailed view sin END Degrees Radians BA DEL CLEAR Submit Hint I give up! Hints:-% deduction per hint. Hints remaining: 2 Feedback: 0%, deduction per feedback.

Explanation / Answer

given

f ' = 683 nm = 683 X 10-9 m

fo = 575 nm = 575 X 10-9 m

VO = speed of observer

V = speed of light = 3 X 108 m/s

using equation is

f ' = ( V + VO / V ) fo

683 X 10-9 = ( 3 X 108 + VO / 3 X 108 ) 575 X 10-9

1 + VO / 3 X 108 = 683 / 575

1 + VO / 3 X 108 = 1.187

VO / 3 X 108 = 1.187 - 1

VO / 3 X 108 = 0.187

VO = 0.561 X 108 m/s

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