(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 shifted 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 692 nm) as yellow (wavelength of 588 nm). (Treat the traffic light as stationary, and assume the Doppler shift formula for sound works for light as well.) Grade Summary Deductions Potential 100 v= Submissions 415161 -k Attempts remaining: 1 1% per attempt) detailed view cotanO asinacosO atan0 acotanO sinhO coshO tanhO cotanho ODegrees Radians Submit Hint I give up! Hints: 1% deduction per hit. Hints remaining:- Feedback: 0%deduction per feedback. All celent © 2017 Expen TA.uc

Explanation / Answer

here,

the wavelength of red light , lamdar =

the wavelength of yellow light , lamday =

as the observer is moving towards the source ,so vr is positive

fy = (c + vr)/( c + vs) * f0

1/lamday = (c + vr)/( c + vs) * 1/lamdar

692 = ( 3 * 10^8 + vr)/( 3 * 10^8) * 588

solving for vr

vr = 5.3 * 10^7 m/s

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