A bumper sticker says, if you drive fast enough at a red light it will appear gr
ID: 1660498 • Letter: A
Question
A bumper sticker says, if you drive fast enough at a red light it will appear green. Determine how fast you would have to travel for a red light (442*10^12 Hz) to look green (566*10^12 Hz). Give your answer in m/s, miles per hour, and as a percentage of the speed of light. Using algebra. A bumper sticker says, if you drive fast enough at a red light it will appear green. Determine how fast you would have to travel for a red light (442*10^12 Hz) to look green (566*10^12 Hz). Give your answer in m/s, miles per hour, and as a percentage of the speed of light. Using algebra.Explanation / Answer
We need to use the formula of Doppler shift for stationary source, moving observer.
f' = [(v + v0)/v]*f
where,
vo = Velocity of the Observer,
v = Velocity of light in medium,
f = Real frequency,
f' = Apparent frequency.
Rearranging in terms of v0 :
vo = vf'/f - v
= [(3*108)(566*1012)/(442*1012)] - (3*108)
= 8.4 x 107 m/s (ans)
In mph:
speed = 8.4 x 107 x 2.24
= 1.88 x 108 mph (ans)
As a percentage:
c = 3 x 108 m/s
Thus,
vo/c =(8.4 x 107)/(3x108)
vo/c = 0.28
vo = 0.28c (ans)
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