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P01-10

# P01-10 - P01.10 Running a red light You're caught running a...

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P01.10 Running a red light You're caught running a red light on Hwy 316. Attempting to impress the skeptical patrol officer with your physics knowledge, you claim that you were traveling so fast that the red light (687 nm) appeared yellow (583 nm) to you. (a) How fast would you have been traveling (in mi/hr) if that had been the case? (b) If you had been traveling that fast and the light actually was yellow, what color would it have seemed to you? Solution: (a) This is a Doppler shift problem, in which what you see ( f or λ ) as the observer is different from what the source produces ( f or λ ), because you are moving relative to the source with speed u. This means using the formula discussed in class: 1 or 1 u f f c u c λ λ = ± = ± For this problem, the sign of u should be positive because you’re moving toward the stoplight. Let’s rearrange the second formula above to solve for u, before plugging in numbers: 1 1 1 u u u c c c λ λ λ λ λ λ ′ = + = = - + Note that both sides of the rearranged equation are dimensionless. For this problem, λ = 583 nm (what you claim to see) and

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P01-10 - P01.10 Running a red light You're caught running a...

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