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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 Spring '08
 SEATON
 Physics, Light, Visible spectrum, NM

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