A speeder tries to explain to the police that the yellow warning lights on the s

Question

A speeder tries to explain to the police that the yellow warning lights on the side of the road looked green to her because of the Doppler shift. How fast would she have been traveling if yellow light of wavelength 576 nm had been shifted to green with a wavelength of 554 nm? (Note: For speeds less than 0.03c, the equation below will lead to a value for the change of frequency accurate to approximately two significant digits. Accordingly, please enter your response to 2 significant digits.)

fo ˜ fs (1 ± u/c)
speed = 11905418.37
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.Check the number of significant figures. m/s

Explanation / Answer

based on the equation you provided, we relate the observed frequency (green) to the emitted frequency (yellow), but first we have to relate wavelength to frequency by

c = f

So f = c/. for yellow:

f = c / 576 = 5.21 x 10^5 hz, for green:

f = c / 554 = 5.42 x 10^5 hz. Now we plug into the doppler equation:

5.42 x 10^5 = 5.21 x 10^5 (1 + v/c), and we solve for v, giving us

5.42/5.21 = 1 + v/c

1.04 = 1 + v/c

0.04 = v/c

v = 0.04 * c = 0.04 * 3x10^8 = 1.2 x 10^7 m/s

So this person was going very, very fast. Shouldnt tell that to the cops.

Hope that helps!

Jonathan

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