4) Suppose you get pulled over for going through a red light. With your knowledge of...

4) Suppose you get pulled over for going through a red light. With your knowledge of physics and the Doppler Effect, you tell the cop that due to the Doppler Effect you didn't even see any light coming from the traffic light and you thought it was broken or not a light. The cop, however, has an equal knowledge of the Doppler Effect and decides to give you a ticket equal to $6 for every mph you were hypothetically traveling to not see the light. If red light is 5.8 x 10¹² Hz and ultraviolet light is 7.2 x 10¹² Hz, how much is the ticket in billions of dollars if 1 m/s = 2.24 mph?

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Expert Solution

This is a question of the Relativistic Doppler effect.

Relativistic Doppler effect explains changes in frequency and wavelength of light observed by the observer when there is a relative motion between observer and light source taking into account the special theory of relativity. The following theory relates them :

where :

is the frequency of light observed by the observer:

is the frequency of light emitted by the source.

is relative speed. Also, v is positive when the observer away from the source and negative when observer moves towards the source.

is the speed of light.

Given :

= 7.2 X 1012 hz

= 5.8 X 1012 hz

= 3 X 108 m/s

putting values in expression and adjusting sign of v as observer is moving towards source :

genius_generous answered 2 years ago

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