Solving Doppler Shift to Calculate Cyclist's Speed

AI Thread Summary
The discussion revolves around calculating the speed of a cyclist using the Doppler effect in the context of a legal case involving a traffic violation. The cyclist claimed that the red light appeared green due to his high speed, prompting the prosecution to impose a fine based on his speed. Participants debated the correct formulation of the equations relating the cyclist's speed to the wavelength shift of the traffic light. One user suggested simplifying the equation to directly relate the cyclist's speed to the wavelength change without introducing unnecessary variables. The conversation emphasizes the importance of clarity and accuracy in applying the Doppler effect to real-world scenarios.
Beatdiz
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Homework Statement


A man riding his bicycle was caught driving through a red traffic light. The man was taken to court and trialled where he claimed he was cycling so quickly that the light had appeared to be green to him due to the Doppler effect. The prosecution accepted his excuse but decided to find him 1 Euro for every km hr by which the cyclist was traveling at.

Combine and re-arrange the following two equations to give an equation that relates to the speed of the cyclist to the shift in the wavelength of the light emitted by the traffic light.


Homework Equations


z=[Δλ] / [λ0] ... Where z is the red/blueshift, λ0 is the original wavelength, Δλ is the change in wavelength

v= z x c ... Where v is the speed of the galaxy, c is the speed of light, z is as above.

The Attempt at a Solution


s = Speed of motorist

s = [(c)(Δλ/λ0)2-c] / [(Δλ/λ0)2+1]

Does my equation look correct as I'm not convinced? Any help would be great.
 
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Is anyone able to help with this please? :)
 
Beatdiz;3288040[h2 said:
The Attempt at a Solution[/h2]
s = Speed of motorist

s = [(c)(Δλ/λ0)2-c] / [(Δλ/λ0)2+1]

Does my equation look correct as I'm not convinced? Any help would be great.

Hi Beatdiz, welcome to PF! :smile:

I do not understand how you arrived at your equation for s.
In your case you do not have to work with "the speed of the galaxy v".
But your v is simply the speed of the bicyclist.
No need to introduce a new symbol s, of which I do not understand what you did with it.

So your equation should simply read:
v = (Δλ/λ0) x c

Cheers!
 
Last edited:
Beatdiz said:
Is anyone able to help with this please? :)

I think you need to start with more realistic examples, like that one:
in a train station, one train arrives exactly each n minutes, always in the same direction.
All the train travels at v speed
Now you take a train in the opposite direction running at v' , you cross a train in the opposite direction each n' minutes.

State n' as a function of the other data.
 
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