# Doppler shift of Light

## Homework Statement

How fast would a motorist have to be traveling for a yellow (l = 595 nm) traffic light to appear green (l = 550 nm) because of the Doppler shift?

## Homework Equations

v=[(c)(f0/fs)2-c] / [(f0/fs)2+1]

## The Attempt at a Solution

v= Speed of motorist
c= Speed of light
f0= Observed wavelength (green, (5.5x10^-7 m)
fs= Source wavelength (yellow, (5.95x10^-7 m)

First of all, am I using the correct equation? Because i'm almost certain my work is correct, since after plugging in the above known numbers, i get 2.35x10^7 m/s for an answer, but this answer is not correct. Any help would be greatly appreciated!

Doc Al
Mentor
First of all, am I using the correct equation?
Looks OK. (Except for some reason you use f to represent wavelength. f usually stands for frequency.)

Because i'm almost certain my work is correct, since after plugging in the above known numbers, i get 2.35x10^7 m/s for an answer, but this answer is not correct.
That answer looks good to me.

oooh i love doppler shift =]

ive always used F(observed)= [c/(c+v)]*F(actual)

Thanks RoryP. I don't know what was wrong with the equation that i posted, but i tried yours out and it worked!

Doc Al
Mentor
ive always used F(observed)= [c/(c+v)]*F(actual)
That equation isn't quite right; it should be:

$$f_{obs} = f \sqrt{\frac{c + v}{c - v}}$$

No worries Cheezay, yeah ive never seen the equation you started with, but then again ive only been doing physics for 2 years now so i might bump into it soon!

Yeah i just checked my notes from 6th form and the equation i used is for c>>v, so dont konw if that makes any difference =]