Question

what would the speed of an observer be if a red(4.688x10^14Hz) traffic light appeared green(5.555x10^14Hz) to the observer?

Answer 1

The frequency shift is 11.5% of the actual frequency. For small shifts, you can use
v/c = (delta f)/f = 0.115

v = 0.115 c = 3.5*10^7 m/s TOWARDS the source.

The exact Doppler shift formula for light is given at
http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

It says that, in this case,
1.115 = sqrt[(1+(v/c)/(1-(v/c)]
1.243 = [(1+(v/c)/(1-(v/c)]
1 + (v/c) = 1.243 - 1.243(v/c)
2.243 (v/c) = 0.243
v/c = 0.108
c = 3.24*10^7 m/s