what would the speed of an observer be if a red(4.688x10^14Hz) traffic light appeared green(5.555x10^14Hz) to the observer?
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
To determine the speed of the observer, we can make use of the Doppler Effect equation. The Doppler Effect is the shift in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave. In this case, the observer is moving towards the source of the light wave, which causes a change in frequency.
The equation for the Doppler Effect is as follows:
f' = f * (v + vo) / (v + vs)
Where:
- f' is the observed frequency
- f is the actual frequency
- v is the speed of light
- vo is the velocity of the observer
- vs is the velocity of the source
In this scenario, the observed frequency is the green frequency (5.555x10^14 Hz) and the actual frequency is the red frequency (4.688x10^14 Hz). We can assume that the speed of light is constant (3x10^8 m/s). We need to solve for the velocity of the observer (vo).
Let's plug in the values into the equation:
5.555x10^14 Hz = 4.688x10^14 Hz * (3x10^8 m/s + vo) / (3x10^8 m/s)
Simplifying the equation:
5.555x10^14 Hz * 3x10^8 m/s = 4.688x10^14 Hz * (3x10^8 m/s + vo)
Now divide both sides of the equation by 4.688x10^14 Hz:
(5.555x10^14 Hz * 3x10^8 m/s) / (4.688x10^14 Hz) = 3x10^8 m/s + vo
Calculate the left side of the equation:
16.665x10^22 m/s = 3x10^8 m/s + vo
Now, isolate vo by subtracting 3x10^8 m/s from both sides:
16.665x10^22 m/s - 3x10^8 m/s = vo
Finding the difference:
16.665x10^22 m/s - 3x10^8 m/s = 16.665x10^22 m/s
Therefore, the speed of the observer would be approximately 16.665 x 10^22 m/s.