what would the speed of an observer be if a red(4.688x10^14Hz) traffic light appeared green(5.555x10^14Hz) to the observer?
a) 2.219x10^8 m/s
b) 4.445x10^8 m/s
c) 5.548x10^7 m/s
d) 8.438x10^7 m/s
e) 2.890x10^6 m/s
To find the speed of the observer, we can use the formula for the Doppler effect. The formula for the Doppler effect with respect to light is:
f' = f((c ± v_obs)/(c ± v_source))
Where:
f' is the observed frequency
f is the source frequency
v_obs is the velocity of the observer
v_source is the velocity of the source
c is the speed of light
In this case, the source frequency (f) is the frequency of the red traffic light, which is 4.688x10^14 Hz. The observed frequency (f') is the frequency that the traffic light appears to the observer, which is 5.555x10^14 Hz (green traffic light). We need to find the velocity of the observer (v_obs).
Let's consider the observer is moving towards the light source. This means the observer is approaching the source, so the sign of the velocity of the observer (v_obs) is negative.
Now, let's substitute the known values into the formula:
5.555x10^14 Hz = 4.688x10^14 Hz * ((3.0x10^8 m/s - v_obs) / (3.0x10^8 m/s + 0))
Simplifying the equation gives us:
(3.0x10^8 m/s - v_obs) = (5.555x10^14 Hz / 4.688x10^14 Hz) * 3.0x10^8 m/s
(3.0x10^8 m/s - v_obs) = 3.0x10^8 m/s * 1.182
Now, solve for v_obs:
v_obs = 3.0x10^8 m/s - (3.0x10^8 m/s * 1.182)
v_obs = 3.0x10^8 m/s - 3.546x10^8 m/s
v_obs = -5.46x10^7 m/s
Therefore, the speed of the observer would be -5.46x10^7 m/s.
So, none of the given options (a, b, c, d, e) match the calculated result.