How fast should you move away from a 6.0 *10¹⁴ Hz light source to observe waves with a frequency of 4.0 * 10¹⁴ Hz? A)0.20c B)0.39c C)0.45c D)0.51c E)0.76c

Question

Quizplus · Accepted Answer

The formula for the observed frequency of a moving wave source is:
f' = f((c±v)/(c±vs))
where f is the frequency of the source, c is the speed of light, v is the speed of the observer, and vs is the speed of the source.
In this case, f = 6.0×1014 Hz, f' = 4.0×1014 Hz, vs = c, and we want to solve for v. Plugging in the values and solving for v:
4.0×1014 = 6.0×1014 ((c-v)/(c-v/c))
0.67 = ((c-v)/(c-v/c))
0.67(c-v/c) = c-v
0.67c - 0.67v/c = c - v
0.67v/c = 0.33c
v/c = 0.33/0.67
v = 0.492c
Therefore, the speed at which the observer should move away from the light source is 0.492c, which is closest to option B (0.39c).

How Fast Should You Move Away from a 6