Derivation of the Doppler formula for light. A source and observer of EM waves move relative to each other at velocity v. Let v be positive if the observer and source are moving apart from each other.
The source emits an EM wave at frequency fs (measured in the source frame). The time between wavefronts as measured by the source is Ts = 1/fs. 

(a) In the observer's frame, how much time elapses between the emission of wavefronts by the source? Call this Ts′. 

(b) Ts′ is not the time that the observer measures between the arrival of successive wavefronts because the wavefronts travel different distances. Say that, according to the observer, one wavefront is emitted at t = 0 and the next at t = Ts′. When the first wavefront is emitted, the distance between source and observer is d. When the second wavefront is emitted, the distance between source and observer is d + vTs′. Each wavefront travels at speed c. Calculate the time To between the arrival of these two wavefronts as measured by the observer. 

(c) The frequency detected by the observer is fo = 1/To. Show that fo is given by Eq. (22-24):

Transcribed Image Text:

fo=fs 1 - v/c 1 + v/c