Introduction to Classical Mechanics · Problem 11.66
Relativity (Dynamics) — Morin
Physics — Mechanics · doppler-effect-relativity
Problem
As mentioned in Remark 2 of Section 11.8.2, it is possible to solve the transverse Doppler effect for Case 1 by working in the frame of the observer, provided that you account for the longitudinal component of the source's motion. Solve the problem this way and reproduce Eq. (11.52).