Introduction to Classical Mechanics · Problem 11.67
Relativity (Dynamics) — Morin
Physics — Mechanics · doppler-effect-relativity
Problem
Twin A stays on the earth, and twin B flies at speed v to a distant star and back. The star is a distance L from the earth in the earth--star frame. Use the Doppler effect to show that B is younger by a factor γ when she returns (don't use any time dilation or length contraction results). Do this in the following two ways; both are doable by working in either A's frame or B's frame(s), so take your pick.
(a) A sends out flashes at intervals of t seconds (as measured in his frame). By considering the numbers of redshifted and blueshifted flashes that B receives, show that TB=TA/γ.
(b) B sends out flashes at intervals of t seconds (as measured in her frame). By considering the numbers of redshifted and blueshifted flashes that A receives, show that TB=TA/γ.