Introduction to Classical Mechanics · Problem 11.37

Relativity (Kinematics) — Morin

Physics — Mechanics · seeing-the-light

Problem

A

and

B

leave from a common point (with their clocks both reading zero) and travel in opposite directions with relative speed

v

. When

B

's clock reads

T

, he (

B

) sends out a light signal. When

A

receives the signal, what time does his (

A

's) clock read? Answer this question by doing the calculation entirely in (a)

A

's frame, and then (b)

B

's frame. (This problem is basically a derivation of the longitudinal Doppler effect, discussed in Section 11.8.1.)