Measuring an Event — Question 7

Question 7

A two-way exchange separates clock offset from flight time

Two stationary clocks have constant offset $b=t_B-t_A$ at simultaneous events. A sends at reading 1, B receives at 5, B replies at 8, and A receives at 8, all in microseconds. Vacuum flight time T is the same both ways.

1. Derive equations for T and b from the four timestamps.

2. Find the offset and separation, using $c=3.00\times10^8\,\mathrm{m/s}$.

Question 7 - Solution

A two-way exchange separates clock offset from flight time

(a) Method and calculation

$$5-1=T+b,\qquad8-8=T-b.$$$$\boxed{T=\tfrac12[(5-1)+(8-8)]=2\,\mu\mathrm s}.$$

(b) Interpretation and further calculation

$$\boxed{b=\tfrac12[(5-1)-(8-8)]=2\,\mu\mathrm s}.$$$$\boxed{L=cT=600\,\mathrm m}.$$

Physical check

The reply delay cancels because its send timestamp is recorded. These are offset clocks, not yet synchronized clocks.