Optical fiber signal timing · Physics Brawl 2014 #FoL.7
Physics · optics
Problem
Consider computer X, which is connected by two optical fibres to two other computers A and B. The total length of these optical fibres together is l=3.0 km. A signal from computer A, bearing a message that it was sent at the time 1413753899.2135753 s (Unix timestamp of the time counter at computer A) reached computer X at the time 1413753899.2135921 s (Unix timestamp of the time counter at computer X). Similarly, a signal from computer B was received by computer X at time 1413753906.4599004 s, bearing the message that it was sent at the time 1413753906.4598925 s. Assume that the time counters of computers A and B are synchronized, but that the time counter of computer X is either gaining or lagging behind. Luckily, this deviation stays constant in time. Also, do not take into account either the effects of relativity or the time to process the signals. Assuming that the speed of propagation of signals along the fibres is c=2.0⋅108 m·s−1, find the length of the fibre between A and X.