Past exam of the mathematical methods II course of the University of Oxford / 2017 / 10 / b / ii / Solution

Reflection at a fixed end has displacement coefficient $-1$. The light-string pulse therefore returns from the wall with amplitude $-4A_i/3$ and width $2w$. It is inverted and travels left at $40\mathrm{m}{\mathrm{s}}^{-1}$. Taking the first junction encounter as time zero, its centre reaches the wall after $2/40=0.05\mathrm{s}$ and returns to the junction after $0.10\mathrm{s}$; a finite pulse takes its own duration to complete each encounter.