= Solution
After the first encounter, the reflected pulse travels backwards through the heavy string with amplitude $A_i/3$ and width $w$. The transmitted pulse has amplitude $4A_i/3$ and speed $40\,\mathrm{m\,s^{-1}}$. Its temporal duration is unchanged at the stationary junction, so its spatial width doubles to $2w$. Both pulses retain the original displacement sign.
\Image[/past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2017-pulse-reflections.png]
{title=Pulse splitting, inversion at the fixed wall and the first return through the junction}
{description=Original compact-pulse examples with incident width 0.4 metres. The junction is at zero and the fixed wall at two metres; amplitudes are normalized by the initial heavy-string pulse amplitude.}
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