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

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- Solution i

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

4 A_{i} /3

40 m s^{- 1}

. Its temporal duration is unchanged at the stationary junction, so its spatial width doubles to

2 w

. Both pulses retain the original displacement sign.

Figure 1.
Pulse splitting, inversion at the fixed wall and the first return through the junction
. 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. Details.

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