 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2015/11/e/i/solution

k_{1} = k_{2}

. The junction relations then give

r = 0, t = 1, R = 0, T = 1 .

There is no mechanical-impedance discontinuity, so no reflected wave is needed to satisfy displacement and force continuity. The transmitted displacement is in phase with the incident wave and has the same amplitude; all incident power crosses the junction.

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