 Solution

ID: past-exam-of-the-physics-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/section-a/a9/solution

The transverse-wave impedance of a string is

Z = T μ

for common tension

T

. The density ratio four gives

Z_{2} / Z_{1} = 2

. Continuity of displacement and transverse force gives transmitted amplitude ratio

t = 2 Z_{1} / (Z_{1} + Z_{2}) = 2/3

T = \frac{Z _{2}}{Z _{1}} ∣ t ∣^{2} = \frac{8}{9} .

The reflected fraction is

1/9

, checking energy conservation. Squaring the displacement amplitude alone would give the wrong transmitted power.

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