 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2018/paper-2/section-b/b9/e/iii/solution

There is no reflected wave when the characteristic mechanical impedances match:

Z_{1} = Z_{2} ⟺ ρ_{1} = ρ_{2}

for the same tension. Then

r = 0

C / A = 1

and

T = 1

. If tensions were independently adjustable, the general condition would be

T_{1} ρ_{1} = T_{2} ρ_{2}

, together with transverse-force matching; equality of densities alone would no longer be the universal criterion.

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