A wave travelling on string 1 is partially reflected at a junction with string 2. The two strings have impedances Z₁ and Z₂. What fraction of the incident average power is reflected?
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Question

A wave travelling on string 1 is partially reflected at a junction with string 2. The two strings have impedances Z₁ and Z₂. What fraction of the incident average power is reflected?

G1 Physics · Accepted Answer

The displacement-amplitude reflection coefficient is r = Aᵣ/Aᵢ = (Z₁−Z₂)/(Z₁+Z₂). For incident and reflected waves travelling on the same string, the power ratio equals the square of the amplitude ratio. Therefore the reflected power fraction is R = r² = [(Z₁−Z₂)/(Z₁+Z₂)]². Correct option: B.