Two strings under the same tension have linear densities μ₁ = μ and μ₂ = 4μ. A displacement wave of amplitude 6 mm is incident from string 1. If the magnitude of the reflected displacement amplitude is N mm, find N.
Physics · Wave Motion · reflection ,refraction of string wave and superposition of wave
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Question

Two strings under the same tension have linear densities μ₁ = μ and μ₂ = 4μ. A displacement wave of amplitude 6 mm is incident from string 1. If the magnitude of the reflected displacement amplitude is N mm, find N.

Physics · Wave Motion · reflection ,refraction of string wave and superposition of wave

G1 Physics · Accepted Answer

The impedances satisfy Z₂ = 2Z₁. The reflection coefficient is Aᵣ/Aᵢ = (Z₁−Z₂)/(Z₁+Z₂) = (1−2)/(1+2) = −1/3. Therefore, Aᵣ = −(1/3)(6 mm) = −2 mm. Its magnitude is 2 mm. Hence, N = 2.