Two strings are under the same tension and have linear densities μ₁ = 9μ and μ₂ = μ. A wave of displacement amplitude 8 mm is incident from string 1 onto string 2. If 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 are under the same tension and have linear densities μ₁ = 9μ and μ₂ = μ. A wave of displacement amplitude 8 mm is incident from string 1 onto string 2. If 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 are proportional to the square roots of the linear densities. Therefore, Z₁ = 3Z, Z₂ = Z. The reflection coefficient is Aᵣ/Aᵢ = (Z₁−Z₂)/(Z₁+Z₂) = (3−1)/(3+1) = 1/2. Hence, Aᵣ = (1/2)(8 mm) = 4 mm. Therefore, N = 4.