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. If the transmitted 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. If the transmitted displacement amplitude is N mm, find N.

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

G1 Physics · Accepted Answer

Here, Z₁ = 3Z, Z₂ = Z. The displacement transmission coefficient is Aₜ/Aᵢ = 2Z₁/(Z₁+Z₂) = 6Z/(4Z) = 3/2. Thus, Aₜ = (3/2)(8 mm) = 12 mm. A transmitted displacement amplitude can exceed the incident amplitude because the transmitted string has a different impedance; energy conservation must be checked using power, not amplitude alone. Hence, N = 12.