A lossless junction connects two stretched strings having impedances Z₁ and Z₂. What fraction of the incident average power is transmitted into string 2?
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Question

A lossless junction connects two stretched strings having impedances Z₁ and Z₂. What fraction of the incident average power is transmitted into string 2?

G1 Physics · Accepted Answer

The displacement transmission coefficient is Aₜ/Aᵢ = 2Z₁/(Z₁+Z₂). Average wave power is proportional to ZA² for fixed angular frequency. Therefore, 𝒯 = Pₜ/Pᵢ = (Z₂/Z₁) [Aₜ/Aᵢ]². Substituting, 𝒯 = (Z₂/Z₁) [2Z₁/(Z₁+Z₂)]² = 4Z₁Z₂/(Z₁+Z₂)². For an ideal lossless junction, R+𝒯 = 1. Correct option: A.