For a lossless junction between two stretched strings of impedances Z₁ and Z₂, which relations are correct for displacement amplitudes and average powers?
Select all that apply

Question

For a lossless junction between two stretched strings of impedances Z₁ and Z₂, which relations are correct for displacement amplitudes and average powers?

G1 Physics · Accepted Answer

The boundary conditions at the junction give Aᵣ/Aᵢ = (Z₁−Z₂)/(Z₁+Z₂), Aₜ/Aᵢ = 2Z₁/(Z₁+Z₂). The reflected wave is on the same string as the incident wave, so R = (Aᵣ/Aᵢ)². For a lossless junction, conservation of average power gives R+𝒯 = 1. Therefore all four statements are correct.