Two semi-infinite strings of linear mass densities μ₁ and μ₂ are joined and maintained under the same tension. A transverse wave is incident from string 1 towards string 2. If μ₂ > μ₁, which statement about the reflected displacement wave is correct?
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Question

Two semi-infinite strings of linear mass densities μ₁ and μ₂ are joined and maintained under the same tension. A transverse wave is incident from string 1 towards string 2. If μ₂ > μ₁, which statement about the reflected displacement wave is correct?

Options

G1 Physics · Accepted Answer

For a stretched string, the wave impedance is Z = √(Tμ). Because μ₂ > μ₁, we have Z₂ > Z₁. The displacement-amplitude reflection coefficient is Aᵣ/Aᵢ = (Z₁−Z₂)/(Z₁+Z₂). Since Z₂ > Z₁, this coefficient is negative. A negative reflected displacement amplitude means a phase reversal of π. Correct option: B.