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Two strings with linear mass densities mu₁ = 25 g/cm and mu₂ = 9 g/cm are joined together. What is the ratio of the amplitude of the reflected wave to the amplitude of the incident wave for transverse vibrations?

1. 9/16
2. 3/4
3. 1/4
4. 1/3

Correct answer: 1/4

Solution

Wave speed in a string: v = sqrt(T/mu). At constant tension T, v proportional to 1/sqrt(mu). So v₁ proportional to 1/5 and v₂ proportional to 1/3. Amplitude reflection coefficient: r = (v₂ - v₁)/(v₂ + v₁) = (1/3 - 1/5)/(1/3 + 1/5) = (2/15)/(8/15) = 1/4.

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