String 1 is connected with string 2. The mass per unit length in string 1 is $μ_{1}$ and the mass per unit length in string 2 is 4 $μ_{1}$ . The tension in the strings is T. A travelling wave is coming from the left. What fraction of the energy in the incident wave goes into string2?

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1/8

4/9

2/3

8/9

answer is D.

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Detailed Solution

$\begin{array}{l} \frac{E_{r}}{E_{1}} = {(\frac{A_{r}}{A_{1}})}^{2} = {(\frac{v_{2} - v_{1}}{v_{1} + v_{2}})}^{2} = 1 / 9 \\ T h e r e f o r e, \frac{E_{t}}{E_{1}} = 8 / 9 \end{array}$

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