Wave motionHardBloom L3
Question
A string consists of two parts attached at x = 0. The right part of the string (x > 0) has mass μr per unit length and the left part of the string (x < 0) has mass μl per unit length. The string tension is T. If a wave of unit amplitude travels along the left part of the string, as shown in the figure, what is the amplitude of the wave that is transmitted to the right part of the string?
Options
A.1
B.$\frac{2}{1 + \sqrt{\mu_{l}/\mu_{r}}}$
C.$\frac{2\sqrt{\mu_{l}/\mu_{r}}}{1 + \sqrt{\mu_{l}/\mu_{r}}}$
D.$\frac{\sqrt{\mu_{l}/\mu_{r}} - 1}{\sqrt{\mu_{l}/\mu_{r}} + 1}$
Solution
Sol. 
A = 1
At – Amplitude of transmitted wave.
At= $\left\lbrack \frac{2\sqrt{µ_{c}}}{\sqrt{µ_{c}} + \sqrt{µ_{r}}} \right\rbrack$
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