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If the amplitude of incident wave is A, what are amplitudes of reflected and transmitted waves ?

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Solution

Let the wave speed in first wire be $v_{1}$ and wave speed in second wire be $v_{2}$ .
Thus $r = \frac{A_{r}}{A_{i}} = \frac{v_{2} - v_{1}}{v_{2} + v_{1}} = - \frac{1}{3}$
$⟹ A_{r} = - \frac{A}{3}$
$t = \frac{A_{t}}{A_{i}} = \frac{2 v_{2}}{v_{1} + v_{2}} = \frac{2}{3}$
$⟹ A_{t} = \frac{2 A}{3}$

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