In a partial stationary wave pattern that forms as a result of reflection of waves from an obstacle the ratio of the amplitude at an antinode and a node is β = 1.5 . What percentage of the energy pass

Question

In a partial stationary wave pattern that forms as a result of reflection of waves from an obstacle the ratio of the amplitude at an antinode and a node is β = 1.5 . What percentage of the energy passes across the obstacle?

TestHub · Accepted Answer

A1 = incident amplitude, A2 = reflected amplitude: $\frac{A _{1} + A _{2}}{A _{1} - A _{2}} = \frac{3}{2} \Rightarrow \frac{A _{1}}{A _{2}} = 5$

Energy ∝ (amplitude)²: $\frac{ε _{T}}{ε _{I}} = 1 - \frac{ε _{R}}{ε _{I}} = 1 - (\frac{1}{5})^{2} = \frac{24}{25}$

$% energy transmitted = \frac{24}{25} \times 100 = 96$

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