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In a stationary wave pattern that forms ...

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

Text Solution

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The correct Answer is:
A, B, C, D
`A_(max)/A_(min) = A_i+A_r/A_i-A_r`
This ratio is given as 1.5 or `3/2`.
`:. A_i+A_r/A_i-A_r = 3/2` or `(1+(A_r)/(A_i))/(1-(A_r)/(A_i)) = 3/2 `
Solving this equation, we get `A_r/A_i = 1/5 `
` :. I_r/I_i = (A_r/A_i)^2 = 1/25`
or `I_r = 0.04 I_i `
i.e. `4%` of the incident energy is reflected or `96%` energy passes across the obstacle.
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