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In a stationary wave that forms as a res...

In a stationary wave that forms as a result of reflection of waves from an obstacle, the ratio of the amplitude at an antinode to the amplitude at node is 6. What percentage of energy is transmitted?

Text Solution

Verified by Experts

The correct Answer is:
D
Let `a_i and a_r` be the amplitudes of incident and
reflected waves.

Then,
`(a_i + a_r)/(a_i-a_r) = 6`
Hence, `a_r/a_i = 5/7`
Now, `E_r/E_i = (a_r/a_i)^2 = (5/7)^2 `
= 0.51
or percentage of energy reflected is
`100 xx (E_r /E_i) = 51%`
So, percentage of energy transmitted will be
`(100 - 51)%` or `49 % ` .
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