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The incident wave can be reflected or transmitted. (I think we must assume that none is absorbed or scattered.) The reflected wave interferes with the incident wave, producing a standing wave. But the reflected wave is weaker than the incident wave - ie the amplitude is smaller. So there is not complete constructive and destructive interference. The nodes are not zero amplitude.
If the incident wave has amplitude A and reflected wave has amplitudd of rA.
Then they generate stabding wave of amplitude (1+r)A at antinodes and (1-r)A at nodes.
We are given that
(1+r)A/ (1-r)A = 1.5 = 3/2
r = 1/5
The energy in the wave is proportional to amplitude squared, so the fraction of incident energy in the reflected wave is (1/5)² = 1/25 = 4%
The fraction of energy in the transmitted wave is (100-4) = 96%
Regards
Arun (askIITians forum expert)
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