Two wave with same frequency and wave number are propagating in the same direction. The ratio of their amplitude is 5:1 . If interference occurs, the ratio of maximum and minimum intensity should be
A
9:4
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B
3:2
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C
1:4
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D
4:1
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Solution
The correct option is A9:4 The ratio of maximum and minimum amplitudes corresponding to constructive and destructive interference is, AmaxAmin=A1+A2|A1−A2|=A1+A2A1−A2
Given: A1A2=51 Using componendo and dividendo, A1+A2A1−A2=5+15−1=64 ⇒AmaxAmin=64 ∴AmaxAmin=32 Also intensity of wave, I∝A2 ⇒ImaxImin=(AmaxAmin)2 ∴ImaxImin=(32)2=94