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Question

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 A 9:4
The ratio of maximum and minimum amplitudes corresponding to constructive and destructive interference is,
AmaxAmin=A1+A2|A1A2|=A1+A2A1A2

Given: A1A2=51
Using componendo and dividendo,
A1+A2A1A2=5+151=64
AmaxAmin=64
AmaxAmin=32
Also intensity of wave,
IA2
ImaxImin=(AmaxAmin)2
ImaxImin=(32)2=94

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