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Two waves of equal frequencies have thei...

Two waves of equal frequencies have their amplitude in the ratio of 5:3. They are superimposed on each other. Calculate the ratio of the maximum to minimum intensities of the resultant wave.

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The correct Answer is:
A
Given, `A_1/A_2 = 3/5`
`:.sqrt(I_1/I_2) = 3/5 `
Maximum intensity is obtained, where
` cos phi = 1 `
and ` I_(max) = (sqrtI_1+sqrtI_2)^2`
Minimum intensity is found, where
` cos phi = -1 `
and ` I_(min) = (sqrtI_1+sqrtI_2)^2`
` Hence, I_(max)/I_(min) = (sqrtI_1+sqrtI_2)/(sqrtI_1 -sqrtI_2)^2 = (sqrt(I_1/I_2)+1)/(sqrt(I_1/I_2)-1)^2`
` = ((3//5)+1)/((3//5)-1))^2 = 64/4 = 16/1` .
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