Ratio of intensities of two waves is 9:1. If these two are superimposed, what is the ratio of maximum and minimum intensities?

Options

A. `10:8`
B. `9:1`
C. `4:1`
D. `2:1`

Answer

C

Explanation

`I_(max)=(sqrt(I_(1))+sqrt(I_(2)))^(2)=[sqrt((I_(1))/(I_(2)))+1]^(2)`
`I_(max)=(sqrt(I_(1))-sqrt(I_(2)))^(2)=[sqrt((I_(1))/(I_(2)))-1]^(2)`
`:.(I_(max))/(I_(min))=([sqrt((9)/(1))+1])/([sqrt((9)/(1))-1]^(2))=([3+1]^(2))/([3-1]^(2))`
`=(16)/(4)=(4)/(1)`