Two periodic waves of intensities `I_(1)` and `I_(2)` pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

Options

A. `(sqrt(I_(1))-sqrt(I_(2)))^(2)`
B. `2(I_(1)+I_(2))`
C. `I_(1)+I_(2)`
D. `(sqrt(I_(1))+sqrt(I_(2)))^(2)`

Answer

B

Explanation

`I=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cos phi`
`I_("max")=(sqrt(I_(1))+sqrt(I_(2)))^(2)`
`I_("min")=(sqrt(I_(1))-sqrt(I_(2)))^(2)`
`I_("max")+I_("min")`
`(sqrt(I_(1))+sqrt(I_(2)))^(2)+(sqrt(I_(1))-sqrt(I_(2)))^(2)`
`=(I_(1)+I_(2)+2sqrt(I_(1)I_(2)))+(I_(1)+I_(2)-2sqrt(I_(1)I_(2)))`
`2(I_(1)+I_(2))`