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

Answer

D

Explanation

Resultant intensity of two peridic waves is given by
`I=I_(1)+I_(2)+2sqrt(I_(2)I_(2))cosdelta`
where `delta` is the phase difference between the waves.
For maximum intensity,
`delta=2npi,n=0,1,2,......etc.`
Therefore, for zero order maxima, `cosdelta=-1`
`I_(min)=I_(1)+I_(2)-2sqrt(I_(1)I_(2))`
`=(sqrt(I_(1))-sqrt(I_(2)))^(2)`
Therefore, `I_(max)+I_(min)=(sqrt(I_(1))+sqrtI_(2))^(2)+(sqrtI_(1)-sqrtI_(2))^(2)`
`=2(I_(1)+I_(2))`