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 periodic waves is given by
`I=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cos delta`
where, `delta` is the difference between the waves.
For maximum intensity, `delta=2n pi, n=0,1,2,…,` etc.
Therefore, for zero order maxima, `cos delta=1`
`I_("max")=I_(1)+I_(2)+2sqrt(I_(1)I_(2))=(sqrt(I_(1))+sqrt(I_(2)))^(2)`
For minimum intensity, `delta=(2n-1)pi, n=1,2,...,`
Therefore, for Ist order minima,
`cos delta=-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))+sqrt(I_(2)))^(2)+(sqrt(I_(1))-sqrt(I_(2)))^(2)=2(I_(1)+I_(2))`