When two progressive waves of intensity `I_(1)` and `I_(2)` , but slightly different frequencies superpose, the resultant intensity fluctuates between

Options

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

Answer

A

Explanation

Resultant of two intensities `l_(1)` and `l_(2)` is given by
`I_("Resultant") = l_(1) + l_(2) + 2sqrt(I_(1)I_(2) cos phi)`
Maximum value of intensity is at `phi =0`
and minimum value of intensity is at `phi = 180^(@)`
`therefore` Maximum intensity is, `I_(rms) = I_(1) + I_(2) + 2sqrt(I_(1) + I_(2)) cos 0^(@) = (sqrt(I_(1)) + sqrt(I_(2))^(2))`
and the minimum intensity is, `I_("min") = I_(1) + I_(2) +2sqrt(I_(1)I_(2)) cos 180^(@)`
`(sqrt(I_(1) - sqrt(I_(2))^(2)))`