Two identical sources of sound `S_(1) and S_(2)` produce intensity `I_(0)` at a point `P` equidistant from each source .
(i) Determine the intensity of each at the point `P`.
(ii) If the power of `S_(1) ` is reduced to `64%` and phase difference between the two sources is varied continuously , then determine the maximum and minimum intensities at the point `P`.
(iii) If the power of `S_(1)` is reduced by `64%` , then determine the maximum and minimum intensities at the point `P`.

Explanation

(i) Both the sources produce maximum at the point `P`.
Thus , `I_(max) = I_(0) = ( sqrt (I_(1)) + sqrt(I_(2)))^(2)`
Since the sources are identical , therefore , `I_(1) = I_(2) = I`. ltbr. `I_(0) = 4 I or I = I_(0)//4`
(ii) Now `I_(1) = 0.64 I = 0.16 I_(0)` ltbr. And `I_(2) = I = 0.25 I_(0)`
`I_(max) = ( sqrt( I_(1)) + sqrt( I_(2)))^(2) = 0.81 I_(0)`
`I_(min) = (sqrt( I_(1)) - sqrt(I_(2)))^(2) = 0.01 I_(0)`
(iii) Now `I_(1) = ( 1 - 0.64) I_(0) = 0.36 I = 0.09 I_(0)`
And `I_(2) = I = 0.25 I_(0)`
`I_(max) = ( sqrt(I_(1)) + sqrt(I_(2))) ^(2) = 0.64 I_(0)`
`I_(min) = ( sqrt(I_(1)) - sqrt(I_(2)))^(2) = 0.04 I_(0)`