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.

Two identical sources of sound S_(1) and S_(2) produce intensity I_(0)

1.	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.
Answer» Solution :(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)`