The ratio of intensities between two coherent sound sources is `4:1` the difference of loudness in decibels between maximum and minimum intensities, when they interfere in space, is

Options

A. `10 log (2)`
B. `20 log (3)`
C. `10 log (3)`
D. `20 log (2)`

Answer

B

Explanation

`(I_(1))/(I_(2)) = (4)/(1) or sqrt((I_(2))/(I_(2))) = (2)/(1)`
`:. (I_(max))/(I_(min)) = [ (sqrt(I_(1)//I_(2)) + 1)/(sqrt(I_(1) //I_(2)) -1)]^(2) = [( 2 + 1)/( 2 - 1)]^(2) = 9`
`:. L_(1) - L_(2) = 10 log ((I_(max))/(I_(min))) = 10 log 9 = 20 log 3`