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

Given `(I_1)/(I_2)=(4)/(1)`
We know `Ipropa^2`
`:. (a_1^2)/(a_2^2)=(I_1)/(I_2)=(4)/(1)` or `:. (a_1)/(a_2)=(2)/(1)`
`(I_(max))/(I_(min))=((a_1+a_2)^2)/((a_1-a_2)^2)=((2+1)/(2-1))^2`
`=((3)/(1))^2=(9)/(1)`
Therefore, difference of loudness is given by
`L_1-L_2=10log_(10).(I_(max))/(I_(min))=10log(9)`
`=10log3^2=20log3`