The difference of loudness in decibels `(dB)` between maximum and minimum intensities of two coherent sound sources as they interfere in space is `20log3`. Find the ratio of intensities of two coherent sound sources:

Options

A. `2`
B. `4`
C. `4sqrt2`
D. `8`

Answer

B

Explanation

`L_1-L_2=20log3=10log9` (i)
But `L_1-L_2=10log(I_(max))/(I_0)-10log(I_(min))/(I_0)`
or `L_1-L_2=10log(I_(max))/(I_(min))` (ii)
Compare (i) and (ii)
`(I_(max))/(I_(min))=9=([(I_(1)//I_(2))^((1)/(2))+1]^2)/([(I_(1)//I_(2))^((1)/(2))-1]^2)=((x+1)^2)/((x-1)^2)`
On solving `x=sqrt(I_(1)//I_(2))=2`
`(I_1)/(I_2)=4`