A point source is emitting sound in all directions. The ratio of distance of two points from the point source where the difference in loudness levels is 3 dB is: `(log_(10)2=0.3)`.

Options

A. `(1)/(2)`
B. `(1)/(sqrt2)`
C. `(1)/(4)`
D. `(2)/(3)`

Answer

B

Explanation

`dB=10log((I)/(I_0))=10log((K//r^(2))/(I_0))`
`=10[log(K')-2logr]`
`dB_1=10(logK'-2logr_1)`
`dB_2=10(logK'-2logr_2)`
`3=dB_1-dB_2=20 log((r_2)/(r_1))`
`(0.3)=log((r_2)/(r_1))^2implies((r_1)/(r_2))=(1)/(sqrt2)`