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)/(sqrt(2))`
C. `(1)/(4)`
D. `(2)/(3)`

Answer

B

Explanation

`dB = 10 log ((I)/(I_(0)) = 10 log ((K //r^(2))/(I_(0)))`
`= 10 [ log (K') - 2 log r]`
`dB_(1) = 10 (log K' - 2 log r_(1))`
`dB_(2) = 10 (log K' - 2 log r_(2))`
` 3 = dB_(1) - dB_(2) = 20 log ((r_(2))/(r_(1)))`
`(0.3) = log ((r_(2))/(r_(1)))^(2)`
`((r_(1))/(r_(2))) = (1)/(sqrt(2))`