A small speaker delivers `2 W` of audio will one detect `120 dB` intensity sound ? [Given reference intensity of sound as `10^(-12) W//m^(2)`]

Options

A. 30cm
B. 20cm
C. 40cm
D. 10cm

Answer

C

Explanation

`beta = 10 log_(10)((p)/(4 pi r^(2) I_(0) , 120 )= 10 log_(10)((p)/(4 pi r^(2) I_(0)))`
`rArr (p)/(4 pi r^(2) I_(0) = 10^(12)` ` rArr p=10^(-12) xx 10^(12) xx 4 xx pi r^(2)` `rArr r=sqrt((p)/(4 pi)) = sqrt((2 xx 7)/(4 xx 22)) = sqrt((7)/(44)) ~~ 0.4`
`r = 40 cm`