A small speaker delivers 3W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as `10 ^(-12) W// m ^(2) ] ("in " m ) `
(Take `(3)/(pi) = 0. 96 , sqrt ( 0.96) = 0.98)`

Answer

`0.49`

Explanation

Given, audio output = 3W
Intensity, `I = 12dB`
`I _(0) = 10 ^(-12) W// m ^(2)`
From loudness relation,
`implies dB = 10 log "" ( I )/( I _(0))`
`implies 120 = 10 log ((1)/( I _(0)))`
`implies I = 1 W // m ^(2)`
Final intensity `= (P _(cell))/( 4 pi r ^(2))`
`implies I = ( P _(alpha )A)/( 4pi r ^(2))`
`implies r = sqrt ((3)/( 4pi (1)))= ( 0.98 )/(2) = 0.49 m`