At a distance `r=100m` from a point isotropic source of the sound of frequency `200 Hz` the loudness level is equal to `L=50d B`. The audiblitiy threshold at this frequency corresponds to the sound intensity `I_(0)=0.10n W//m^(2)`. The damping coefficient of the sound wave is `gamma =5.0 . 1.0^(-4) m ^(-1)` . Find the sonic power of the source.

Explanation

Express `L` in bels. (i.e.`L=5 ` bels).
Then the intensity at the relevant point `(` at a distance `r` from the source `)` is `I_(0)10^(L)`
Had there been no damping the intensity would have been `, e^(2 gamma r ) I_(0). 10^(L)`
Now this mustan equal the quantity
`(P)/(4pi r ^(2))`, where` P=` sonic power of the source .
Thus `(P)/(4pi r ^(2))e^(2 gamma r) I_(0).10 ^(L)`
or ` P= 4pi r ^(2) e^(2 gamma r ) I_(0) . 10^(L)=1.39 W`.