At a distance `20 m` from a point source of sound the loudness level is `30 dB`. Neglecting the damping, find
(a) the loundness at `10 m` from the source
(b) the distance from the source at which sound is not heard.

Explanation

`(a)` As there is no damping, so
`L_(r_(0))=10 log ((I)/( I_(0))) =10 log .(1//2rho a^(2)omega^(2) v// r_(0)^(2))/(1//2 rho a^(2) omega^(2) v )=-20 log r _(0)`
Similarly `L_(r)=-20 log r `
So, `L_(r)-L_(r_(0))=20 log ( r_(0)//r)`
or `L_(r)=L_(r_(0))+20 log ((r_(0))/( r))=30 ++20xxlog ((20)/(10))=36 dB`
`(b)` Let `r` be the sought distance at which the sound is not heard.
So, `L_(r)=L_(r_(0))+20 log ((r_(0))/(r))=0` or, `L_(r_(0))=20 log ((r)/(r_(0)))` or `30=20 log ((r)/( 20))`
So, `log _(10)((r)/(20))=3//2 `or ` 10-^((3//2))=r//20`
Thus `r=200sqrt(10)=0.63 km.`
Thus for `r gt 0.63km` no sound will be heard.