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At a distance 20 m from a point source o...

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.

Text Solution

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The correct Answer is:
A, B, C, D
(a) Intensity due to a point source varies with distance `r` from it as `I prop (1)/(r^(2))`
or `(I_(1))/(I_(2)) = ((r_(2))/(r_(1)^(2)))^(2)`
Now,`L_(1) = 10 log .(I_(1))/(I_(o))`
and `L_(2) = 10 log .(I_(2))/ (I_(o))`
`:. L_(1) - L_(2) = 10[log .(I_(1))/(I_(o))- log .I_(2)/(I_(o))]`
= `10 log .(I_(1))/(I_(2))- 10 log.(r_(2)/(r_(1)))^(2)`
Substituting, `L_(1) = 30dB, r_(1) = 20 m` and `r_(2)= 10 m`
we have `30 - L_(2) = 10 log ((10)/(20))^(2) = - 6.0`
or `L_(2) = 36 dB`
(b) `L_(1) - L_(2) = 10 log .((r_(2))/(r_(1)))^(2)`
sound is not heard at a point where `L_(2) = 0`
or `30 = 10 log. ((r_(2))/(r_1))^(2)`
`:.(r_(2)/(r_1))^(2)= 1000` or `(r_(2))/(r_(1))=31.62`
`:. r_(2) = (31.62) (20) ~~ 632 m`
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