Answer :
Given that,
At 3.00 m from a source that is emitting sound uniformly in all directions, the sound level is 60.0 dB.
To find,
The distance from the source would the sound level be one-fourth the sound level at 3.00 m.
Solution,
The intensity from a source is inversely proportional to the distance.
Let I₁ = 60 dB, r₁ = 3 m, I₂ = 60/4 = 15 dB, r₂ =?
Using relation :
[tex]\dfrac{I_1}{I_2}=\dfrac{r_2^2}{r_1^2}\\\\r_2^2=\dfrac{I_1r_1^2}{I_2}\\\\r_2^2=\dfrac{60\times (3)^2}{15}\\\\r_2=6\ m[/tex]
So, at a distance of 6 m the sound level will be one fourth of the sound level at 3 m.