Answer:
The new intensity becomes (1/9) of the initial intensity.
Explanation:
A source radiates sound uniformly in all directions and its intensity is proportional to the distance as follows :
[tex]I\propto \dfrac{1}{r^2}[/tex]
Let I₁ and I₂ be the intensities at a distance r₁ and r₂. So,
[tex]\dfrac{I_1}{I_2}=\dfrac{r_2^2}{r_1^2}[/tex]
We have, r₂ = 3r₁
[tex]\dfrac{I_1}{I_2}=\dfrac{9r_1}{r_1}\\\\\dfrac{I_1}{I_2}=9\\\\I_2=\dfrac{I_1}{9}[/tex]
Hence, the new intensity becomes (1/9) of the initial intensity.
