Question

If a source radiates sound uniformly in all directions and you triple your distance from the sound source, what happens to the sound intensity at your new position

Answer 1

The new intensity becomes (1/9) of the initial intensity.

Step-by-step explanation:

A source radiates sound uniformly in all directions and its intensity is proportional to the distance as follows :

`I\propto (1)/(r^2)`

Let I₁ and I₂ be the intensities at a distance r₁ and r₂. So,

`(I_1)/(I_2)=(r_2^2)/(r_1^2)`

We have, r₂ = 3r₁

`(I_1)/(I_2)=(9r_1)/(r_1)\\\\(I_1)/(I_2)=9\\\\I_2=(I_1)/(9)`

Hence, the new intensity becomes (1/9) of the initial intensity.