At a distance of 5.0 m from a point source, the intensity of sound is 1.0 10⁻⁸ W m ⁻² . Determine the intensity at a distance of 25 m from the source.

Step-by-step solution

For a point source, the intensity of sound I is inversely proportional to the square of the distance r from the source. I 1 r^2 I₂ I₁ = ( r₁ r₂ )^2 Given I₁ = 1.0 10⁻⁸ W m ⁻² , r₁ = 5.0 m , and r₂ = 25 m . I₂ 1.0 10⁻⁸ = ( 5.0 25 )^2 I₂ 1.0 10⁻⁸ = ( 1 5 )^2 = 1 25 I₂ = 1.0 10⁻⁸ 25 = 0.04 10⁻⁸ W m ⁻² I₂ = 4.0 10⁻¹⁰ W m ⁻²