Question

If a point source of sound has an output power of of 100 Watts and it emits the sound equally in all directions what is the intensity (powers per unit area) at distances 5,10,15, and 20 meters from the source. Does that follow inverse square law? Please provide detail of how to solve. Thank you!

Answer 1

Intensity is power /unit area

power emitted = 100 w

power is emitted uniformly in all directions.

d= 5 m

The power is distributed over an area of sphere of radius 5m

area of the sphere = 4r² = 314.16 sq.m

Intensity I₅ = 100/314.16 = 0.318 w/sq.m

d= 10

total area = 1256.64 sq.m

Intensity I₁₀ = 0.0796 w/sq.m

d= 15

I₁₅ = 100/(4*15² ) = 0.0354 w/sq.m

d=20

I₂₀ = 100/(4*20² ) = 0.0199 w/sq.m