Question

Chapter 17, Problem 095 The sound intensity is 0.0070 W/m2 at a distance of 13 m from an isotropic point source of sound. (a) What is the power of the source? (b) What is the sound intensity 6.3 m from the source? (c) What is the sound level 13 m from the source?

Answer 1

Sound intensity at a distance of 13 m from the source = I₁ = 0.007 W/m²

Initial distance = R₁ = 13 m

Power of the source = P

P = I₁(4R₁²)

P = 4(0.007)(13)²

P = 14.866 W

Sound intensity at a distance of 6.3 m from the source = I₂

New distance = R₂ = 6.3 m

I₁(4R₁²) = I₂(4R₂²)

I₁R₁² = I₂R₂²

(0.007)(13)² = I₂(6.3)²

I₂ = 0.0298 W/m²

Sound level at 13 m from the source = ₁

₁ = 98.45 dB

a) Power of the source = 14.866 W

b) Sound intensity 6.3 m from the source = 0.0298 W/m²

c) Sound level 13 m from the source = 98.45 dB