A sound source emits 20.0 W of acoustical power spread equally in all directions.The threshold of hearing is .What is the sound intensity level 30.0 m from the source? A) 92.5 dB B) 81.5 dB C) 1.77 × 10^-3 dB D) 1.77 × 10^-3 W E) -27.5 dB

Question

Quizplus · Accepted Answer

The sound intensity at a distance r from a point source emitting power P uniformly in all directions is given by:
I = P/4πr²

Here, P = 20 W and r = 30.0 m.

So, I = 20/(4π(30.0)²) = 1.77 × 10⁻³ W/m²

The threshold of hearing, I₀ = 1.0 × 10⁻¹² W/m²

The sound intensity level (SIL) is given by:
SIL = 10 log(I/I₀) dB

So, SIL = 10 log[(1.77 × 10⁻³)/(1.0 × 10⁻¹²)] = 92.5 dB

Therefore, the correct choice is A.

A Sound Source Emits 20