Question

A woman stands a distance d from a loud motor that emits sound uniformly in all directions. The sound intensity at her position is an uncomfortable 4.3×10-3 W/m2. At a distance 2.7 times as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing?

Answer 1

a). Intensity= Power of Source/ Area

Now we know that Intensity from a source is same on a spherical area around the source. Thus we'll have Intensity as

  

Thus for a same source. we'll have

Now let the initial distance be d₁= d and Initial intensity be I₁. Final distance will be d₂= 2.7d and Final Intensity be I₂, then using the above formula,

using all given values,

  

(ANS)

b). The sound level of Intensity is given by

  

where I_r= Threshold Intensity of hearing= 10^-12 W/m²

   then using value from part a, we'll get

(ANS)