A sound wave has an intensity of 0.32 W/m² at a distance r from the source.  If the distance is increased by 0.5m, the sound level is decreased by 2.0 dB.  Assume the loudspeaker emits sound in all directions. Find the distance r.

a. The distance r = m

The intensity I of sound is related to the sound level b through the relationship:

 

 

where I₀ is the reference intensity = 10^-12 W/m² (for

I = 10^-12 W/m², b = 0).  We can calculate the sound level   b_ at the location r₁ using the above relation:

 

 

The sound level at the location r₂ = r₁ + 0.5 m is b₂ given by

 

 

 

 

 

We know that since the power P of the source is         constant, that is P₁ = P₂,

 

 

 

 

 

 But