A sound wave has an intensity of 0.32 W/m² at a distance r from the source.  If the distance is increased by 0.50m, the sound level is decreased by 2.0 dB.  Assume the loudspeaker emits sound isotropically, 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. 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  and is given by

 

For a source emitting sound isotropically

 

 

 

 

 

 

 

 

But r₂ = r₁ + 0.5 m.