A point source emits sound waves with an average power output of 80.0 W (a) Find the intensity 3.00 m from the source. (b) find the distance at which the intensity of the sound is `1.00xx10^-8(W)/(m^2)`

Explanation

a. Imagine a small loudspeaker sending sound out at an average rate of 80.0 W uniformly in all directions. You are standing 3.00 m away from the speakers. As the sound propagates, the energy of the sound waves is spread out over and ever expanding sphere. We evaluate the intensity from a given equation, so we categorize this example as substitution problem. Because a point emits energy in the form of spherical waves, use Eq. (ii) to find the intensity:
`I=(p_(avg))/(4pir^2)=(80.0W)/(4pi(3.00m)^2)=0.707(W)/(m^2)`
This intensity is close to the threshold of pain.
b. solve for r from above equation and use the given value for I:
`r=sqrt((p_(avg))/(4piI))=sqrt((80.0W)/(4pi(1.00xx10^-8(W)/(m^2)))=2.52xx10^4m`