Answer to Question #2276 in Mechanics | Relativity for adam

Question

A longitudinal wave spreads radially from a source with power 345 W. What is the intensity 40.0 meters away? answer in W/m^2.

Answer 1

For a spherical sound source, the intensity in the radial direction as a function of distance r from the centre of the source is:
I_r=P_ac/(4πr² )
Here, P_ac =345 W (upper case) is the sound power and A the surface area of a sphere of radius r.
Thus the sound intensity decreases with 1/r² the distance from an acoustic point source, while the sound pressure decreases only with 1/r from the distance from an acoustic point source after the 1/r - distance law.
So we have
I_r=P_ac/(4πr² )=345/(4π 40² )=345/(4*π*1600)=0.017 W/m² .