Answer to Question #2277 in Mechanics | Relativity for chris

Question

Sound spreads radially in all directions from a source with power 15.3 W. If the intensity you experience is 3.00×10−6 W/m2, how far away are you from the source? answer in meters.

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 =15.3 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 ) → r²=P_ac/(4πI_r ) → r= √(P_ac/(4πI_r )) = √(15.3/(4*π*3*10⁶ )) = 0.637*10^-3 m.