# Answer to Question #2277 in Mechanics | Relativity for chris

Question #2277

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.

Expert's answer

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

Here, P

So we have

I

_{r}=P_{ac}/(4πr^{2})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}/(4πr^{2}) → r^{2}=P_{ac}/(4πI_{r}) → r= √(P_{ac}/(4πI_{r})) = √(15.3/(4*π*3*10^{6})) = 0.637*10^{-3}m.Need a fast expert's response?

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