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_{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.

I

Here, P

So we have

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