Answer to Question #2276 in Mechanics | Relativity for adam

Question #2276
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.
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:
Ir=Pac/(4πr2 )
Here, Pac =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
Ir=Pac/(4πr2 )=345/(4π 402 )=345/(4*π*1600)=0.017 W/m2 .

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