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  4. A source of sound emits 200 π W power which is uniformly distributed over a sphere of 10 m radius. What is the loudness of sound on the surface of a sphere?

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Q. A source of sound emits 200 $ \pi $ W power which is uniformly distributed over a sphere of 10 m radius. What is the loudness of sound on the surface of a sphere?

MGIMS WardhaMGIMS Wardha 2007

Solution:

Intensity of sound, $ I=\frac{P}{A} $ $ =\frac{200\pi }{2\pi \times {{(10)}^{2}}} $ $ =1\,W/{{m}^{2}} $ $ \therefore $ Loudness, $ L=10\text{ }{{\log }_{10}}\frac{I}{{{I}_{0}}} $ $ =10\text{ }{{\log }_{10}}\frac{1}{{{10}^{-12}}} $ $ =10\text{ }{{\log }_{10}}{{10}^{12}} $ $ =120\,dB. $