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  4. A sound has an intensity of 2× 10-8W text/m2 . Its intensity level in decibels is ( log 102=0.3 )

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Q. A sound has an intensity of $ 2\times {{10}^{-8}}W\text{/}{{m}^{2}} $ . Its intensity level in decibels is $ \left( {{\log }_{10}}2=0.3 \right) $

CMC MedicalCMC Medical 2007

Solution:

$ L=10\,{{\log }_{10}}\left( \frac{I}{{{I}_{0}}} \right) $ $ \therefore $ $ L=10{{\log }_{10}}\left( \frac{2\times {{10}^{-8}}}{{{10}^{-12}}} \right) $ $ (\because {{I}_{0}}={{10}^{-12}}W\text{/}{{m}^{2}}) $ $ L=10\,{{\log }_{10}}(2\times {{10}^{4}}) $ $ L=10\,[{{\log }_{10}}2+{{\log }_{10}}{{(10)}^{4}}] $ $ L=10\,(4.3) $ $ L=43\,decibel $