The Intensity of sound of loudness level $$60dB$$ is n×$$10$$−$$4$$ $$watt/m2$$ . Find n.

β$$=10log10II0$$ ⇒$$60=10log10$$ $$II0$$ ⇒$$I=I0$$×$$106$$ ⇒$$I=10$$−$$12$$×$$106$$ ⇒$$I=10$$−$$6$$ $$watt/m2$$ ⇒$$I=0.01$$×$$10$$−$$4$$ $$watt/m2$$

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Question

The Intensity of sound of loudness level 60dB is $n \times 10^{- 4} w a t t / m^{2}$ . Find n.

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Solution

$β = 10 \log_{10} (\frac{I}{I_{0}}) \Rightarrow 60 = 10 \log_{10} (\frac{I}{I_{0}}) \Rightarrow I = I_{0} \times 10^{6} \Rightarrow I = 10^{- 12} \times 10^{6} \Rightarrow I = 10^{- 6} w a t t / m^{2} \Rightarrow I = 0.01 \times 10^{- 4} w a t t / m^{2}$

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