Explanation:
In this exercise we have intensity expressed in [tex]W/m^2[/tex] as [tex]11.3 W/m^2[/tex]. So we want to know intensity expressed in dB. We know some facts:
[tex]I(dB)=10log(\frac{I}{I_{0}}) \\ \\ \\ But: \\ \\ I_{0}=1\times 10^{-12}W/m^2 \\ \\ I(W/m^2)=11.3W/m^2 \\ \\ \\ Substituting: \\ \\ I(dB)=10log(\frac{11.3}{1\times 10^{-12}}) \\ \\ I(dB)=10log(1.13\times 10^{13}) \\ \\ I(dB)=10(13.5) \\ \\ \boxed{I(dB)=130.5dB}[/tex]
[tex]Isolating \ I: \\ \\ log(\frac{I}{1\times 10^{-12}})=\frac{115}{10} \\ \\ log(\frac{I}{1\times 10^{-12}})=11.5 \\ \\ \frac{I}{1\times 10^{-12}}=10^{11.5} \\ \\ \frac{I}{1\times 10^{-12}}=3.16\times 10^{11} \\ \\ I=(1\times 10^{-12})(3.16\times 10^{11}) \\ \\ I=3.16\times 10^{-12}\times 10^{11} \\ \\ I=3.16\times 10^{-12+11} \\ \\ \boxed{I=3.16\times 10^{-1}W/m^2}[/tex]
