Answer:
Intensity=[tex]I=3.16\times 10^{-7}\ W\ m^{-2}[/tex]
Explanation:
Given:
[tex]\beta=55\ dB\\I_o=10^{-12}\ W\ m^{-2}[/tex]
The sound level [tex]\beta[/tex] in dB with intensity [tex]I[/tex]
and reference intensity [tex]I_0[/tex] is given by:
[tex]\beta(dB)=10 \log_{10}(\frac{I}{I_0})[/tex]
Plugging in values.
[tex]55=10 \log_{10}(\frac{I}{10^{-12}})[/tex]
Dividing both sides by 10.
[tex]\frac{55}{10}=\frac{10 \log_{10}(\frac{I}{10^{-12}})}{10}[/tex]
[tex]5.5=\log_{10}\frac{I}{10^{-12}}[/tex]
The above can be written as
[tex]10^{5.5}=\frac{I}{10^{-12}}[/tex]
Multiplying both sides by [tex]10^{-12}[/tex]
[tex]10^{5.5}\times 10^{-12}=10^{-12}\times \frac{I}{10^{-12}}[/tex]
[tex]10^{(5.5-12)}=I[/tex]
[tex]10^{(-7.5)}=I[/tex]
∴ [tex]I=3.16\times 10^{-7}\ W\ m^{-2}[/tex]
Intensity =[tex]I=3.16\times 10^{-7}\ W\ m^{-2}[/tex]
