Answer:
[tex] db = 10 log_{10} (\frac{I}{I_o})[/tex]
With db =112 db, [tex]I_o =10^{-12} W/m^2[/tex] and solving for I the intensity we have:
[tex] \frac{db}{10}= log_{10} (\frac{I}{I_o})[/tex]
[tex] \frac{112}{10}= log_{10} (\frac{I}{10^{-12}})[/tex]
Now we can exponentiate with base 10 and we got:
[tex] 10^{11.2} = \frac{I}{10^{-12}}[/tex]
And solving we got:
[tex] I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}[/tex]
Step-by-step explanation:
We knwo that the loudnes os 112 db and we want to find the intensity. So then we can use the following formula:
[tex] db = 10 log_{10} (\frac{I}{I_o})[/tex]
With db =112 db, [tex]I_o =10^{-12} W/m^2[/tex] and solving for I the intensity we have:
[tex] \frac{db}{10}= log_{10} (\frac{I}{I_o})[/tex]
[tex] \frac{112}{10}= log_{10} (\frac{I}{10^{-12}})[/tex]
Now we can exponentiate with base 10 and we got:
[tex] 10^{11.2} = \frac{I}{10^{-12}}[/tex]
And solving we got:
[tex] I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}[/tex]
