Question

The loudness of s pile driver is 112dB . About how many times the sound intensity of a pile driver? round to the nearest ten

Answer 1

Answer:

$db = 10 log_{10} (\frac{I}{I_o})$

With db =112 db, $I_o =10^{-12} W/m^2$ and solving for I the intensity we have:

$\frac{db}{10}= log_{10} (\frac{I}{I_o})$

$\frac{112}{10}= log_{10} (\frac{I}{10^{-12}})$

Now we can exponentiate with base 10 and we got:

$10^{11.2} = \frac{I}{10^{-12}}$

And solving we got:

$I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}$

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:

$db = 10 log_{10} (\frac{I}{I_o})$

With db =112 db, $I_o =10^{-12} W/m^2$ and solving for I the intensity we have:

$\frac{db}{10}= log_{10} (\frac{I}{I_o})$

$\frac{112}{10}= log_{10} (\frac{I}{10^{-12}})$

Now we can exponentiate with base 10 and we got:

$10^{11.2} = \frac{I}{10^{-12}}$

And solving we got:

$I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}$