Question

the loudness in decibels of sound is defined as 10 log I/I0, where I is the intensity of the sound in watts per square meter (W/m2). I0, the intensity of a barely audible sound, is equal to 10 -12 W/m2. town regulations require the loudness of construction work not to exceed 100 dB. suppose a construction team is blasting rock for a roadway. one explosion has an intensity of 1.65 X 10-2 W/m2. is the explosion in violation of town regulations? which physical value do you need to calculate to answer the question? what values should you use for I and I0

Answer 1

As the problem states, to solve this, we are going to use the equation $L= log \frac{I}{I_{0} }$
where 
$L$ is the loudness in dB
$I$ is the intensity of a sound 
$I_{0}$  is the minimum intensity detectable by the human ear

We know for our problem that $I=1.65*10^{-2}$; we also now that the minimum intensity detectable by the human ear is $10^{-12)W/m^{2}$, so $I_{0}=10^{-12}$. Lets replace those values in our equation to find $L$:
$L=log \frac{1.65*10^{-2} }{10^{-12}}$
$L=10.22dB$

Qe can conclude that since the explosion is under 100dB, it does not violates the regulation of the town. We used tow physical values to calculate the answer: the intensity of the sound of the explosion, $I=1.65*10^{-2}W/m^2$, and the minimum intensity detectable by the human ear $I_{0}=10^{-12}W/m^{2}$.