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

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

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

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, [tex]I=1.65*10^{-2}W/m^2[/tex], and the minimum intensity detectable by the human ear [tex]I_{0}=10^{-12}W/m^{2}[/tex].