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Tom [10]
2 years ago
5

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
Mathematics
1 answer:
Oxana [17]2 years ago
3 0
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}  <span>is the minimum intensity detectable by the human ear
</span>
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}.
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