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 (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 (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)`.