Answer:
140dB
Explanation:
In this problem you will be using the decibel scale to analyze a small firecracker that emits 1200 of peak power
In order to find to find the peak intensity in dB we must first determine the intensity in W/m^2 that the firecracker is producing:
I= P/(4π[tex]r^{2}[/tex])
I= 1200/(4π [tex]1^{2}[/tex]) =>96W/m^2
now the intensity in decibels can be calculated by using the dB conversion equation
β= 10log ( [tex]I / I_{o}[/tex] )dB
[tex]I_{o}[/tex] is a reference intensity in the above formula i.e for sound waves and its value is [tex]10^{-12}[/tex] W/m^2
β=10log( [tex]\frac{96 W/m^{2} }{10^{-12}W/m^{2} }[/tex] )dB => 10log(9.6x[tex]10^{13}[/tex] )dB
β= 140dB
therefore, at a distance of 1 m from the firecracker the peak intensity β is 140dB
