Ear Damage from a Small Firecracker

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The discussion centers on calculating the peak intensity in decibels from a small firecracker emitting 1200 watts of peak power. The initial calculation used the formula B = 10log(I/Io) but incorrectly defined the area for sound propagation. It was pointed out that sound waves propagate spherically, requiring the use of a spherical area formula rather than a circular one. The correct area for sound intensity at a distance of 1 meter should be 4πr². This clarification is essential for accurately determining the peak intensity in decibels.
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Lets say there is a small firecracker that emits 1200 of peak power.
What is the peak intensity B in decibels at a distance of 1 m from the firecracker?


This is what i have tried:

B = 10log(I/Io)

I = 1200/pi Since I = power/area and the area is pir^2, pi(1m)^2

Io=( 10^-12 W/m^2)


So B= 10log([1200/pi] / [10^-12 ]) and i get around 135.83 , however the answer is incorrect


Can someone help please? THank you
 
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Check the way you defined area for waves that propagate in space.
 
So the area is not a circle?
 
No, sound waves are spherical waves and travel in three dimensional space.
 

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