Ear Damage from a Small Firecracker

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SUMMARY

The discussion centers on calculating the peak intensity in decibels (B) from a small firecracker emitting 1200 watts of peak power at a distance of 1 meter. The formula used is B = 10log(I/Io), where Io is 10^-12 W/m². The initial calculation incorrectly assumes the area for sound propagation is circular, while it should be spherical. The correct area for sound waves is derived from the formula for the surface area of a sphere, leading to a revised calculation for peak intensity.

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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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