Sound Level at 4km from Explosion: Calculate & Subtract dB

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SUMMARY

The discussion focuses on calculating the sound level at a distance of 4km from a firework explosion, given an initial acoustic pressure of 10N/m² at 400m. The speed of sound is established at 343m/s, with air absorption quantified at 7dB/km. The key conclusion is that when calculating sound intensity loss, one must subtract 21dB (7dB/km multiplied by 3.6) instead of 28dB (7dB/km multiplied by 4), as the intensity at 400m has already experienced some absorption loss.

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A firework is detonated many meters above the ground. At a distance of 400m from the explosion, the acoustic pressure reaches a maximum of 10N/m2. Assume the speed of sound is constant at 343m/s, the ground absorbs all sound falling on it, and the air absorbs sound energy by the rate of 7dB/km. What is the sound level at 4km from the explosion?

I have calculated the sound level at a distance 4km away from the explosion without the absorption. However why do we have to subtract (7*3.6)dB from that answer instead of (7*4)dB ?
 
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When you say you calculated the intensity without the absorption you ignore the fact that intensity given to you 400m away has already underwent some loss. Hence to subtract intensity lost over the total 4km would be actually to subtract intensity over the 400m stretch twice.
 

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