A firework charge is detonated many metres above the ground. At a distance of 400 m from the explosion, the acoustic pressure reaches a maximum of `10.0(N)/(m^2)`. Assume that the speed of sound is constant at 343`(m)/(s)` throughout the atmosphere over the region considered, the ground absorbs all the sound falling on it, and the air absorbs sound energy at the rate of 7.00 `(dB)/(km)`. What is the sound level (in decibels) at 4.00 km from the explosion?

Explanation

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Calculate Maximum Intensity
The maximum intensity \( I_{\text{max}} \) can be calculated using the formula:
\[ I_{\text{max}} = \frac{(\Delta P_{\text{max}})^2}{2 \rho v} \]
where:
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