Fireworks Sound level at difference distances

[norcal36]

Homework Statement

A firework goes off high above you, a distance d1=500m from your head, and you hear an acoustic pressure of 10Pa. Your sister is a distance d2=4.00x10^3 at the same time. If air absorbs 7.00 db/km in sound energy what sound level does your sister hear? Density of air=1.2kg/m^3....Speed of sound=343m/s.

Relevant Equations

I=pmax^2/2*density*velocity
I=power/Area
10log(I/I0)

This is the work I've done so far...

I=p^2/2dv...I=(10)^2/2(1.2)(343)=.12112

I(A)=P...(.12112)(4pi(500)^2)=380522.366

I=P/A...380522.366/4pi(4000)^2=.0018925

10log(I/I0)...10log(.0018925/10^-12)=92.77db

92.77-7(4)=64.77db

I am winging it and that's the closest I can get to the right answer which is 68.3db...

Any Guidance would be greatly appreciated!

 

[mfb]

The 10 Pa at your place already had 3.5 dB absorption from the air in the first 0.5 km. You only need to consider 3.5 km more, that increases the sound level by 3.5 dB relative to your calculation and produces a perfect match.