Intensity of periodic sound waves

[kreil]

The problem is this:

A firework charge is detonated many meters above the ground. At a distance of 400m from the explosion, the acoustic pressure reaches a maximum of 10.0 N/m². Assume that the speed of sound is constant at 343 m/s throughout the atmosphere over the region considered, that the ground absorbs all the sound falling on it, and that the air absorbs sound energy as described by the rate 7.0 dB/km.

What is the sound level (dB) at 4.00km from the explosion?

I know that

\beta = 10 log \left \frac{I}{I_0} \right

and that

I=\frac{P}{A}=\frac{1}{2} p v w^2 {s^2_{max}}

where p is the density of air, v is the speed of sound, w is the angular frequency and s_max is the amplitude of the position function s(x,t)=s_maxcos(kx-wt).

but I am having trouble correctly solving for I, and so I can't get the book answer of B=65.6 dB. Any help is appreciated.

Note: the equation I obtained for this problem taking into account the damping of the sound in air is:

\beta = 10 log \frac{I}{I_0}+br

where b=-7 dB/km and r=4.0km is the distance from the explosion.

 

[kreil]

Basically, I'm not sure how to use the acoustic pressure or ground damping in the problem.

 

[Astronuc]

\beta = 20 log \left \frac{P}{P_0} \right

and the ground absorption means no reverberation or reflection, so one only need to be concerned with acoustic pressure.

Is there an example of how to use the energy loss rate (db/km)?

One is given two distances, 0.4 km and 4.0 km, and the acoustic pressure at 0.4 km.

 

[kreil]

What reference pressure should I use in that equation?

If the acoustic pressure at 0.4km is 10, then at 4.0km it will be 1.

It doesn't say how to use the energy loss rate, so I guessed. Now that I look at it, it doesn't look right. Any ideas?