# Measuring the sound of fireworks.

1. Jun 3, 2012

### charmedbeauty

1. The problem statement, all variables and given/known data

A firework charge is detonated many metres above the ground. At a distance of d1 = 590 m from the explosion, the acoustic pressure reaches a maximum of ΔPmax = 10 Pa (see figure below). Assume the speed of sound is constant at 343 m/s throughout the atmosphere over the region considered and the ground absorbs all the sound falling on it. Assume that the density of air is 1.2 kg/m^3. What is the sound level at a distance of d2 = 3.50 ×103 m from the explosion?

2. Relevant equations

3. The attempt at a solution

so we know that pmax=10Pa when observer is 590m away

so
10= 343×1.2×ω×590

solving for ω

ω= 10 / (343×590×1.2)

now to find p when Smax= 3.50×103

p = 343×1.2×(10 /(343×590×1.2))×(3.5×103)

p= 59.322

I= P /4∏r2

I= 59.322 / 4∏(3.5×103)2

I= 3.8536×10-7

β=10log10(3.85361×10-7 / 10-12)

β = 55.859 dB

this seem like the right method.??.thanks

Last edited: Jun 3, 2012