Intensity of periodic sound waves

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SUMMARY

The discussion centers on calculating the sound level in decibels (dB) from a firework explosion, specifically at a distance of 4.00 km. The maximum acoustic pressure at 400 m is given as 10.0 N/m², with the speed of sound assumed to be 343 m/s. The sound absorption rate is specified as 7.0 dB/km. The correct sound level at 4.00 km from the explosion is determined to be 65.6 dB, calculated using the formula B(dB) = 10 log(I/I₀) and the intensity derived from the acoustic pressure.

PREREQUISITES
  • Understanding of sound pressure levels and decibel calculations
  • Familiarity with the formula B(dB) = 10 log(I/I₀)
  • Knowledge of acoustic intensity and its relationship to pressure
  • Basic principles of sound absorption in the atmosphere
NEXT STEPS
  • Study the effects of distance on sound intensity and levels
  • Learn about sound absorption coefficients in various environments
  • Explore the relationship between acoustic pressure and intensity in detail
  • Investigate practical applications of sound level calculations in engineering
USEFUL FOR

Students in physics or engineering, acoustics researchers, and professionals involved in sound design or noise control will benefit from this discussion.

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Homework Statement


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?



Homework Equations




B(dB)=10log(I/Io); I=(deltaPmax)^2/(2pv)=Power/Area


The Attempt at a Solution



I plug the data into the equations but it give me the wrong answer. I don t know why the answer is 65.6dB. Especially how to use the acoustics pressure?
 
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