Intensity of periodic sound waves

In summary, a firework charge detonated above the ground creates an acoustic pressure that reaches a maximum of 10.0 N/m2 at a distance of 400m. The speed of sound is constant at 343 m/s and the ground and air absorb sound energy. To calculate the sound level at 4.00km, the equation B(dB)=10log(I/Io) can be used, where I=(deltaPmax)^2/(2pv) and the rate of sound absorption is 7.0 dB/km. The correct answer is 65.6dB, but the student is unsure how to use the acoustic pressure in the equation.
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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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1. What is the definition of intensity of a periodic sound wave?

The intensity of a periodic sound wave is the amount of energy that passes through a unit area of the medium in the direction of the wave per unit time.

2. How is the intensity of a periodic sound wave measured?

The intensity of a periodic sound wave is measured in watts per square meter (W/m²) using a sound level meter.

3. What is the relationship between intensity and amplitude of a periodic sound wave?

The intensity of a periodic sound wave is directly proportional to the square of its amplitude. This means that as the amplitude of the wave increases, its intensity also increases.

4. Can the intensity of a periodic sound wave be changed?

Yes, the intensity of a periodic sound wave can be changed by altering its amplitude or distance from the source. It can also be affected by factors such as the medium through which it travels and any obstructions in its path.

5. How does the intensity of a periodic sound wave affect human perception of loudness?

The intensity of a periodic sound wave is directly related to the perceived loudness of the sound. As the intensity increases, the sound is perceived as louder. This is why sounds with higher intensities are often described as being louder than sounds with lower intensities.

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