Sound Level at 4km from Explosion: Calculate & Subtract dB

In summary, at a distance of 4km from a firework explosion, the sound level would be lower due to absorption of sound energy by the air. The sound level is calculated by subtracting the sound energy lost over the 400m stretch twice, instead of just once, which explains the difference between subtracting (7*3.6)dB and (7*4)dB from the original sound level calculation without absorption.
  • #1
semc
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A firework is detonated many meters above the ground. At a distance of 400m from the explosion, the acoustic pressure reaches a maximum of 10N/m2. Assume the speed of sound is constant at 343m/s, the ground absorbs all sound falling on it, and the air absorbs sound energy by the rate of 7dB/km. What is the sound level at 4km from the explosion?

I have calculated the sound level at a distance 4km away from the explosion without the absorption. However why do we have to subtract (7*3.6)dB from that answer instead of (7*4)dB ?
 
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  • #2
When you say you calculated the intensity without the absorption you ignore the fact that intensity given to you 400m away has already underwent some loss. Hence to subtract intensity lost over the total 4km would be actually to subtract intensity over the 400m stretch twice.
 

1. How do you calculate sound level at 4km from an explosion?

To calculate the sound level at 4km from an explosion, you can use the inverse square law equation: sound level = original sound level - 20log(distance/ reference distance). The reference distance is typically 1 meter, so in this case it would be 20log(4000/1) = 20log(4000) = 66.02 dB.

2. What is the reference distance in the inverse square law equation?

The reference distance in the inverse square law equation is the distance at which the original sound level is measured. This distance is typically 1 meter, but can vary depending on the situation.

3. How do you subtract decibels (dB)?

To subtract decibels, you can use the formula: final decibels = 10log(10^(original decibels/10) - 10^(subtracted decibels/10)). This formula takes into account the logarithmic nature of decibels and ensures an accurate subtraction.

4. What is the sound level at 4km from an explosion?

The sound level at 4km from an explosion can vary depending on the intensity of the explosion and the surrounding environment. However, using the inverse square law equation, the sound level at 4km can be estimated to be approximately 66.02 dB.

5. How does distance affect sound level?

Distance has a significant effect on sound level due to the inverse square law. This law states that as distance from a sound source increases, the sound level decreases by 6 decibels for every doubling of distance. In other words, the sound level decreases exponentially as distance increases.

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