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# Physics Question

1. A fireworks shell explodes H=110 m above the ground, creating colorful sparks. How much greater is the sound level of the explosion for a person at a point directly below the explosion than for a person a horizontal distance of L=190 m away?

### 1 Answer by Expert Tutors

Robert A. | Certified Teacher and Engineer - Tutoring Physics, Maths, and SciencesCertified Teacher and Engineer - Tutorin...
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Lets assume that the sound from the explosion radiates in all directions from the firecracker equally.
Then what we have is a point source.
For light the intensity varies inversely as the square from a point source.  For sound, just like light, this is true since as you move farther away the source it has to spread out to cover the growing surface of the sphere of that radius.

Now I do not know what level student you are or level physics you are taking, but the same is also true for all EM radiation, signals, light, magnetism, ...
The variation from a line source (infinitely long line) is linear. You can prove it by integration and Gauss's law.
The variation from a plane (an infinite plane) is null. Also can be proven by an integration and Gauss's law.

This is why in stores they use long lines of tube lights instead of small round bulbs.
This is why they will also arrange those lights (or the rectangular 2x4 ft lights) to try and simulate a plane.
If the ceiling looks like a plane of light it is just as bright at the floor as 10 ft high.  But I digress.

So you can see you have a point source.  The intensity from the source will vary as an inverse square.  You will have to determine what the question is asking by "sound level": the sound intensity, sound pressure, perceived loudness - remember there are decibels (20 dB) involved for some and not other ways to measure sound.  You will also have to ignore any reflections of the sound from the ground unless you want to do some nasty calculus.

It also is unclear to me what the position of the 2nd person is.  Is the second person on the ground horizontally 190 m away from the first and so the distance from the explosion is the hypotenuse SQRT(110^2 + 190^2), or is the second person up in the air horizontally 190 m from the sound.  i.e. what are the two distances (110  and 190) or (110 and 219.5)?