Sound Intenisty at a Football Game

[nsp2]

When a single person shouts at a football game, the sound intensity level at the center of the field is 63.3dB. When all the people shout together, the intensity level increases to 115dB. Assuming that each person generates the same sound intensity at the center of the field, how many people are at the game?

I have been trying to figure this out for a very long time, I was wondering if someone could help out, much obliged

 

[greeniguana00]

I think it's safe to assume that everyone is located an equal distance from the center of the field (otherwise we'd need more information). The first trick is to look at the decibel scale. dB is a logarithmic scale in reference to the power of the sound.

If the power of two sounds are power1 and power2, the difference between their dB values (dB1 and dB2) is described by this equation:

(dB1 - dB2) = 10 * log(power1/power2)

You know dB1 and dB2, so you should be able to solve for power1/power2. This will give you power1 relative to power2, and since you know many people one of them represents, you should be able to find how many people the other represents as well.

 

[rcgldr]

Another factor to consider is the shape of the sound source. In the case of a single person, it's a point source, with power diminishing with the square of distance. In the case of a large crowd, it's a plane source, where the sound doesn't diminish significantly within a certain range of the plane source.