Decibels - Combination of sound sources

When several sound sources are combined, each of which generating a certain amount of dB_spl, we can't simply sum up these values, but rather the following empirical formula must be used:

Equation 3.6. Combination of sound sources 

Let's take a look at an example with two sound sources each having a 90dB_spl intensity.

We would have:

Equation 3.7. Application of the formula for combined sound sources 

This equation also gives us a very important empirical rule, namely: if you sum up two identical sound sources you will have an increase of 3dB_spl, and not simply double the value. So, if we have a P.A. system^{[4 ]} which produces an acoustic pressure of 100dB_spl, and we add another identical P.A. system to it, we'd obtain an overall acoustic pressure of 103dB_spl. To get to 106dB_spl we'd have to add another two P.A.s which would sum up to 4 systems, and so on.