Decibels - Combination of sound sources

When several sound sources are combined, each of which generates a certain amount of dB_spl, it isn't possible to simply sum up these values, but we should rather use the following empirical formula:

Equation 3.6. Combination of sound sources 

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

We'd have:

Equation 3.7. Application of the formula for combined sound sources 

From this equation too, we can obtain a very important empirical formula: if you sum up two identical sound sources you will have an increase of 3dB_spl (not double the value!). So, if we have a P.A system ^{[3 ]} which produces an acoustic pressure of 100dB_spl, and we add another identical P.A system 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.