How much does one more violin add to the sound level of a section of n violins?
Let’s make a few simplifying assumptions: that each violin radiates the same power P (not usually the case in amateur orchestras!), that the listener is equally distant from all of them (hard to arrange) and that there is no simple phase relationship among the sounds from the different violins (this one is safe). Consider n violins, each with power P, that produce total power nP. Say that the intensity, at our listener’s ear, due to one violin is I1. Thanks to our simplifying assumptions, the intensity due to n violins is then In = nI1. At this stage, you may need to look at our section on decibels, sound level and loudness.
