Hey I am not sure if this is the right community for this question, might check if the physics community can answer it.
Basically, if I am going to have a room with 15 machines that produce 80dB each how loud will it be in that room?
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The formula for this would be
10*log10(10^(dB1/10) + 10^(dB2/10) + 10^(dB3/10) etc…)
So in your case having 15 noise sources at 80dB each would come out to about 91.8dB
You can also use this dB calculator to add together noise levels. Of course, this doesn’t take into account the real world factors like the size of the room or distance between machines and where you stand or move.
The sound power density i.e. intensity, which could be measured as watts per squaremeter, is for one machine 10^8 i.e. 100 million times as much as the hearing treshold intensity. That's what 80dB means.
If we assume that the machines are by no means synchronized i.e. the make their noises totally independently of each other, the total intensity is 15 x 10^8 times the hearing treshold. In decibels that's 10x(log(15 x 10^8)) dB = 91.8dB. That's already said in another answer.
If the number of machines is N and everyone of them outputs A dB of non-synchronous noise use the next formula for the total noise level:
Noise level = (A + 10(log(N))) dB
The situation is totally different if the machines run in sync. The theoretical maximum noise level (assuming even the smallest vibrations are in exact sync) is 10x(log(15 x 15 x 10^8)) db = 103.5dB. One can prove it by air pressure calculations. The intensity is proportional to the square of the air pressure fluctuation amplitude.
The general formula for the total noise of N exactly synced A dB noise sources:
Noise level = (A + 20(log(N))) dB
In practice such exact sync is true only if the machines are speakers driven by the same signal, so 91.8dB is the better practical guess. In exact sync case 103.5dB is not present everywhere, it's the peak level in places where the noises are summed with same phase angles. Respectively there are places where the noise level is substantially lower. To prove this needs knowing the interference and standing wave concepts.
BTW hopefully the 80dB for one machine was measured in the same room. If not, the effect of reflection and absorbtion is unknown and the result is unusable.