# How much many dB will a room be?

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?

• I'm not confident giving an answer here but if I did it would involve things like addition and subtraction in multiple waveforms, standing waves, sound absorption, diffusion, and perceived loudness. Too many variables for me! May 8, 2022 at 9:14

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.

• I still get the feeling that as you walked through the room the noise would comb filter in and out like crazy. 90dB of constantly-changing nausea-inducing thrum feels like just the kind of place I don't want to be for more than about 15 seconds ;) May 8, 2022 at 17:13
• So does size of the room, affect this? If I were to have a much smaller room for the same number of machines I feel like it would be much louder than if the machines were spread out in a much larger area.
– Joe
May 17, 2022 at 17:58

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.

• so 10^8 is 80 decibels? So in your formulas where do I put in the number of machines and their decibels?
– Joe
May 16, 2022 at 13:05
• @Joe I inserted general formulas. BTW log is 10-base logarithm, the one which in calculators gives log(10)=1, log(100)=2, log(1000)=3 etc...
– user35252
May 16, 2022 at 13:27
• how would size of room and the spread of the machines affect this?
– Joe
May 17, 2022 at 18:10
• Do you have a place where I can get information on this topic, like some book or online source?
– Joe
May 18, 2022 at 16:08
• Acoustics is a branch of engineering like electronics, designing vessels, motors, houses etc. It's complex because everything which produces, reflects or absorbs sound in the room and also around it must be taken into the account. Search for acoustics engineering books. I mean books, no simple formula makes it. Sorry. For people who design plants and other working environments there surely exist concentrated texts which skip theatres or concert halls. For a start see this: researchgate.net/publication/…
– user35252
May 18, 2022 at 16:41