Decibel level addition of multiple noise sources If I have four computer fans of which each is said to run at 46 dB, and they run close to each other, how loud is the whole system?
I somehow recall from my physics course that 10 decibel more means twice the noise, is that right?
So would it be 66 dB for four such fans then?
 A: 10 decibels means ten times the power density of sound.  That is chosen so that ten decibels equals one bel, and a one bel increase simply adds a zero on the end of the sound power density.  Twenty decibels multiplies by 10 twice, so twenty decibels is an overall 100-fold increase in the sound.  
That means one decibel multiplies the sound by the smaller amount $10^{.1} = 1.259$.  
For example, a two decibel increase multiplies the sound by $1.259^2 = 1.585$.  If you keep going up to ten decibels, we recover $1.259^{10} = 10$.
With four fans, the power they put into sound is four times as much.  If you work it out, you'll find that six decibels gives a noise energy increase of $1.259^6 = 3.98$.  Four fans put out a sound 6 decibels higher than one fan, so you're left with 46+6 = 52 decibels.
If you want to calculate it for an arbitrary number of fans $n$, you would need to solve
$$1.259^x = n$$
or, leaving it in terms of a power of ten,
$$(10^{.1})^x = 10^{.1x} = n$$
This is solved by a logarithm.
$$.1x = \log_{10}n$$
$$x = 10 \log_{10}n$$
For example, if you had 1000 fans, you'd have $n=1000$.  The logarithm base ten of 1000 is 3, so your sound level would be 30 decibels greater for 1000 fans than for one fan.
A: First, dB means nothing by itself. You need to give a reference level, like dBW or dB SPL.  We'll assume dB SPL.
Second, noise measurements from a point source like this require a distance measurement to be meaningful, since the level drops off with distance.  We'll assume you're measuring at the same distance in both cases, and the fans are equidistant from the SPL meter.
Fans have some noise that is correlated between them (hum), and some that is uncorrelated (whoosh).  The two types of noise combine differently.  Without knowing what the noise is, it's impossible to know.


*

*If all the fans are producing the same exact tone, in phase, and no white noise, they will sum like any other signal. I believe the answer is 58 dB, using the formula below.

*If two fans are producing tones with exact opposite polarity of the other two fans, the noise will completely cancel out, and produce a total of -∞ dB.  :)

*If all the fans are producing uncorrelated white noise, the total will be 52 dB

*

*http://www.sengpielaudio.com/calculator-leveladding.htm   

*https://en.wikipedia.org/wiki/Sound_pressure#Multiple_sources
I think the sums would be:


*

*correlated: $10 \log_{10}\left(\frac{{(4  p_{\mathrm{{rms}}}})^2}{{p_{\mathrm{ref}}}^2}\right)\mbox{ dB}$

*uncorrelated: $10 \log_{10}\left(4\frac{{p_{\mathrm{{rms}}}}^2}{{p_{\mathrm{ref}}}^2}\right)\mbox{ dB}$ 

