Yes, it's the cooling down. This happens mostly with CRT monitors (I've own a lot) and could still happen with LCD monitors (rarely, mostly occurs in cold temperature). Electronic components wouldn't be the source at all.
Capacitors don't make a noise when it discharges gradually which is assumed. If it does then the world would be a bad place to live (too much dB).
Things I can say to be NOT the source of sound are:
electrical components: The only electrical components that makes a noise are speakers and relays. Both are eliminated as a source since a speaker probably don't exist in a typical CRT and, though a relay may, a relay only makes a single tick sound - a quiet one.
static: it can't be static, a crack and static sound barely have similarities.
To be concise, the sound is simply the case. That's why this seems to happen more often in colder weather is because when the monitor is turned on it heats up (especially CRTs) expanding the case a bit, and during cool down, the manufactured plastic will start to change shape in edges causing the sound, and in colder environments this will tend to be more pronounced because the collapse in a greater magnitude is like to occur more.
Apparently the search term I was missing was "Brownian motion". With that, I found several leads. They contradict each other somewhat, but I can at least post a partial answer:
Geisler - Sound to Synapse: Physiology of the Mammalian Ear:
Estimates for the first of these sources, the pressure fluctuations due to the Brownian motion of air molecules impinging on the eardrum, are about 2 µPa (−20 dB SPL), when the frequency bandwidth relevant for the detection of a 3 kHz tone is included (Harris. 1968). Calculations using this number suggest that the behavioral thresholds of humans for 3 kHz tones are not limited by this Brownian motion, but that those for the most sensitive of cats may approach it (Green. 1976)
Dallos - The Auditory Periphery Biophysics and Physiology:
By assuming a 1000-Hz bandwidth, Harris computed that the Brownian motion of air molecules generates a mean pressure fluctuation of 1.27×10−5 dyne/cm2 [−24 dB SPL]. The usually accepted value of sound pressure corresponding to free-field listening threshold is 18 dB above the pressure level of thermal fluctuations. Thus one can immediately see that Brownian motion of air molecules is certainly not the limiting factor of our hearing sensitivity.
There's another available with more details:
Harris - Brownian motion and the threshold of hearing:
We can avoid the calculation of the Brownian noise at the eardrum by using the Brownian noise in a free field and comparing that with the minimum audible field (MAF) instead of the minimal audible pressure (MAP).
If we use frequency limits of 2500 Hz and 3500 Hz. we obtain a root mean square (rms) pressure fluctuation of 98 db below 1 dyne/cm2 [−24 dB SPL]. The MAF2 is about 80 db below 1 dyne/cm2 at 3000 Hz. This is 18 db above the estimate of Brownian noise. It seems clear from this calculation that Brownian noise in the air is not a limiting factor to the threshold of hearing.
2.5 kHz to 3.5 kHz is not the total bandwidth that would be picked up by a microphone, though.
Yost & Killian - Hearing Thresholds:
By making some assumptions about the acoustic energy present in the Brownian motion of air molecules, it can be shown that a sound presented at 0 dB SPL is only 20-30 dB more intense than that being produced by Brownian motion
So −20 to −30 dB SPL.
Howard & Angus - Acoustics and Psychoacoustics:
At 4kHz, which is about the frequency of the sensitivity peak, the pressure amplitude variations caused by the Brownian motion of air molecules, at room temperature and over a critical bandwidth, correspond to a sound pressure level of about −23 dB. Thus the human hearing system is close to the theoretical physical limits of sensitivity. In other words there would be little point in being much more sensitive to sound, as all we would hear would be a ”hiss” due to the thermal agitation of the air!
I would still like to know:
- How this is derived
- What the spectrum is, and if it's different from the violet spectrum in water, why?
- What the 20 Hz-to-20 kHz and A-weighted values are
Update
I believe I've found an answer in these two papers, though both have errors that make it difficult to be sure:
- Harris, G. G. Brownian motion in the cochlear partition. J Acoust. Soc. Am. 44: 176-186, 1968
- L. J. Sivian and S. D. White, On minimum audible sound fields. Journal of the Acoustical Society of America, 1933, 4, 288-321
Harris's equation 1 is taken from Sivian-White, but seems erroneous. The original is dimensionally consistent, at least:
$$\overline P = \left [ \int^{f_2}_{f_1}{P_f}^2\cdot df \right ]^{1/2} = \left [ \frac{8 \pi \rho k T} {3c} ({f_2}^3-{f_1}^3)\right ]^{1/2}$$
where $\overline P$ is RMS pressure, $\rho$ is density of air, $k$ is Boltzmann's constant, $T$ is temperature, $c$ is speed of sound, and $f_1$ and $f_2$ are the bandwidth limits.
Sivian-White then calculate $5\times 10^{-5}$ bars for 1000–6000 Hz, which... also seems erroneous. That's equal to 5 Pa, or 108 dB SPL? If I calculate over the same range, I get 5.3×10−11 bars = 5.3 µPa = −11.6 dB SPL, which seems more reasonable.
Now Harris says:
Also, a more accurate estimate of the Brownian noise would take into account the properties of a semi-rigid eardrum in an ear canal and not treat the tympanic membrane as an infinite reflecting wall. We can avoid this type of calculation by using the Brownian noise in a free field and comparing that with the minimum audible field (MAF) instead of the minimum audible pressure (MAP). The free-field Brownian motion is 3 dB less than that given by Eq. 1 owing to the fact that the waves traveling in opposite directions are not correlated in a free field, but are at a reflecting wall
When I use Sivian's equation and Harris' −3 dB with Harris' frequency band of 2500–3500 Hz, I get Harris' answer of 1.273×10−5 dyne/cm2 (= 1.27 μPa = −24 dB SPL) so it seems like I'm doing it right.
But they're interested only in whether the self-noise of air is close to the threshold of hearing in the most sensitive band. Calculating total SPL, in the same way but over 20 Hz to 20 kHz, I get 21.8 μPa, very close to 0 dB SPL. Coincidence?
This equation also lets us calculate the spectral density, which seems to be violet noise, increasing by 6 dB every octave, same as the underwater reference in the question:
Best Answer
I assume you're talking about "coolers" as in CPU-coolers or other cooling systems in computers. The noise-spectrum from such a fan is not white strictly speaking, you can see it measured on this page. The spectrum is fairly level if you look at small parts though and ignore the tonal components.
Anyway, by your definition, two uncorrelated white noise sources add without interference. The "peaks and troughs" (sound pressures) don't add up coherently (in ideal sources of course :), but they don't cancel each other perfectly either. Therefore the sound power is doubled. By definition the RMS-amplitude (proportional to the sound pressure) is then multiplied by $\sqrt 2$. The sound intensity is proportional to the sound power and hence is doubled as well.
I actually simulated this in Matlab, because the terminology with sound power, sound energy, sound levels, sound pressures etc is daunting, misleading and confusing.. I'm specifically avoiding talking about decibels.
So yes you do get a doubling of power when adding uncorrelated white-noise sources.. and when perfectly adding a single source, you quadruple the power. By definition the RMS amplitude is the root of the above.