# How does the Brownian motion of air molecules compare to the threshold of human hearing as a function of frequency?

This fantastic question essentially asks what is the noise floor of air? Both the answer given on that thread and the value stated by Microsoft are around -23 or -24 dBSPL.

However, overall loudness is only one metric. What does the amplitude of the noise in dBSPL look like when graphed out as a function of frequency in the audible range? How does the shape and level of the curve defined by that graph compare to the threshold of human hearing as described by the equal loudness contour?

• The first post you linked to begins to address your question in the "Update" section at the end of the answer by user endolith. It gives the equation for (and an example graph of) theoretical spectral power, which also depends on temperature, pressure, density etc. From there, you should be able to use an equal-loudness contour set as described in your link to correct this to what the perceived-loudness would be for the observer the equal-loudness contour set applies to. Commented Jul 1, 2020 at 19:58

My understanding is that we are talking here about the molecules tapping on the eardrum, i.e. the shot noise - similar to the noise of the rain drops. It is a white noise, i.e. its spectrum has the same amplitude at all frequencies.

On a deeper level however there are at least two characteristic timescales that would limit the width of the spectrum:

• the collision time between the molecule and the wall
• the intermolecular scattering time, which characterizes the density fluctuations of the air

it is also important to note that the air consists of several types of molecules (nitrogen, oxygen, carbon dioxide and some others), each of which is characterized by its own scattering times.

• The answer by user endolith to first post that the asker links to has a section on this in the "Update" section at the end; there, it points to two references that give a theoretical spectral power curve apparently more akin to violet noise. Commented Jul 1, 2020 at 20:00

It depends.

1. The threshold of human hearing is adaptive and varies depending on the preceding noise level (for a couple of hours). After a shift in an anechoic chamber, engineers start hearing how their own blood goes through veins, food being digested, etc. The threshold can not be assigned a "fixed" value. The "usual" -94dBPa was suggested as a median value in a certain experiment with a few dozen of people, tones, and headphones. Now, such an experiment would be deemed unscientific.

2. People are very different. There can not be a common "threshold" because it means nothing. My hearing at ~25yo was 20dB better than "normal", and I know people who are even better than me. Some blind people show absolute wonders when it comes to their abilities to "see" with their ears.

3. The methodic used in the MS chamber: The best existing mic, by B&K, is -2dBA. Thus, to obtain a lower figure of room noise, they compared the noise of a mic in total silence (inside a very heavy box) with the noise of the same mic in the room. Then they assume that the noise in the room is sqrt(self_nse^2+room_nse^2). Self mic noise is mostly the thermal noise of preamp (the diaphragm noise is high-freq and low), so the robustness of the methodic is not unquestionable.

I would find the Hollywood assumption that you hold your breath, then no living creature can hear you, quite ... inspiring.