If your statement was correct, humans would not be able to hear white noise, whereas obviously (to any hearing person who has ever been exposed to white noise) we can.
White noise requires that we hear a number of frequencies, but also requires that the frequencies are of sufficient amplitude to move the ear drum.
But that is just the TLDR. I am trying to keep this simple, but it is not simple, so here is the next level of complexity.
The issue is not only frequency, but also amplitude and duration.
Since Brownian motion is not sufficient to significantly affect the ear drums (in any real life situation), instead of worrying about the air, you need to be worrying about the liquid in the inner ear.
This liquid is in a precisely shaped reservoir (the cochlea) that will amplify certain sound waves at certain points (it is more complicated than this, but this is a generally accurate simplification); hair cells at each point respond (fire) in response to the amplified waves. Brownian motion cannot and will not set up a standing wave at any frequency for a time period or with an intensity that you would be able to perceive.
It may be helpful to picture the difference in intensity produced by a particle of water versus a wave; one you will not feel (it cannot push you or the hair cell with enough force to be detected), but the other certainly can. We are talking a difference of multiple orders of magnitude.
I'm not certain that I understand your argument, so I may have responded incorrectly. Let me know if you need any clarification.
Edit: removed a redundant sentence.
I'm not certain that I understand your argument, so I may have responded incorrectly. Let me know if you need any clarification.
On re-reading, I actually misunderstood your original point and my argument has nothing to do with your original point.
I would still want to point out a few things that may make what is going on clearer.
First, Brownian motion amplitude rises as temperature rises. So while the Brownian motion of temperatures typically found in the ear, or in the air near the ear, is small enough that the ear can't detect it, as you say, if ...
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