The Quietest Sound Possible & The Quietest Sound Ever Recorded/Measured

Bob S

Mamallian hearing is very complex. I was referring to insect hearing. Insects use binaural directional hearing to find mates or prey. Because of the minimal number of auditory axons and spiking nerve pulses, they cannot encode amplitudes sufficiently well. So they developed physiological features to convert amplitude disparity to a phase disparity. Human hearing is much more complex.
See the website for the aneochic chamber. This anechoic chamber, at -9.4 dB, is deemed the "Quietest place on Earth"
http://www.tcbmag.com/industriestren.../104458p1.aspx
Why should the hearing threshold be much lower than this? What is the hearing threshold? In fact, should (or could) hearing be much better than the kTB limit (4 x 10^-15 milliwatts per kHz). Do biological neurological (vision, auditory) systems have a lower limit than kTB?

Rap

For anyone who wants to play with numbers, I did a little calculation and came up with the standard deviation of pressure ([itex]\delta P[/itex]) is (I think) given by [tex]\delta P=\frac{1}{\sqrt{A \Delta t}}\left(\frac{2\pi m P^3}{n}\right)^{1/4}[/tex] where A is the area of the microphone or barometer diaphragm, [itex]\Delta t[/itex] is the averaging time, P is pressure, m is the mass of an "air molecule", and n is the number density of those molecules. It depends on temperature through [itex]P=nkT[/itex].

I think you could play around with this by supposing the microphone diaphragm has a mass and its connected to a spring with some spring constant and decay constant, a decaying harmonic oscillator. That would give you a bandwidth, averaging time, and you could calculate the position of the diaphragm and the noise effects and figure out what is the quietest sound it could sense.

sophiecentaur

I reckon that the anechoic chamber figure is no more than a measured value. As it's 10dB lower than the 'threshold' figure for good hearing then it's got to be 'good enough' for most purposes. But would it really be as low as the sound level if you put that chamber in a in a deep mine, for instance (no water drips, of course)?

@Rap.
I wonder how you could modify your formula for a perfectly matched transducer (which is how I would approach the problem if it were Radio Engineering) with a frequency response like that of the Ear. The formula doesn't seem to have a higher frequency limit, but I guess your following 'mechanical' description introduces it. Wouldn't it be easier to insert the human 20kHz upper limit and a 20Hz lower limit (both arbitrary but near enough)? I'm not sure how to make this step, though. Can you do it?

Rap

From http://en.wikibooks.org/wiki/Sensory...panic_membrane, using A=(0.009 meter)^2 for the area of a human eardrum, [itex]\Delta t[/itex]=1/20000 second for the averaging time, m=28.8 AMU for the mass of an "air molecule" with AMU=-1.66e-27 kilograms, P=101325 Pascal = 101325 kg/meter/sec^2 and n=P/kT with T=300 K, I get [itex]\delta P[/itex] = 2.97e-5 Pascal for the effective standard deviation of pressure on the human eardrum.

At http://www.engineeringtoolbox.com/so...ity-d_712.html I found that the lowest intensity sound wave a human can hear is I=10e-12 watts per meter^2 and [itex]I=P^2/\rho c[/itex] where [itex]\rho[/itex] is density and c is the speed of sound, so Pmin=[itex]\sqrt{I \rho c}[/itex]. Using [itex]\rho=nm[/itex] and c=331 meter/sec^2, I get Pmin=1.9e-5 Pascal.

Hmm. Pretty close. It makes me suspect I didn't make any huge errors in the derivation. If this is valid, it means the lowest intensity sound wave the human ear can hear is just about at the level of the Brownian motion of the eardrum due to random pressure fluctuations. Which makes evolutionary sense.

I'm not sure how to translate this into your terms involving bandwidth, but I think its assuming a bandwidth from 0 hz out to 20,000 hz. I don't know right now how to introduce the 20 hz lower limit, but that would reduce the [itex]\delta P[/itex] and maybe make the numbers match even better.

I also stumbled across an interesting quote concerning tinnitus (ringing in the ear) at http://www.tinnitusjournal.com/detal...igo.asp?id=328 - "As the overlying gelatinous tectorial membrane becomes decoupled from the hair cell, the Brownian Motion of the air particles in front of the tympanic membrane is detected. "

sophiecentaur

Well done there on the calculation. It convinces me even if only on the grounds that there would be no point in human sound detection going below the noise level and evolution never does more than it absolutely has to!
There is just the small matter of the sound weighting curve that should really be applied when determining the audibility of a sound and this relates also to noise. This relates to actual Signal to Noise ratio when comparing audibility of coherent sounds and noise level. Perhaps this is all asking too much and I should be well satisfied with the news that we hear about as well as we would ever need to.
Pardon? My left hand battery is going flat wheeeeeeeeeee! But life is so much more mellow with the buggers turned off.

RomanL

Wow, this was an amazing discussion guys - thanks a lot! I have learned that it is much more complicated and much more exciting than I initially assumed. So there is a thermal limit that is similar to the human threshold of hearing (cca. 0 to -10 dB), but narrow band receivers could do much better than that - apparently up to a theoretical limit of about -144 dB. That's awesome!