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

[RomanL]

Apparently, there is a limit to the maximum sound amplitude that depends on the medium in which the sound in question travels. In the atmosphere, the limit is supposedly around 194 Db, arising from the fact that in sound above this level, the pressure throughs would exceed atmospheric pressure and there can be no negative absolute pressure, so the throughs would be cut-off, which means the pressure waves would no longer have sinusoid waveform (I guess it could be argued that they are still sound).

What I am wondering about is if there is a limit on the other end of the scale (if so, it would probably also be medium dependent) and if so, what is it and why is it there? Young children can supposedly hear up to -5 Db or even -10 Db at certain frequencies and some animals can apparently beat even that (my internet searches yielded -10 Db, -15 Db or even close to - 20 Db peak sensitivity for cats), so if there is a lower limit it must lie somewhere below that. One source had some owl hearing sensitivity pegged at between -90 and -100 Db, but I found no other source to corroborate it and other sources yielded owl sensitivities somewhere in the cat range I described above. Unfortunately, I did not manage to find the lowest sound recorded by human-made equipment, so that yielded no clues at all.

I would presume that below some amplitude of vibration, the air molecules no longer reach each other to propagate the sound, so that would provide some sort of lower limit and random effects might drown out any sound before that, but that is just my speculation and I don't know what decibel limits (assuming my speculation is even correct) this would impose in the atmosphere.

Anyway, I have been wondering about this for a while and have finally decided to ask some experts, so I registered here and voila this is my first post. I am hoping somebody here can shed some light on the matter. Thanks!

 

[mfb]

Well, gas consists of individual particles with chaotic motion. Therefore, the noise of these individual particles can be considered as a lower limit for sound - every sound intensity below that will be smaller than the random noise.
In resistors, this can be measured. I am not so sure about air.

 

[Rap]

What I am wondering about is if there is a limit on the other end of the scale (if so, it would probably also be medium dependent) and if so, what is it and why is it there? Young children can supposedly hear up to -5 Db or even -10 Db at certain frequencies and some animals can apparently beat even that (my internet searches yielded -10 Db, -15 Db or even close to - 20 Db peak sensitivity for cats), so if there is a lower limit it must lie somewhere below that. One source had some owl hearing sensitivity pegged at between -90 and -100 Db, but I found no other source to corroborate it and other sources yielded owl sensitivities somewhere in the cat range I described above. Unfortunately, I did not manage to find the lowest sound recorded by human-made equipment, so that yielded no clues at all.

Sound is pressure variations. Pressure of a gas is not a fixed constant number, even when the gas has no sound waves being induced in it. Pressure is a statistical thing, so there is always sound in the air, but its noise. Pressure is from the molecules bouncing around randomly, and they don't always bounce equally in each direction. The amount they bounce around is higher for higher temperatures, so the colder it gets, the less noise there is. So the quietest sound you can have is the sound of the noise. I don't know what that is in decibels at room temperature.

 

[RomanL]

OK, so the random Brownian motion of particles is probably where the lower limit of sound probably lies. Fair enough - does anybody know what that would be converted to decibels and how low did we manage to get as far as measurement goes with our instrumentation?

 

[Rap]

OK, so the random Brownian motion of particles is probably where the lower limit of sound probably lies. Fair enough - does anybody know what that would be converted to decibels and how low did we manage to get as far as measurement goes with our instrumentation?

Well, I don't think it is Brownian motion, its the Maxwell velocity distribution of the gas molecules.

I think you have to constrain the problem a little more by picking a frequency, like $\nu$=262 hz (about middle C) and asking "whats the quietest middle C I can measure?"

Then you have to think about the bandwidth of your microphone. The amount of noise it detects is proportional to the bandwidth. If you had a bandwidth function that was a delta function (zero width), then I guess you could theoretically have zero noise and you could measure any level of middle C. So I guess the question of what is the quietest middle C you can measure boils down to what's the smallest bandwidth microphone I can design? Then you can figure out the noise level, and that would be about the quietest middle C you could measure.

I don't know enough about microphones to know what that smallest bandwidth is.

 

[RomanL]

Well, I don't think it is Brownian motion, its the Maxwell velocity distribution of the gas molecules.

I think you have to constrain the problem a little more by picking a frequency, like $\nu$=262 hz (about middle C) and asking "whats the quietest middle C I can measure?"

Then you have to think about the bandwidth of your microphone. The amount of noise it detects is proportional to the bandwidth. If you had a bandwidth function that was a delta function (zero width), then I guess you could theoretically have zero noise and you could measure any level of middle C. So I guess the question of what is the quietest middle C you can measure boils down to what's the smallest bandwidth microphone I can design? Then you can figure out the noise level, and that would be about the quietest middle C you could measure.

I don't know enough about microphones to know what that smallest bandwidth is.

Hmm, that does make a lot of sense. If you cut out the noise by having a very narrow bandwidth, I guess the noise does not matter as a limit. Well, thanks, that does give me something to ponder.

 

[Bob S]

You can use this online calculator to convert sound dB levels so sound pressure (Pascals) or watts per square meter. For example, 0 dB (SPL) = 0.00002 Pascals, or 1 x 10^-12 watts per square meter.
http://www.sengpielaudio.com/calculator-soundlevel.htm
This anechoic chamber, at -9.4 dB, is deemed the "Quietest place on Earth"
http://www.tcbmag.com/industriestrends/technology/104458p1.aspx
The lowest possible external (to microphone) sound level might be the random motion of air molecules at 300 kelvin.

 

[sophiecentaur]

The notion of 'minimum sound level' should really relate to 'minimum detectable sound level', I think. Once you introduce the idea of detecting the sound then you are into the realms of Signal to Noise Ratio, and that will involve the bandwidth used for the measurement. So, with a sufficiently narrow band filter, the noise power admitted into the detector can be reduced to a level at which an arbitrarily low signal can still be detected (as with radio and other signals).
In the end, what counts is the statistics of spotting a regular (known /wanted) variation in amongst random variations (noise / random thermal motion of the air molecules) and just how long your measurement needs to take before you can say the sound is there or not there.

 

[ImaLooser]

The notion of 'minimum sound level' should really relate to 'minimum detectable sound level', I think. Once you introduce the idea of detecting the sound then you are into the realms of Signal to Noise Ratio, and that will involve the bandwidth used for the measurement. So, with a sufficiently narrow band filter, the noise power admitted into the detector can be reduced to a level at which an arbitrarily low signal can still be detected (as with radio and other signals).
In the end, what counts is the statistics of spotting a regular (known /wanted) variation in amongst random variations (noise / random thermal motion of the air molecules) and just how long your measurement needs to take before you can say the sound is there or not there.

That's right. I have read that if human hearing were any more sensitive we would be able to hear the Brownian motion of the eardrum. But it would still be possible to hear sounds below this level with statistical methods. The quieter the sound, the more data you would need to detect it with some level of confidence. Eventually the interval would become impractical.

The other thing is that cats and owls don't really need to "hear" the sound. They just want to identify a mouse and figure out where it is.

 

[Rap]

The notion of 'minimum sound level' should really relate to 'minimum detectable sound level', I think. Once you introduce the idea of detecting the sound then you are into the realms of Signal to Noise Ratio, and that will involve the bandwidth used for the measurement. So, with a sufficiently narrow band filter, the noise power admitted into the detector can be reduced to a level at which an arbitrarily low signal can still be detected (as with radio and other signals).
In the end, what counts is the statistics of spotting a regular (known /wanted) variation in amongst random variations (noise / random thermal motion of the air molecules) and just how long your measurement needs to take before you can say the sound is there or not there.

Hmm - so suppose I have a microphone, finite bandwidth, so there's noise on it. Can I test whether there is a faint middle C on it by sampling the sound wave in windows of 1/262 second, and keep adding them up? Eventually the signal will overcome the noise. So that means even with signals below the noise amplitude, I can detect them with the right setup?

 

[willem2]

Hmm - so suppose I have a microphone, finite bandwidth, so there's noise on it. Can I test whether there is a faint middle C on it by sampling the sound wave in windows of 1/262 second, and keep adding them up? Eventually the signal will overcome the noise. So that means even with signals below the noise amplitude, I can detect them with the right setup?

It's indeed possible. You need a sampling rate bigger than twice the frequency, and the frequency has to be stable over the entire interval.
If your signal is y(t) and its frequency f, you need to average sin (2 pi f t) * y[t] for a number of frequencies around the signal frequency to check that the signal is present and bigger than the noise at that frequency.

 

[sophiecentaur]

Hmm - so suppose I have a microphone, finite bandwidth, so there's noise on it. Can I test whether there is a faint middle C on it by sampling the sound wave in windows of 1/262 second, and keep adding them up? Eventually the signal will overcome the noise. So that means even with signals below the noise amplitude, I can detect them with the right setup?

Right, in principle but I think your idea of filtering in that 'digital' way would need sprucing up somewhat in this context. If you are after the 'lowest' levels, you need to try very hard. Analogue filtering, initially, can be extremely good value and there is a lot to be said for a simple band pass filter. Also, a high degree of Oversampling helps to spread the quantising noise (the distortion due to digitising). Needless to say, your ADC would need to have as many bits as possible.

It is the noise Power added to your signal in a given bandwidth that counts. It doesn't matter if there is a high 'spike' now and again as long as you can average it out (filtering). You'll still be able to be sure whether your wanted signal is there or not.

 

[RomanL]

This is a really interesting discussion. So it seems, Brownian motion is not really as limiting at the lower end of the sound amplitude scale as I thought it would be... That's unexpected, but certainly exciting.

At the very least, assuming space is quantized, there is a limit on molecule displacement based on Planck's length, which would limit minimum possible sound, but surely there would be limits long before that and certainly there would be detection limits way, way before that. I guess the random motion of molecules isn't one of these limits though...

 

[RomanL]

That's right. I have read that if human hearing were any more sensitive we would be able to hear the Brownian motion of the eardrum. But it would still be possible to hear sounds below this level with statistical methods. The quieter the sound, the more data you would need to detect it with some level of confidence. Eventually the interval would become impractical.

Very interesting - so Brownian motion of the eardrum produces noise somewhere in the vicinity of - 10 dB (supposedly the approximate detectable sound in some young children at the point of peak frequency sensitivity)?

The other thing is that cats and owls don't really need to "hear" the sound. They just want to identify a mouse and figure out where it is.

Hmm, but surely they have to 'hear' the sound to be able to do that. They have to be able to identify the mouse squeak (or sound of their movement, or whatever sound it is they home in on), so they have to 'detect'/'hear' the sound first.

Most sources I have come across on the web pegged cat and owl hearing at about -15 dB to -20 dB at best, though I have seen one source that ascribed peak hearing sensitivity better than -90 dB to the barn owl (but I haven't seen this corroborated by any other source and it seems pretty ridiculous - think about it: a sensitivity to sound pressures 100 million times smaller than those detectable by young children or about 1 billion times smaller than those detectable by adult humans... yeah, I highly doubt the credibility of that).

 

[sophiecentaur]

I would think that insect antennae can pick up sound vibrations that are much quieter than what a cat or owl can pick up.

I have to reiterate the point about the Bandwidth of the detector that's involved. If an insect happens to be interested in only a narrow range of frequencies then it can detect them at a lower level than humans because it will be using a narrow band receiver.
If Owls don't need to 'hear' music, speech and mains hum then they can also have more frequency selective hearing - which makes their hearing more sensitive in a narrow band.
The comments about brownian motion are, in effect, about random noise additions to the signal. Hearing is just another example of a communications / measurement channel and the same concepts apply.

 

[Bob S]

I have to reiterate the point about the Bandwidth of the detector that's involved. If an insect happens to be interested in only a narrow range of frequencies then it can detect them at a lower level than humans because it will be using a narrow band receiver.

Insect hearing is more complex than just hearing a sound. Insects use directional hearing to find mates (crickets) or find suitable places to plant eggs (flies in crickets). Furthermore, the auditory signals are neuron pulses (spikes) of relatively constant amplitude and limited spike rate, so the amplitude disparity (from a directionally-sensitive ear) over a narrow frequency band is converted to a phase disparity (or timing disparity) using physiological features.
Using http://www.sengpielaudio.com/calculator-soundlevel.htm to convert 0 dB(SPL) to power, we get 1 x 10^-12 watts per square meter, or 1 x 10^-15 milliwatts per square mm. The quietest sound possible in the aneochic chamber is ≈ -10 dB(SPL), so the ear does not need to be any better than ≈ 1 x 10^-16 milliwatts per square mm for a 1 mm² ear.
The thermal noise limit in electrical circuits (and perhaps also biological circuits) is kTB= 4 x 10^-15 milliwatts per kHz (= -144 dBm/kHz*). So how good does the ear need to be (in milliwatts per kHz) before it reaches the thermal noise limit?

* 0 dBm is 1 milliwatt. A good microwave receiver is ≈ kTB + 3 dB = -111 dBm/MHz.

 

[sophiecentaur]

Bob S

Insect hearing is more complex than just hearing a sound

That is severly understating what we do when we "hear sound". It's just another form of signal processing. An insect would have great difficulty in interpreting sound that we find perfectly informative in one way or another. Afaik, our stereo perception relies on phase and timing information to some extent and not just on relative L-R amplitude ratio although we can make sense of simple 'pan-pot' image placing.

The quietest sound possible in the aneochic chamber is ≈ -10 dB(SPL)

Are you saying that thermal motion of the air molecules at room temperature produces this level? It seems rather a high value, to me. Or are you referring to hearing threshold?

 

[Bob S]

From Bob S: Insect hearing is more complex than just hearing a sound.

That is severly understating what we do when we "hear sound". It's just another form of signal processing. An insect would have great difficulty in interpreting sound that we find perfectly informative in one way or another. Afaik, our stereo perception relies on phase and timing information to some extent and not just on relative L-R amplitude ratio although we can make sense of simple 'pan-pot' image placing.

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.

From Bob S: The quietest sound possible in the aneochic chamber is ≈ -10 dB(SPL)

Are you saying that thermal motion of the air molecules at room temperature produces this level? It seems rather a high value, to me. Or are you referring to hearing threshold?

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]

Hmm - so suppose I have a microphone, finite bandwidth, so there's noise on it. Can I test whether there is a faint middle C on it by sampling the sound wave in windows of 1/262 second, and keep adding them up? Eventually the signal will overcome the noise. So that means even with signals below the noise amplitude, I can detect them with the right setup?

For anyone who wants to play with numbers, I did a little calculation and came up with the standard deviation of pressure ($\delta P$) is (I think) given by $$\delta P=\frac{1}{\sqrt{A \Delta t}}\left(\frac{2\pi m P^3}{n}\right)^{1/4}$$ where A is the area of the microphone or barometer diaphragm, $\Delta t$ 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 $P=nkT$.

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]

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?

From http://en.wikibooks.org/wiki/Sensor...d_speech/Outer_&_middle_ear/tympanic_membrane, using A=(0.009 meter)^2 for the area of a human eardrum, $\Delta t$=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 $\delta P$ = 2.97e-5 Pascal for the effective standard deviation of pressure on the human eardrum.

At http://www.engineeringtoolbox.com/sound-intensity-d_712.html I found that the lowest intensity sound wave a human can hear is I=10e-12 watts per meter^2 and $I=P^2/\rho c$ where $\rho$ is density and c is the speed of sound, so Pmin=$\sqrt{I \rho c}$. Using $\rho=nm$ 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 $\delta P$ 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/detalhe_artigo.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!