Why can I hear noise (white noise / pink noise / brown noise), but not hear temperatures?
EDIT FOR CLARIFICATION Air temperature is caused by air molecules moving randomly at high speed, white noise is caused by air molecules moving randomly at high speed, what’s the difference? Why does white noise fill the room with sound instead of just raising the temperature slightly?
My hand-wavy-sounds-like-science-technobable guess is that temperature does fill the air with sound, but most of the energy of that sound is at far too high frequencies for my eardrums to detect (in part because my eardrums are emitting noise at a those frequencies). Maybe the average wavelength of thermal noise is roughly the mean free path length of the air molecules, so the average frequency of the noise is roughly 5 GHz. But I just making stuff up and really don’t know.
You can’t hear temperatures because if the temperatures of air were high enough to make enough noise for you to hear, you would be incinerated.
http://physics.stackexchange.com/questions/110540/how-loud-is-the-thermal-motion-of-air-molecules goes over this. There is a lot of error in that thread, but the parts that are right show up a few times and calculate the white noise sound level of room temperature air at about −20 dB SPL. SPL of 0 dB is the approximate threshold of human hearing. dB is a logarithmic scale such that every 10 dB increase is a 10X higher power. So −20 dB SPL is about 1/100 the average sound power level that would just barely be audible by a human. This is calculated at something close to room temperature, about 23 C which is about 300 K.
How hot would air have to get to have its thermal fluctuations audible as sound to humans? Any thermal power (at sufficiently low frequencies which situation applies here) is proportional to the temperature. So to increase the thermal sound level from −20 dB to 0 dB, the sound power needs to be increased by a factor of 100. So this would happen at an absolute air temperature of 30000 K, or about 29700 C. For us Americans, that is 53500 F. Super crazy hot, hotter than the sun.
So wait a minute, am I saying that a white noise generator generating 0 dB (barely audible) white noise is heating the air to super-solar temperatures? That doesn’t pass the smell test: if it was true my ears would be burning off when exposed to any white noise loud enough for them to hear. But the answer is, we are only generating white noise over a very small frequency range in order to hear it. Even a high fidelity white noise generator will have a bandwidth covering about 50 Hz to 20,000 Hz. But the “natural” bandwidth of thermal fluctuations is found from quantum mechanical considerations: BW = T * kb/h or bandwidth is Temperature(in Kelvin) times Boltzmann’s constant divided by Planck’s constant. That ratio kb/h turns out to be about 20 GHz per degree K. So thermal noise loud enough to hear would have a bandwidth of 600,000 GHz or 6e14 Hz. TO an approximation, thermal power is proportional to bandwidth, so a 20 kHz white noise generator putting out 0 dB SPL is putting out only 20000⁄600000000000 = 1⁄30000000000 the power level associated with a 30000 K source. So in terms of TOTAL energy, a band-limited white noise source is delivering way less than 1 K of extra temperature to your ears, even though in terms of energy density (power per bandwidth), it sounds hotter than the sun.
Much of the thread below covers some of this, but perhaps I add a little detail with what I write. As to blackbody radiation, yes that is appropriate to use here and its upper frequency limit has nothing to do with electromagnetics, or not fundamentally. It is a quantum mechanical limit. At a high enough frequency, the quantum of energy becomes comparable to the thermal energy, and so at higher frequencies than that those frequencies can’t be effectively generated by thermal sources. This is true for both photons (electromagnetic energy quantized) and phonons (sound or vibration energy quantized).
Hope this is clear enough to add more light than heat to the discussion. Or in this case, more sound than heat :)
The peak frequency of thermal noise at room temperature is far higher than 5 GHz, it’s actually closer to 30 THz. I’m not exactly sure about the biology here and whether Brownian motion of air molecules excites the hair cells in your cochlea. I’m guessing that it does, but even so, the range of frequencies you can hear (20-20,000 Hz) carries only a very, very tiny fraction of the thermal energy. Someone should do the calculations; my guess is that it’s far below the detection threshold.
Another thing to keep in mind is that at equilibrium, you have thermal excitation everywhere. You might as well ask why you don’t hear or see or smell the thermal excitation in your own brain.
whether Brownian motion of air molecules excites the hair cells in your cochlea
As far as I remember, you need to hit the resonant frequency of a particular hair to trigger a “sound” response, so frequencies higher than 20KHz might excite them, but if you’re not getting resonance, nothing triggers.
As far as I remember, you need to hit the resonant frequency of a particular hair to trigger a “sound” response, so frequencies higher than 20KHz might excite them, but if you’re not getting resonance, nothing triggers.
No this is wrong. Each hair is excited by the amount of its particular resonant frequeny in the sound hitting it. If a violin note is heard, that note only has a few discrete frequencies in it and so a few hairs are very excited about it and the brain (of the trained violinist with perfect pitch anyway) goes “oh, A 440.” If white noise loud enough to hear is hitting the ear, then essentially all the hairs are excited because all frequencies are present in white noise, and the brain goes “sounds like the ocean.”
As to excitement by sound above 20 kHz, a very high frequency ultrasound, say at 100 kHz, can be modulated with the vibrations associated with a violin string, much as sound can be modulated on radio carriers. Such ultrasound hitting a human ear can actually cause the appropriate hairs to be excited so that the brain goes “oh, A 440.” The phenomenon relies on the non-linear response of cochlear hairs and highly directional speakers based on this effect have been built and demonstrated. See for example http://www.holosonics.com/
Lower q factor means a higher spread of frequencies can trigger them. Mammalian hair cells have q factors of 5-10. Q=10 is pretty high for a biological resonator, but pretty low compared to, say, even crude electronic equipment. A typical LC oscillator has Q of 100 or more.
Another thing to keep in mind is that at equilibrium, you have thermal excitation everywhere. You might as well ask why you don’t hear or see or smell the thermal excitation in your own brain.
I think you are suggesting something like: if I was detecting thermal vibration by the vibration of a membrane due to thermally induced air pressure I wouldn’t because the temperature is the same in the air on both sides of the membrane and therefore the thermal air pressure on each side of the membrane is the same and so fails to move the membrane. If this is what you are suggesting it is wrong, and in a basic enough way to merit explanation.
Sound is pressure changing in time. Thermal vibration follows a random distribution. The air on each side of a membrane at the same temperature will have the same statistics of pressure change on each side of the membrane, but not the same instantaneous pressure on each side of the membrane. If the random pressure exceeds p1 25% of the time an is less than p0 25% of the time, then 6.25% of the time there will be a pressure difference of at least p1 - p0 on the membrane, and a different 6.25% of the time there will be an opposite sign pressure difference of at most p0 - p1 where we have chosen p1 to be the higher pressure than p0. So thermal vibrations will absolutely cause a membrane to vibrate randomly. Further, it is the case that the magnitudes of p1 and p0 rise as temperature rises as temperature rises, so we expect the membrane to be moved more when surrounded by hotter air than it does when surrounded by cooler air.
SO it is the case that generally heating air makes its average pressure rise if it is in a constrained volume, and a membrane will certainly not be displaced on average if it has air on each side at the same average pressure, but it is the temporal or time variations that produce sound, and the time variations on each side of the membrane for most conditions you can create in the lab are uncorrelated, and so the membrane vibrates randomly and with an amplitude that rises as the temperature of the air rises.
I don’t make that suggestion at all. I’m pointing out that sound receptors are just neurons, and if the thermal vibrations in your ear can excite some set of neurons than the thermal vibrations impinging on the dendrites of any neuron in your body—including inside your brain—should also elicit a response.
That is a little like suggesting that a sound recorder is just electronics and shouting at any electronics should elicit a response. Bringing it back to the neurons,
loud enough sound on any neuron will probably excite it
However the sensitivity of neurons connected in the ear to sound is thousands or millions or billions (not bothering to calculate it) higher than the sensitivity of a random neuron in the brain to sound
A random neuron responding to sound won’t feel like sound. If a pain neuron is activated by sound, it will appear as pain, if a hot neuron activated by sound will appear as heat, etc.
So as hot as the air has to be to excite your cochlear apparatus, and thus the neurons connected to it, it probably has to be thousands or millions times hotter to excite the neurons directly in your brain. And long before it gets to that temperature your brains has been cooked, then dessicated, then burned, and finally decomposed into a plasma of atoms and electrons flying about separately, and probably at the temperatures we are talking about, the protons and neutrons are smashed apart into a cloud of subatomic particles.
Brownian motion of air molecules excites the hair cells in your cochlea
Your cochlea is filled with a liquid called endolymph, not air.
A hair cell that was triggered by Brownian motion would be useless. All inner hair cells are tuned to certain vibrations in the endolymph that are greater than those caused by Brownian motion.
A hair cell that was triggered by Brownian motion would be useless. All inner hair cells are tuned to certain vibrations in the endolymph that are greater than those caused by Brownian motion.
Brownian motion is motion of air that, considered as vibrations, has a broad range of frequencies in it. Which means that an ear exposed to air experiencing a sufficiently high level of brownian motion will have many or all of its inner hair cells excited. 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.
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.
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 you were to raise the temperature, the Brownian motion would be higher amplitude and would eventually rise to a point where it was detectable. This is a pretty academic point: the temperatures required to hear the brownian motion would harm the ear so in practical terms your statements are right enough.
If vibrations in the air cause the endolymph to have pressure waves in it which then cause cochlear hairs to move, it is still quite reasonable to describe that as air vibrations making cochlear hairs move. Introducing the endolymph is a clarification at best, not a correction.
Oh! So you’re saying the spectrum of the acoustic noise at a given temperature will be the spectrum of black body radiation! Yes, I could definitely believe that. That is high-frequency indeed.
Sort of. Blackbody radiation is electromagnetic in nature, however under some ideal assumptions you can assume that the molecules emitting that radiation are also vibrating at roughly the same spectrum. ‘vibrating’, though, can mean a lot of different things; this is related to the microscopic properties of the substance and its degrees of freedom. In an ideal gas, it’s taken to mean the particle collision frequency spread (but not necessarily the frequency of particle collisions). If you consider heat to be composed of a disordered collection of phonons, then you could definitely say that this is ‘sound’, but it’s probably neater to draw a distinction between thermal phonons (high-entropy, low free energy) and acoustic phonons.
The reasoning behind blackbody electromagnetic radiation applies equally well to thermal vibrations in solids and gases. Meaning the spectral limits derived from a quantum consideration of the quantization of electromagnetic radiation (into photons) applies equally well to the quantum considerations of vibrational radiation (into phonons).
“Thermal” photons are indistinguishable individually from photons from other sources. The thing that makes a thing thermal is the distribution and prevalence of photons in time and frequency, those from a thermal source follow a well understood set of statistics, while photons from other sources clearly deviate from that. So a photon arising from a cell phone tower’s radio transmitter reacts similarly with a cell phone’s radio receiver as a photon at a similar frequency arising from thermal emission from the air. Physics can’t distinguish between these two photons which is why it is a major effort in building radio communications to get enough signal-sourced photons compared to the thermal-sourced photons so that the signal-sourced photons dominate, and therefore the signal can be accurately derived from their detection.
Similarly with phonons. Vibrations because something is hot are indistinguishable from vibrations from a vocal cord. It is the statistical distribution of the vibrations in time and frequency that defines a thermal set of vibrations. And again, to hear what someone is saying, it is important to get enough phonons from their vocal cords into your ears compared to the phonons from other sources in order to accurately enough derive the intended information.
Thermal noise or other white noise, and a symphony, have the same kind of phonons and both can be heard by the same kinds of ears. They carry different kinds of information (they sound different) because of their different time and frequency statistics.
Black-body radiation is electromagnetic radiation, so I’m a bit confused how that’s connected with acoustic noise. As to molecule collisions, I’m not sure vibrations at sufficiently high frequency can be called “acoustic” at all.
As to molecule collisions, I’m not sure vibrations at sufficiently high frequency can be called “acoustic” at all.
Your reasoning here carries useful information. For example, when you are dealing with vibrations whose frequency is so high that the wavelength of the vibration is less than the average spacing between molecules in a gas, or in a solid lattice, then a lot of what you calculate about the detection and interactions with lower frequency vibrations no longer applies.
However, the same limitations apply to electromagnetic radiation. For example we think of vacuum or empty space as transparent to EM radiation, and it is as long as the EM frequency is low enough frequency. But high enough frequency EM radiation, empty space is opaque to it! For example, at high enough frequencies, a single photon has enough energy to create a positron-electron pair in free space. Photons at that frequency don’t travel very far before they are destroyed by such a spontaneous generation of particles.
So in principle, EM radiation and acoustic vibrations are the same in this respect: as long as you are considering frequencies “low enough” that they don’t rip apart the medium in which the wave exists, they behave in the ways we usually think of for sound and light. But above those frequencies, they rip apart the media they are traveling through, even if that medium is so-called empty space.
For example, at high enough frequencies, a single photon has enough energy to create a positron-electron pair in free space. Photons at that frequency don’t travel very far before they are destroyed by such a spontaneous generation of particles.
So what kind of energies are we talking about here, and what distances?
Photons with over 1 Million electron volts of energy can create a positron-electron pair, but only when near another massive particle (like the nucleus of an atom). The other massive particle is moved in the interaction but is otherwise not-necessarily changed. https://en.wikipedia.org/wiki/Pair_production. This process has been demonstrated experimentally. The mean free path of the energetic photon near an atomic nucleus is something down on the atomic scale, the experiment I read about used a piece of gold foil and generated lots of positron-electron pairs.
A single photon in otherwise empty space cannot create a pair of particles I was wrong when stating that. However, space with nothing but two photons in it can create matter. Two photons each with a bit over 511 million electron volts of energy can collide and result in the creation of a positron and an electron. https://en.wikipedia.org/wiki/Two-photon_physics Alternatively a single 80 Tera Electron Volt photon can collide with a very low energy photon to create an electron-positron pair. This effect actually makes our existing universe opaque to photons above 80 TeV because our universe is filled with approximately 0.0003 eV photons known as the Cosmic Microwave Background radiation. This background radiation is left-over radiation from the big bang which by now has cooled down to about 3 Kelvin in temperature. I don’t know any of the actual mean-free-paths associated with this, just that they are much shorter than interstellar distances.
white noise is caused by air molecules moving randomly at high speed
This is wrong. What you hear is sound waves, that is, rarefaction/compression zones in the air, pressure differentials. They are a phenomenon at a different scale than molecules. In particular, the energy involved is different. “White noise” means the frequencies are uniformly distributed.
Essentially, an air molecule doesn’t have enough energy to register at your hearing sensors, that is, to move your eardrum (or cochlear hairs).
Essentially, an air molecule doesn’t have enough energy to register at your hearing sensors, that is, to move your eardrum (or cochlear hairs).
Though, now that I’m thinking about it, if the white noise generator I bought to help me sleep is really good at producing white noise with uniform power at high enough frequencies, an air molecule would have enough energy to move my eardrums. I would also be on fire.
And if my white noise generator is really really good at producing white noise with power uniform across all frequencies, the noise’s mass-energy will cause my bedroom to collapse into a black hole and I will be unable to leave a 5 star review on Amazon.
Yes white noise is an ideal that can never be realized in reality, like a perfectly rigid object, or a frictionless wheel, or an absolute zero freezer. White noise would carry infinite power.
To clarify what I believe is the question: Why can’t solipsist hear brownian motion?
The question is pretty good; Brown Noise derives its name from brownian motion, or rather the discoverer of such, as it is the frequency (or set of frequency) that brownian motion produces.
I’d -guess- the answer is that the motion all cancels out on the average, approximately, and the remaining statistical noise isn’t energetic enough to be perceived.
Why can I hear noise (white noise / pink noise / brown noise), but not hear temperatures?
EDIT FOR CLARIFICATION Air temperature is caused by air molecules moving randomly at high speed, white noise is caused by air molecules moving randomly at high speed, what’s the difference? Why does white noise fill the room with sound instead of just raising the temperature slightly?
My hand-wavy-sounds-like-science-technobable guess is that temperature does fill the air with sound, but most of the energy of that sound is at far too high frequencies for my eardrums to detect (in part because my eardrums are emitting noise at a those frequencies). Maybe the average wavelength of thermal noise is roughly the mean free path length of the air molecules, so the average frequency of the noise is roughly 5 GHz. But I just making stuff up and really don’t know.
You can’t hear temperatures because if the temperatures of air were high enough to make enough noise for you to hear, you would be incinerated.
http://physics.stackexchange.com/questions/110540/how-loud-is-the-thermal-motion-of-air-molecules goes over this. There is a lot of error in that thread, but the parts that are right show up a few times and calculate the white noise sound level of room temperature air at about −20 dB SPL. SPL of 0 dB is the approximate threshold of human hearing. dB is a logarithmic scale such that every 10 dB increase is a 10X higher power. So −20 dB SPL is about 1/100 the average sound power level that would just barely be audible by a human. This is calculated at something close to room temperature, about 23 C which is about 300 K.
How hot would air have to get to have its thermal fluctuations audible as sound to humans? Any thermal power (at sufficiently low frequencies which situation applies here) is proportional to the temperature. So to increase the thermal sound level from −20 dB to 0 dB, the sound power needs to be increased by a factor of 100. So this would happen at an absolute air temperature of 30000 K, or about 29700 C. For us Americans, that is 53500 F. Super crazy hot, hotter than the sun.
So wait a minute, am I saying that a white noise generator generating 0 dB (barely audible) white noise is heating the air to super-solar temperatures? That doesn’t pass the smell test: if it was true my ears would be burning off when exposed to any white noise loud enough for them to hear. But the answer is, we are only generating white noise over a very small frequency range in order to hear it. Even a high fidelity white noise generator will have a bandwidth covering about 50 Hz to 20,000 Hz. But the “natural” bandwidth of thermal fluctuations is found from quantum mechanical considerations: BW = T * kb/h or bandwidth is Temperature(in Kelvin) times Boltzmann’s constant divided by Planck’s constant. That ratio kb/h turns out to be about 20 GHz per degree K. So thermal noise loud enough to hear would have a bandwidth of 600,000 GHz or 6e14 Hz. TO an approximation, thermal power is proportional to bandwidth, so a 20 kHz white noise generator putting out 0 dB SPL is putting out only 20000⁄600000000000 = 1⁄30000000000 the power level associated with a 30000 K source. So in terms of TOTAL energy, a band-limited white noise source is delivering way less than 1 K of extra temperature to your ears, even though in terms of energy density (power per bandwidth), it sounds hotter than the sun.
Much of the thread below covers some of this, but perhaps I add a little detail with what I write. As to blackbody radiation, yes that is appropriate to use here and its upper frequency limit has nothing to do with electromagnetics, or not fundamentally. It is a quantum mechanical limit. At a high enough frequency, the quantum of energy becomes comparable to the thermal energy, and so at higher frequencies than that those frequencies can’t be effectively generated by thermal sources. This is true for both photons (electromagnetic energy quantized) and phonons (sound or vibration energy quantized).
Hope this is clear enough to add more light than heat to the discussion. Or in this case, more sound than heat :)
The peak frequency of thermal noise at room temperature is far higher than 5 GHz, it’s actually closer to 30 THz. I’m not exactly sure about the biology here and whether Brownian motion of air molecules excites the hair cells in your cochlea. I’m guessing that it does, but even so, the range of frequencies you can hear (20-20,000 Hz) carries only a very, very tiny fraction of the thermal energy. Someone should do the calculations; my guess is that it’s far below the detection threshold.
Another thing to keep in mind is that at equilibrium, you have thermal excitation everywhere. You might as well ask why you don’t hear or see or smell the thermal excitation in your own brain.
As far as I remember, you need to hit the resonant frequency of a particular hair to trigger a “sound” response, so frequencies higher than 20KHz might excite them, but if you’re not getting resonance, nothing triggers.
No this is wrong. Each hair is excited by the amount of its particular resonant frequeny in the sound hitting it. If a violin note is heard, that note only has a few discrete frequencies in it and so a few hairs are very excited about it and the brain (of the trained violinist with perfect pitch anyway) goes “oh, A 440.” If white noise loud enough to hear is hitting the ear, then essentially all the hairs are excited because all frequencies are present in white noise, and the brain goes “sounds like the ocean.”
As to excitement by sound above 20 kHz, a very high frequency ultrasound, say at 100 kHz, can be modulated with the vibrations associated with a violin string, much as sound can be modulated on radio carriers. Such ultrasound hitting a human ear can actually cause the appropriate hairs to be excited so that the brain goes “oh, A 440.” The phenomenon relies on the non-linear response of cochlear hairs and highly directional speakers based on this effect have been built and demonstrated. See for example http://www.holosonics.com/
That’s a somewhat crude way of putting it; when studying a resonator it’s better to look at the q factor: https://en.wikipedia.org/wiki/Q_factor
Lower q factor means a higher spread of frequencies can trigger them. Mammalian hair cells have q factors of 5-10. Q=10 is pretty high for a biological resonator, but pretty low compared to, say, even crude electronic equipment. A typical LC oscillator has Q of 100 or more.
I think you are suggesting something like: if I was detecting thermal vibration by the vibration of a membrane due to thermally induced air pressure I wouldn’t because the temperature is the same in the air on both sides of the membrane and therefore the thermal air pressure on each side of the membrane is the same and so fails to move the membrane. If this is what you are suggesting it is wrong, and in a basic enough way to merit explanation.
Sound is pressure changing in time. Thermal vibration follows a random distribution. The air on each side of a membrane at the same temperature will have the same statistics of pressure change on each side of the membrane, but not the same instantaneous pressure on each side of the membrane. If the random pressure exceeds p1 25% of the time an is less than p0 25% of the time, then 6.25% of the time there will be a pressure difference of at least p1 - p0 on the membrane, and a different 6.25% of the time there will be an opposite sign pressure difference of at most p0 - p1 where we have chosen p1 to be the higher pressure than p0. So thermal vibrations will absolutely cause a membrane to vibrate randomly. Further, it is the case that the magnitudes of p1 and p0 rise as temperature rises as temperature rises, so we expect the membrane to be moved more when surrounded by hotter air than it does when surrounded by cooler air.
SO it is the case that generally heating air makes its average pressure rise if it is in a constrained volume, and a membrane will certainly not be displaced on average if it has air on each side at the same average pressure, but it is the temporal or time variations that produce sound, and the time variations on each side of the membrane for most conditions you can create in the lab are uncorrelated, and so the membrane vibrates randomly and with an amplitude that rises as the temperature of the air rises.
I don’t make that suggestion at all. I’m pointing out that sound receptors are just neurons, and if the thermal vibrations in your ear can excite some set of neurons than the thermal vibrations impinging on the dendrites of any neuron in your body—including inside your brain—should also elicit a response.
That is a little like suggesting that a sound recorder is just electronics and shouting at any electronics should elicit a response. Bringing it back to the neurons,
loud enough sound on any neuron will probably excite it
However the sensitivity of neurons connected in the ear to sound is thousands or millions or billions (not bothering to calculate it) higher than the sensitivity of a random neuron in the brain to sound
A random neuron responding to sound won’t feel like sound. If a pain neuron is activated by sound, it will appear as pain, if a hot neuron activated by sound will appear as heat, etc.
So as hot as the air has to be to excite your cochlear apparatus, and thus the neurons connected to it, it probably has to be thousands or millions times hotter to excite the neurons directly in your brain. And long before it gets to that temperature your brains has been cooked, then dessicated, then burned, and finally decomposed into a plasma of atoms and electrons flying about separately, and probably at the temperatures we are talking about, the protons and neutrons are smashed apart into a cloud of subatomic particles.
Some minor side notes:
Your cochlea is filled with a liquid called endolymph, not air.
A hair cell that was triggered by Brownian motion would be useless. All inner hair cells are tuned to certain vibrations in the endolymph that are greater than those caused by Brownian motion.
Brownian motion is motion of air that, considered as vibrations, has a broad range of frequencies in it. Which means that an ear exposed to air experiencing a sufficiently high level of brownian motion will have many or all of its inner hair cells excited. 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.
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 you were to raise the temperature, the Brownian motion would be higher amplitude and would eventually rise to a point where it was detectable. This is a pretty academic point: the temperatures required to hear the brownian motion would harm the ear so in practical terms your statements are right enough.
If vibrations in the air cause the endolymph to have pressure waves in it which then cause cochlear hairs to move, it is still quite reasonable to describe that as air vibrations making cochlear hairs move. Introducing the endolymph is a clarification at best, not a correction.
Do you happen know a back-of-the-envelope way to get that 30 THz figure?
https://en.wikipedia.org/wiki/Wien%27s_displacement_law
Oh! So you’re saying the spectrum of the acoustic noise at a given temperature will be the spectrum of black body radiation! Yes, I could definitely believe that. That is high-frequency indeed.
Sort of. Blackbody radiation is electromagnetic in nature, however under some ideal assumptions you can assume that the molecules emitting that radiation are also vibrating at roughly the same spectrum. ‘vibrating’, though, can mean a lot of different things; this is related to the microscopic properties of the substance and its degrees of freedom. In an ideal gas, it’s taken to mean the particle collision frequency spread (but not necessarily the frequency of particle collisions). If you consider heat to be composed of a disordered collection of phonons, then you could definitely say that this is ‘sound’, but it’s probably neater to draw a distinction between thermal phonons (high-entropy, low free energy) and acoustic phonons.
The reasoning behind blackbody electromagnetic radiation applies equally well to thermal vibrations in solids and gases. Meaning the spectral limits derived from a quantum consideration of the quantization of electromagnetic radiation (into photons) applies equally well to the quantum considerations of vibrational radiation (into phonons).
“Thermal” photons are indistinguishable individually from photons from other sources. The thing that makes a thing thermal is the distribution and prevalence of photons in time and frequency, those from a thermal source follow a well understood set of statistics, while photons from other sources clearly deviate from that. So a photon arising from a cell phone tower’s radio transmitter reacts similarly with a cell phone’s radio receiver as a photon at a similar frequency arising from thermal emission from the air. Physics can’t distinguish between these two photons which is why it is a major effort in building radio communications to get enough signal-sourced photons compared to the thermal-sourced photons so that the signal-sourced photons dominate, and therefore the signal can be accurately derived from their detection.
Similarly with phonons. Vibrations because something is hot are indistinguishable from vibrations from a vocal cord. It is the statistical distribution of the vibrations in time and frequency that defines a thermal set of vibrations. And again, to hear what someone is saying, it is important to get enough phonons from their vocal cords into your ears compared to the phonons from other sources in order to accurately enough derive the intended information.
Thermal noise or other white noise, and a symphony, have the same kind of phonons and both can be heard by the same kinds of ears. They carry different kinds of information (they sound different) because of their different time and frequency statistics.
Black-body radiation is electromagnetic radiation, so I’m a bit confused how that’s connected with acoustic noise. As to molecule collisions, I’m not sure vibrations at sufficiently high frequency can be called “acoustic” at all.
Your reasoning here carries useful information. For example, when you are dealing with vibrations whose frequency is so high that the wavelength of the vibration is less than the average spacing between molecules in a gas, or in a solid lattice, then a lot of what you calculate about the detection and interactions with lower frequency vibrations no longer applies.
However, the same limitations apply to electromagnetic radiation. For example we think of vacuum or empty space as transparent to EM radiation, and it is as long as the EM frequency is low enough frequency. But high enough frequency EM radiation, empty space is opaque to it! For example, at high enough frequencies, a single photon has enough energy to create a positron-electron pair in free space. Photons at that frequency don’t travel very far before they are destroyed by such a spontaneous generation of particles.
So in principle, EM radiation and acoustic vibrations are the same in this respect: as long as you are considering frequencies “low enough” that they don’t rip apart the medium in which the wave exists, they behave in the ways we usually think of for sound and light. But above those frequencies, they rip apart the media they are traveling through, even if that medium is so-called empty space.
So what kind of energies are we talking about here, and what distances?
Photons with over 1 Million electron volts of energy can create a positron-electron pair, but only when near another massive particle (like the nucleus of an atom). The other massive particle is moved in the interaction but is otherwise not-necessarily changed. https://en.wikipedia.org/wiki/Pair_production. This process has been demonstrated experimentally. The mean free path of the energetic photon near an atomic nucleus is something down on the atomic scale, the experiment I read about used a piece of gold foil and generated lots of positron-electron pairs.
A single photon in otherwise empty space cannot create a pair of particles I was wrong when stating that. However, space with nothing but two photons in it can create matter. Two photons each with a bit over 511 million electron volts of energy can collide and result in the creation of a positron and an electron. https://en.wikipedia.org/wiki/Two-photon_physics Alternatively a single 80 Tera Electron Volt photon can collide with a very low energy photon to create an electron-positron pair. This effect actually makes our existing universe opaque to photons above 80 TeV because our universe is filled with approximately 0.0003 eV photons known as the Cosmic Microwave Background radiation. This background radiation is left-over radiation from the big bang which by now has cooled down to about 3 Kelvin in temperature. I don’t know any of the actual mean-free-paths associated with this, just that they are much shorter than interstellar distances.
This is wrong. What you hear is sound waves, that is, rarefaction/compression zones in the air, pressure differentials. They are a phenomenon at a different scale than molecules. In particular, the energy involved is different. “White noise” means the frequencies are uniformly distributed.
Essentially, an air molecule doesn’t have enough energy to register at your hearing sensors, that is, to move your eardrum (or cochlear hairs).
Though, now that I’m thinking about it, if the white noise generator I bought to help me sleep is really good at producing white noise with uniform power at high enough frequencies, an air molecule would have enough energy to move my eardrums. I would also be on fire.
And if my white noise generator is really really good at producing white noise with power uniform across all frequencies, the noise’s mass-energy will cause my bedroom to collapse into a black hole and I will be unable to leave a 5 star review on Amazon.
Yes white noise is an ideal that can never be realized in reality, like a perfectly rigid object, or a frictionless wheel, or an absolute zero freezer. White noise would carry infinite power.
To clarify what I believe is the question: Why can’t solipsist hear brownian motion?
The question is pretty good; Brown Noise derives its name from brownian motion, or rather the discoverer of such, as it is the frequency (or set of frequency) that brownian motion produces.
I’d -guess- the answer is that the motion all cancels out on the average, approximately, and the remaining statistical noise isn’t energetic enough to be perceived.
The way a sense organ interacts with temperature follows a different mechanism from perception of sound.
What does “hear temperature” mean?
See my edit