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The upper limit of hearing is approximately 15 kHz, dependent on age and other factors. According to the principles of digital signal-processing, such an upper limit would mean that the auditory system samples at least at 30 kHz or more.

Now suppose an ultrasonic signal, say a 40-kHz acoustic frequency - why would I hear nothing, instead of that signal aliased at a 30 kHz sampling rate?

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  • $\begingroup$ one thing i could not understand... if you can't hear above 15kHZ ("upper limit") then your auditory system should sample below 15 kHz. isnt? $\endgroup$ – Always Confused Dec 14 '16 at 6:13
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    $\begingroup$ In order to hear a sound of a given frequency, you have to sample at twice that frequency (really, above twice that frequency). This is the Nyquist rate. Not sure if you're interested enough, but this Youtube video on the concept is really good: youtube.com/watch?v=yWqrx08UeUs $\endgroup$ – Bzrs Dec 14 '16 at 6:32
  • $\begingroup$ When a digital sound is processed by a speaker, the speaker diaphragm travels through every point in space between the two digital bits of data. therefore, all sounds transmitted in air are generated and heard non-digitally, they are continuous signals limited by atomic size, which is bigger than HDD requirements. Frequency is mathematical, but the human cellular ear structures are not mathematical so you can't rate an ear in mathematical way very clearly. $\endgroup$ – com.prehensible Dec 15 '16 at 12:17
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    $\begingroup$ The answer to your question is in here. I scanned through it, but I don't have time right now to write up a formal answer (someone else is welcome to if they would like). Short answer is that, according to this, the exact mechanics of sound perception are still not pinned down, but it likely has something to do with a lack of space within in the cochlea since vibrations at different areas correspond to the perception of different frequencies. $\endgroup$ – kingfishersfire Dec 15 '16 at 18:16
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    $\begingroup$ I don't have time to type up a whole answer right now, but the premise of your question has a major flaw: the Nyquist rate that you are referencing by talking about necessary sampling rates applies to discrete sampling of a waveform; this isn't how auditory information is represented in the cochlea or auditory nerve or anywhere in the brain that we know of, so it does not apply. You could look into "phase locking" which occurs at lower frequencies, but higher frequencies can just as easily be represented by their envelope, or phase information can be distributed across a population. $\endgroup$ – Bryan Krause Dec 15 '16 at 19:39
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Short answer
The cochlea is a tonotopic map with certain physically determined boundaries that determine the range of frequencies perceived. Ultrasonic soundwaves simply do not have a correlate on this map.

Background
The cochlea is a frequency analyzer that basically translates acoustic frequencies into a place-map. High frequencies are encoded basally (up to 20 kHz), low-frequencies apically (down to 20 Hz or so). Hence, it is pretty much a Fourier analyzing system (Fig. 1). This way of analyzing sounds is referred to as the place-coding theory of pitch. The place where a frequency is encoded is mainly dependent on physical characteristics of the basilar membrane in the cochlea. Every part is sensitive to a slightly different frequency then the next. This is caused by gradual variations in the stiffness and width of the basilar membrane, among other less important factors like hair cell length and so forth. The specific physical characteristics determine what specific resonant frequency a particular part of the basilar membrane has. Hence, incoming sounds are torn apart with standing waves, where each frequency results in a standing wave at a particular spot in the cochlea.

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Fig. 1. Tonotopic map of the inner ear. source: Ternopil State Medical University

The frequencies mentioned are physical wavelengths of the acoustic air pressure differences entering the outer and middle ear. The cochlea translates these into fluid-based pressure differences. Hair cels in the cochlea pick up these fluid pressure differences and tranlate them into potential gradient differences.

The sampling rate of hair cells is pretty much infinite, as they work on a continuous membrane voltage, i.e., they are analogue.

The secondary neurons, the spiral ganglion cells, translate these voltage differences into neural spikes and lead them through the auditory nerve to the brain.

Neural spiking follows the acoustic frequencies up to, say 1 kHz (frequency following response). This phenomenon is referred to as the temporal code of pitch hearing. After that, the refractory characteristics cause single fibers to fire only to one in a few wavelength periods. So at the upper limit of hearing, say 20 kHz, a ganglion cell may only fire once every 20 wavelengths or so. No problem, as many others do the same thing. Stochastics cause the wavelength to be nicely encoded in a population of responsive fibers. Furthermore, the auditory cortex contains a tonotopic map, meaning that high frequencies are processed elsewhere then lower frequencies. In other words, the auditory nerve doesn't need to faithfully encode the incoming wave.

A nice example in this are cochlear implants; they stimulate the auditory nerve with electrical currents. The place of the electrodes determines the pitch, not their pulse rate (although it can have an effect).

Now why are you not hearing ultrasounds? Simply because the basilar membrane does not contain regions sensitive to frequencies above 20 kHz or so. This is referred to as the Greenwood map, which depends on species.

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  • $\begingroup$ Thanks for the answer. Just a few questions: re: "The sampling rate of hair cells is pretty much infinite, as they work on a continuous membrane voltage, i.e., they are analogue" don't they have to depolarize, though, which is a discrete event? Is your statement that there is no real limit at all related to this study which showed that OHCs are not limited by their membrane time constant? ncbi.nlm.nih.gov/pmc/articles/PMC3143834 $\endgroup$ – Bzrs Dec 15 '16 at 22:44
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    $\begingroup$ @Bzrs The point is that hair cells voltage is continuous - those cells don't fire spikes. So, no, depolarization is not a discrete event. The most likely explanation is that mechanical deflection of the hair cells causes a channel to open; that open probability is a function of the magnitude of the deflection. The depolarization is analog meaning that it is continuous. You could depolarize by 1 mV, or 2 mV, or 0.5 mV, or 0.1 mV, or anything between. Here we are talking about the inner hair cells, the primary sensory cells, not the OHCs. $\endgroup$ – Bryan Krause Dec 15 '16 at 22:59
  • $\begingroup$ @BryanKrause I know IHCs actually transduce the sound, just was thinking there would have to be a similar mechanism behind their analog quality and it appears that there is (it being the probability of open channels). It's a bit confusing to me since one could see discreteness in some aspects of this, e.g. neurotransmitter release from the IHC is also continuous/analog due to channel state being so, but the release itself is quantal (released in packets of constant quantity) according to "Neurotransmitters and Synaptic Transmission" by Sewell in "The Cochlea" (Springer Auditory Handbook). $\endgroup$ – Bzrs Dec 15 '16 at 23:08
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    $\begingroup$ @Bzrs Yes, there are some aspects that are still somewhat discrete, like neurotransmitter release, but even that is continuous on average: see law of large numbers. Essentially, the membrane potential is setting a probability of release, and release events are frequent enough that the output is roughly continuous, especially because there will be some postsynaptic temporal filtering that smooths the individual release events. $\endgroup$ – Bryan Krause Dec 15 '16 at 23:22
  • $\begingroup$ @Christiaan if freqs above 20 kHz have no representation in the human cochlea, what is your interpretation of the human ultrasound via bone conduction studies? This study claims to rule out lower freq stimulation (ncbi.nlm.nih.gov/pubmed/23384569) and another by the same group shows inhibition of tinnitus after 30 kHz BCU, which they say is evidence that their BCU stimulus activated the cochlea base (ncbi.nlm.nih.gov/pubmed/24530434). Your answer biology.stackexchange.com/a/27901/28436 invokes ossicles and not cochlear representation as the limiter on high freqs. $\endgroup$ – Bzrs Dec 15 '16 at 23:33
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I think that you are misquoting Aliasing.

Digital acoustics is explained in a mathematical sense, Aliasing is a maths concept. Real life acoustics is explained in a physical sense, which talks about reflection, absorption, phase change, harmonic modes, weights... the perception of sound is discussed as psychoacoustics and cortical structures and individual nerve impulse detection thresholds. consider for example the explanation of drum acoustics, it is not digital and on no physical objects will you see the word "Aliasing" used: https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane

Aliasing refers to a digital concept, whereby we devide screens into pixels, and you can't make out objects narrower than a pixel. A wave is at least 2 "/////" points of data, so it requires a 2x window so we have 44k CD's to code 22Khz sounds.

I'll just tackle this precise question, aside from the mis-use of the term Aliasing: why would I hear nothing instead of the signal aliased at a 30 kHz sampling rate?

Pressure waves are continuous and physical sounds... A continous sound or physical object can't be subject to the digital distortion effect "Aliasing" which for example refers to the generation of infinitely high frequencies in between two sampled points of a clock rate...

Because physical sound is continuous, it can't have frequency distortion related to it's sampling rate of 15/30 Khz, it can attenuate and physically react with physical objects including other sound pressure waves and cause physical objects to resonate in different modes of movement.

The sound detection depends on the physical excitation of hairs and nerves that must exceed a threshold of detection. physical objects don't have radical and odd excitation modes when they absorb a frequency that is too high, they can resonate in different modes, but they wack about wildly and produce volume clipping and sound artefacts. Most of the time they don't have a limit of frequency after which they go crazy. the closest you can get to strange frequency modes in physical objects is resonance where the movement builds up into a high kinetic movement like the Tacoma Narrows Bridge. You have to approach the ear as a physical model and not a digital one. I think of the resonant modes of structures in the ear similar to a guitar string or a gong moving in 3D space. This gives you an idea of the nerve signals in the ear: https://www.youtube.com/watch?v=1JE8WduJKV4&t=17s

Almost all sound that is detected inside an ear is distorted by reflection from it's initial shape and source, and thereby it is smudged into reverb similar to light travelling through frosted windows.

Human brains and tissues are not digital and quantized, they aren't even analog, the are cellular with different types/sizes of receptor cells and nerves, variable and organic. You can say they alias only when you talk about perfectly equal sized cell matrix in 2d/3d pattern, like photoreceptors, except that our minds disregard information on cellular scales that aren't useful to us, like a biological version of aliasing would be.

If you study the function of the cochlea you will find that the structures, hairs, membranes are so different from a digital aliasing concept.

Human ears collect high frequency sounds unlike the dished ears of bats and cats and dogs, which are made of stiff cartilage that reflects higher frequencies well, into the ear canal. high frequencies are absorbed very fast by the skin and it takes specialized organs to reflect them to stiff cartilage chambers lined with hairs, each part of which is adapted to further reflect and absorb different frequencies.

The cochlea is organic and cellular, and it is similar to multiple electret microphone diaphragms and cilia all existing inside a complex organ which sends the vibrations to nerves. Sounds have to be collected by dishing and focused onto light and rigid membranes.

There is very much artifacting from all frequencies as they reach the ear. The sounds reflect of different surfaces, although high frequency ones absorb more easily and therefore are heard more linear from the source to the sensor, and have more time precision and more binaural precision.

Sounds don't tend to be generated in the exact same spot(point sources), so if you have for example an insect generating high frequencies, it will make a complex wave shape, that excites a large envelope of air around it, like dropping 5-10 stones into some water, and the outgoing wave will not be a simple form, but a complex series of phase interactions similar water that is excited by a swimmer. In that sense it has some properties of a moiré pattern, but it isn't aliasing, it's complex wave and phase interaction.

An Aliased oscillator on the other hand is a digital sound which contains infinitely high frequencies, because digital encoding forces sudden changes in amplitude to be abrupt, which is different to nature, where sounds are continuous and not discrete sets of values.

As sound travels through air and through flesh, the high frequencies which are all pure sine wave components of the overall sound, will simply be attenuated according to complex spectra of attenuation which correspond to the ambient air conditions, the angle of incidence towards the reflective and transmitting ear vestibules.

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    $\begingroup$ Nice answer, but can you add a couple of references or a good textbook to provide support/further information? $\endgroup$ – fileunderwater Dec 15 '16 at 13:45
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    $\begingroup$ I don't know that I understand what you're saying some of the time, but from your analogies I would guess you come from a visual background. Human ears also have cartilaginous pinnae that help amplify sound. The cochlea is not lined with hairs (did you mean hair cells?). And with regard to high frequency sounds, the place-code of the cochlea does come with particular frequencies being represented in a particular place. I know the ear is not digital and that signals do not come in without a lot of modification. It's a simplification, but my question was conceptual. $\endgroup$ – Bzrs Dec 15 '16 at 19:08
  • $\begingroup$ You can actually bypass the entire impedance from air to fluid/ossicle transfer function aspect of it if you transmit a signal through bone conduction, and indeed studies show that people (even the deaf) can hear higher frequencies this way. In which case the limitation may not be pre-cochlear. ncbi.nlm.nih.gov/pubmed/2063208 ncbi.nlm.nih.gov/pubmed/11234768 $\endgroup$ – Bzrs Dec 15 '16 at 19:17
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    $\begingroup$ This answer makes some good points but a lot of the details are misleading or wrong, especially the comparisons between human and other animal hearing. I think it would be greatly improved if @comprehensible was able to source the real stuff and remove anything they can't find sources for. $\endgroup$ – Bryan Krause Dec 15 '16 at 19:42
  • $\begingroup$ Bzrs,that study talks about brain implants of some kind, ultrasound hearing aid cortical implants. Cats can and bats can hear above 60Khz. they have forward pointing ears with round dish structures that point towards the ear canal. some primates have dished ears, but almost all the human ear convex shape points away from the inner ear. The major mistake in the text is that i have not considered how the human auditory cilia can react to signals of 15Khz in a way that can be compared to a digital encoding of 30Khz which is necessary to detect a peak and trough at 15Khz. $\endgroup$ – com.prehensible Dec 15 '16 at 20:37
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I actually think I realized the answer this morning. The biological equivalent of 'sampling' should occur at the neural level, e.g. after successful transduction. Since properties of the basilar membrane (e.g. stiffness/thickness) AND the transfer function of the ossicles would need to allow passing of a high frequency sound into the cochlea prior to sampling, the excessively high signal may never make it there in the first place.

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  • $\begingroup$ I would agree with what you've said about the properties of the ear, but I'm not sure that the concept of sampling is a good fit on a neuronal level either. Though I would be very interested if you had some info about how it would relate. $\endgroup$ – kingfishersfire Dec 15 '16 at 19:57
  • $\begingroup$ I just found this and will be digging into it as best I can with my limited neuro background: audiology.pagesperso-orange.fr/en/cochlear-sampling-theory.pdf $\endgroup$ – Bzrs Dec 15 '16 at 20:09
  • $\begingroup$ Also, not sure if you saw my answer above, but considering the nature of spiral ganglion fibers innervating different places along the cochlea, and the tonotopic representation of frequency, there's at least potential for these to act as 'channels' which are sampled/filtered/processed in different ways. This was obviously the thought behind some cochlear implants but I admittedly don't know how much it is an accurate reflection of the biological ear. $\endgroup$ – Bzrs Dec 15 '16 at 20:10
  • $\begingroup$ This looks interesting. Thanks for sharing. It looks like our supposition about the limits of the cochlea may have been premature. $\endgroup$ – kingfishersfire Dec 15 '16 at 20:11
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    $\begingroup$ Multiplexing and volley principle is not necessary for detecting or perceiving sounds; phase information is not needed to perceive a sound at a particular frequency, only amplitude. There is no need for the brain to be able to reconstruct the exact waveform of an incoming sound to be able to perceive it, a spectrogram is almost certainly sufficient. Phase information is important for localization of low frequency sounds, however, so it is still important, just not necessary at all frequencies. $\endgroup$ – Bryan Krause Dec 15 '16 at 21:29

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