The Basilar Membrane of the Inner Ear responds to a 'traveling fluid wave from complex frequency vibrations of the 'ear drum'! We experience the 'sensation of sound' when our eardrums move less than the diameter of a hydrogen atom... less than one trillionth of a meter, a picometer!

"I Praise you, Lord, for I am Fearfully and Wonderfully Made"...Ps 139:14 (1000 BC)

The Ear

Two amazing features of our ears are discussed in this article: The Middle Ear, and the Inner Ear.

1. The Middle Ear

The 3 tiniest bones in the human body are connected to 2 circular elastic membranes of different diameters (the tympanic membrane and the oval window) in such a way as to solve a huge problem! Were it not for this.... were it not for this 99.5% of the sound wave energy impinging upon the eardrum would be reflected and would not enter in the cochlea, in other words, it would be lost. We will see that the inner ear, the cochlea, is where all the complex, elaborate processing and discrimination of frequencies takes place! Remember, the Brain cannot process what the brain does not receive!

To fully appreciate the Middle Ear, One must completely understand traveling wave physics, especially wave reflection and impedance matching principles, also hydrodynamics, material science, cellular biology, biochemistry, human physiology etc etc. etc. oh my!.. But then to actually implement this into physical structures such as these 3 tiny bones... wherein the 'texture, strength and pliability of these bones is very precise. such as they provide the perfect low-pass filtering ie. cutoff frequency of 22,000 Hz.... and in the volume of space of a garden pea...? Are you kidding me? .the glory of God is all over this and should be shouted from the mountain tops.... not attributed to this shameful 'thing' called evolution!

Ok, so what this arrangement of 3 tiny bones and 2 membranes of our Middle Ear yield is equivalent to is a hydraulic floor jack installed in your head! Yes, actually two hydraulic floor jacks, one in each ear! The 'bumper jack and the scissor jack we all have in our trunks are fine but neither employs superior hydraulic force multipliers connected in series to them. The superior 'hydraulic floor jack operation is allowing us to multiply forces. The first force produced by the 'bumper jack' section multiplies the force we push down on the long arm so that our force multiplier is simply the ratio of the length of the 2 sections Just picture a father and young daughter on a teeter-totter. If the little girl's length of the teeter-totter is much longer than dad's then she can easily 'lift' him up. But now, connect dad's shorter end to a hydraulic piston where now instead of the length ratios being our force multiplier we have different member diameter ratios of the two membranes, the ear drum, and the oval window, being acted on by two different fluids.... Air (ear drum) and Water (oval window).... water is 800 times denser than air. These 2 Force multiplers do not add to each other... they Multiply! This is the beauty of the hydraulic floor jack principle. Without this installed nothing in the inner ear, cochlea, could take place because the sound energy will not get there So we now have a 2 part apparatus, a hydraulic floor jack .... Lever and Hydraulic, built from 3 tiny bones and 2 tiny membranes!

Here it is...

Image of the Middle Ear and the 3 bones + 2 membranes functioning as a hydraulic floor jack which multiplies the force 22X !

The Lever (teeter-toter) give us a force multiplier: F(out) = Force(in) X L2/L1 .... . ie. Daughter's length/ Dad's length (Incus/Malleus ~ 1.3)

The Hydraulic force multiplier: F(out) = Force(in) X D2/D1 the Eardrum diameter, D2, is 17 times larger than Oval Window diameter, D1. Since they are connected in series, we get to multiply, not add, ie. 1.3 X 17 ...and we get something like a 22X increase force on the one member where it must appear, the oval window separating air from fluid. If not,this entire exercise is futile and we are left deaf! Wow!

Before delving into the glorious world of the cochlea, let's pause here on this statement,,, the Brain cannot process what the brain does not receive. If I may make an analogy that might help us to appreciate the absolute requirement of providing the brain with all the frequency components making up the sounds we hear. So here goes... When we read any text, of course, our purpose, our goal is not to dwell on the actual ink symbols ie. individual letters strung out across the page but rather we are seeking the meaning, thought, or idea being projected by the unique combination of these 'symbols in ink on a page'. Our brains have been 'taught' that combinations of these symbols ie. our 'alphabet letters', can produce meaningful words which when connected to other meaningful words can produce an infinite number of ideas, and thoughts which then, themselves, convey to the reader what the writer wants to communicate. This is what we really wanted... the 'symbols in ink were simply a means to get there! Well ok... in the case of symbol letters connected to make words to sentences to paragraphs, we can play some games ie. we can 'delete' some letters and even words and still retain all the original meaning because the reader can figure out what was trying to be conveyed.

This is not possible in the world of sound! We cannot simply toss out a few frequencies and still keep the exact original sound! In fact, we cannot even alter the 'amplitude of any individual frequency component of this complex waveform and still retain the pure, original sound. it will sound different!

This is so important and is worth repeating. All the frequency and amplitude information contained in the incoming sound wave, this longitudinal compression wave, impingeing on our eardrums, must be presented to our brains, or the sensation we experience, if any, will be different than the original!

And this is so very easy to demonstrate! The piano might be the easiest way to demonstrate this. Simply play any full octave chord... for example Middle C, E, G, and C one octave up from middle C. So using 4 fingers, 1, 2, 3, and 5th finger, we can play 4 notes producing, in this case, a C major chord.

What you have just launched into 3-dimensional space is the following.: At least 20, not just 4, but 20 unique longitudinal compression waves (a fancy name for sound waves) are now impinging on your ears. Remember piano string vibrations contain strong overtones or harmonics or partials, whatever you want to call them. So, At least 4 'harmonics of the fundamental frequency of each of the notes you just played together are causing the air molecules to vibrate at all of these frequencies simultaneously! Ok, now simply replay this C major chord but this time remove one note... any note. Do you hear a difference in the sound now? Of course, you do! And can you see that was only possible if your brain had noticed the removal of the frequencies you deleted by not playing that note. This is why the brain must be fed with all the frequency components of the sound you are producing. The frequencies produced by Middle C are not just one but contain at least 4 overtones added to the 256Hz fundamental frequency. The following image illustrates this:

Middle 'C'...the top waveform is the 'summation' of the bottom 4... our eardrums literally vibrate per the top waveform!

The cochlea will 'deconstruct the upper waveform into the bottom 4! Then the brain processes these 'individual' frequencies which will then produce the 'sensation' we experience from piano's Middle C... Is this not the coolest thing?

And finally, a very important point is this. When we 'read' text, we do so 'serially'... ie one word at a time moving serially, word by word from left to right (for us Westerners anyway). this is not to minimize in any way the incredible brain processing going while reading words off a page. But... but with sound processing things are much different and really more challenging. This is why we must have this 'pre-processor', the Ear. This is because sound waves, unlike letters just sitting there not moving, are striking our eardrums at 1100 ft/sec, or 750 MPH and we must keep up with them! Right? We must process this streaming data immediately as it comes in. If we tire of reading we can 'stop' and get a drink or eat a snack and then later return and pick where we left off not losing a single word... they are not moving but sound ... you better process it while its there or you will lose it. This is why the Ear is so important in deconstructing the complex information into the basic frequency/amplitude components.... immediately and instantaneously before sending to the Brain!

The Inner Ear, (Cochlea)

Well, thanks to the 2 'hydraulic floor jack' force multipliers provided by the Middle Ear apparatus, we can now continue our journey of sound processing because the energy of the air pressure wave will be 'transferred' into the fluid chamber of the cochlea!

What happens here is simply breathtaking! Let's begin this way:

Picture the inside of a grand piano where we have over 200 steel wires of different lengths and different tensions. Each wire is a 'mechanical resonator. When struck by the piano hammer the wire will vibrate, disturbing the air molecules around it at its resonant frequency which is determined by the length, thickness, and tension of the wire. If the pins which attach the wire to the soundboard do not loosen, that wire will always vibrate at the exact frequency it was tuned to. We say this is a mechanical resonator tuned to vibrate at its resonant frequency. This is the world of stringed instruments, adjusting the tension of the strings/wires changes the resonant frequency. The air molecules are undergoing compression and rarefication in sinusoidal manner:

BTW, this image illustrates just exactly what 'sound' is... air molecules striking our eardrum are being compressed and rarefied in sinusoidal fashion. It is important to note that this image represents the simplest of sounds... a single frequency such as A440 from a tuning fork.

Inside the Cochlea the following takes place:

Instead of 200 finely tuned piano 'wires' emanating sound energy when struck by the hammer, we now have 22,000 protein structures called Outer Hair Cells (OHC) absorbing sound energy..These OHC's are embedded into a flexible membrane called the Basilar Membrane (see image at very top of page). Each of these, like piano wires, differs in length and thickness meaning each hair cell will absorb sound energy but only at the frequency which is the resonant frequency of that particular hair cell. This is stunning and not reproducible!

Next, with this in mind, we also know the traveling wave physics of a fluid-filled cylinder are such that if one end of the chamber has an elastic membrane (like the eardrum) and it begins vibrating with 'many' frequencies added together to form a very complex vibration.... the 'individual frequency components will spread out along the one-inch length of this membrane. How cool is that? This feature of the traveling fluid wave could be very useful! Because much like a glass prism spreads out the colors of the rainbow from sunlight due to each color having a different index of refraction.... ie bending angle... so here each frequency component of a sound wave will reach its peak amplitude at a unique distance along the basilar membrane.

This feature. of the spreading out of individual frequency components. is important because now, with this approach, we could detect the presence of individual frequencies if we had 22,000'sensors', each tuned for every frequency from 20 to 20,000 Hz and positioned along this membrane. let me catch my breath......then and only then we would be able to receive all the frequency information present..at once! Yes, all at once !!. without any need to process or 'sift thru' this information one laborious frequency at a time for every single frequency ... as we must do in the Fourier Transform approach! So Cool! No processing is required because we have something like 22,000 hi-Q Bandpass filters working in parallel! You can see, In principle, this is a far far superior, and more elegant method for processing sound. It's simply not possible to overstate this: So, why don't we do it this way? Well, think about it, you must 'manufacture and strategically insert these 22,000 physical structures... ie Bandpass filters....very hi-Q Bandpass filters all along a membrane that is about 1-inch in length.

This 'pea-size' structure runs for a lifetime requiring no external power or maintenance.it's 25 times smaller in size, It runs 40,000 times cooler (lower power), and its performance specifications (frequency and amplitude range and resolution) exceed anything men have designed

(BTW, a piano string will absorb sound energy and start vibration if it's at the frequency of resonance for that string... simply release the damper on A880, then strike A440. Piano string vibrations contain the fundamental frequency AND harmonics. So striking A440 will produce 440, 880, 1320, and 1760 Hz freq vibrations (all added together) so 880 will be the strongest overtone and you can actually hear A880 vibrate by doing the above-mentioned procedure.)

Well, there's more God-given glory to discuss here regarding the Outer Hair Cells of the Cochlea. They possess the ability to amplify sounds that are very low in intensity... very low. They collectively function as a high gain, low noise amplifier of small, faint sounds. This feature is known as the cochlear amplifier. Remember, that the actual sound wave energy impinging upon our eardrums is only a tiny fraction of the total sound emanated from the source...(ie it's inversely proportional to the square of the radius/distance away(. As stated earlier, it can be as low as a deviation of One Billionth of an Atmosphere! This cannot be emphasized enough. These most important sounds of our lives are so extremely weak and faint as to vibrate our eardrums so little, well, as stated above, We experience the 'sensation of sound' when our eardrums move less than the diameter of a hydrogen atom... less than one trillionth of a meter, a picometer. That's because the infinitesimally low energy of these very important, special 'soft' sounds arriving at our eardrums can only move these tympanic membranes (eardrums) that much!

It's truly amazing how our ears solve this problem of amplifying very weak sounds. Take another look at the animation at the top, the Basilar Membrane's behavior. When they are excited by a single frequency. these 22,000 Outer Hair Cells will actually lengthen under very low amplitude conditions... extremely faint sounds! The 'sounds of our lives, reaching our ears are the important sounds, the beautiful sounds. these sounds are the very soft sounds.... laughter of our children, the gentle breeze blowing thru the trees, puppy dogs, kittens, and our babies breathing in the bassinet. Sure we need to hear the approaching train, explosions but....

There is feedback from these energy-absorbing cells OHC's which in turn communicate with 3000 Inner Hair Cells (IHC) will cause the OHC's to lengthen ... which in turn amplifies the sound!!! Yes, and this also causes 'peaking' in the transfer curve which in turn 'fine tunes', increases the Q' and drastically improves frequency selectivity! ...from the image above of the lower BM animation, we see what happens without this feature... the upper animation, as you see, renders s much greater response and in a much more narrow frequency band! Without this amplification and peaking feature of the OHC;s hearing would be nearly impossible, discriminating the laughter of our children from other children, appreciation of beautiful music... we would not have this at all!

As mentioned above, the threshold of hearing is so low that if it were any lower we would have the unfortunate problem of hearing atomic noise, white noise... atoms colliding with each other... all the time! The sound pressure variation impinging on your eardrum from the wind rustling the trees across the street or a cat meowing in the other room could be as low as the pressure variation experienced when jumping on and off a single sheet of onion skin paper! +- one billionth of an atmosphere!... only a few pico-watts of power... which, again, will only move the tympanic membrane less than the diameter of a hydrogen atom - a picometer.

Let's pause for now and remind ourselves that all that has been discussed so far with our Ears, our sense of sound... all of this was designed and programmed and installed 'somewhere' into the DNA to develop from a molecular aggregate 80 microns in diameter... a zygote/fertilized egg! Yes, 12 'fully programmed human beings could fit side by side within the space of 1 mm!

To God be the Glory, great things He has done!

So much more can be written about this glorious technological marvel which is the Human Ear! Just the hundreds of articles about even this amazing protein molecule, Prestin, part of the structural apparatus of the OHC which enables it to lengthen, (in less than 5 microseconds btw) yes physically lengthen to provide amplification and fine-tuning of the incoming sounds....but I will end for now with this:

3000 years ago a young shepherd boy from Judea would sit, nignt after night, under the stars, and with his harp he would praise the God who created and even named all those stars, echoing the words of praise at the top of this article. At that time there was absolutely no scientific knowledge anywhere such as we now have. Today, we have a mountain of scientific evidence and understanding of scientific principles wherein we know that not even a single one of the 22000 OHCs could ever evolve...all of this must have come from an infinitely powerful God who intended us to have and enjoy this beautiful gift... the gift of music and laughter of our children. How does it make him feel to see a world and a church that attributes this glorious gift to something, anything other than Him? ...to be continued

Rick Allen, Feb 2023