The Little Vulgar Book of Mechanics (v0.15.2) - Hearing I

Last updated: April 23rd 2022

Just updated this section of the book: Hearing I

Hearing I #

"Since I had only a diploma for physics, I had very big difficulties to get permission for receiving some heads of cadavers that I could dissect."

Anecdotes from someone's autobiographical notes that I'm reading at the moment. I'll tell you who the author is below.

Why does a death metal vocalist sound similar to a pig?

Why, and in what way, do the two sounds differ from each other?

And how do they both differ from the sound of, say, a bunch of chopsticks falling on a ceramic kitchen floor?

In Sound I we went over the fundamental physics of sound, so it's probably a good idea to read that section before this one, if you don't know what I mean when I say e.g. "frequency." Here we're going to learn about what happens after everything we talked about in Sound I. The actual hearing, as done by your ears and brain.

"Fortunately the solution was simple because in every anatomical institute there are two doors, one in the front [...] and then a back door where the cadavers are taken in and out. I found out that by going through the back door, I could get as many heads as I wanted."

"This permitted me to dissect inner ears of not too old cadavers and that gave the base for all my later work."

"...of not too old cadavers" Good! Never take too long before you dissect cadavers, because, otherwise it'll be like... "Took Too Long, Already Rotten." Come on, I always have to plug my death metal "music."

Anyway, how does your brain separate the guitar solo from the rest of the instruments? How do we go from an ignorant, clueless, purely mechanical, vibrating ear drum, to the recognition, understanding, and appreciation of each individual part as well as the whole mix?

The answer requires a combination of anatomy, physics (that's right: we're not done with waves, even inside the ear), chemistry, and neuroscience.

"I am very thankful to all the people who helped me in that respect. I am especially thankful to one police officer who one day told me that he could have arrested me any time for murder since I carried a human head in my briefcase."

So let this be your grim welcome to Hearing I.

(Don't worry, it won't be too cadaver-heavy. Though we will begin with anatomy.)

Hearing I - Békésy #

"After a certain time, it was quite clear that Hungary will be occupied by the Russians. I don't want to talk about my experiences during the siege of Budapest. It lasted a long time and nobody was sure if he will survive. Most of my friends were killed during that period, my mechanics were deported to Russia and everything became unproductive and there was no way to continue research."

His name was Georg von Békésy (1899-1972).

He was a Hungarian biophysicist who clearly had an interesting life, so I will certainly not do it justice with this short bio. But he studied chemistry in Berne, Switzerland, and got a PhD in physics on the subject "Fast way of determining molecular weight" in Budapest. The WW2 happened, and, while most of his friends died, he kept working on signal quality in telecommunications.

His telecommunications work got him interested in the mechanics of hearing. He was eventually awarded the Nobel Prize in Physiology or Medicine in 1961 for his research on the function of the cochlea in the mammalian hearing organ. Then his lab was destroyed by fire in 1965, and he moved to Honolulu, Hawaii, where he taught at the University of Honolulu, until his death in 1972. He was 73.

His contribution is central to the current understanding of the inner ear, even though he had limited tools. Cadaver heads, optical microscopes, and other basic 1900s technology. He basically had to blast super high level sound waves onto dead human ears, which isn't exactly how you experience your favorite Bach Toccata! So in Hearing I we are going to learn also from more recent developments made possible by modern technology.

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Hearing I - Cochlea I #

"It turned out that for certain frequencies, let's say for high frequencies, the maximum of the travelling vibrations was near the entrance to the inner ear and for low frequencies, it was far away. This way, it became evident that there is mechanical discrimination of frequency done in the inner ear." – GEORG VON BÉKÉSY (1899-1972), My experiences in different laboratories.

The cochlea. That magnificent spiral, fluid-filled labyrinth in the inner ear.

It's a coiled duct. Coiled like the shell of a snail, it consists principally of two fluid-filled channels (actually three, but I'm leaving the third one out in this section), basically tubes, whose cross sectional areas start large and get narrower as they coil together upwards. These internal channels are separated by a membrane. And this membrane supports all along its edge an organ that detects and amplifies motion. The cochlea is the ear's filtering and amplification system.

This membrane that separates the two main fluid-filled tubes (the scalae) is called the basilar membrane (BM). It interacts with the fluid in the tubes, and is constrained by their shape, which affects the way it forms a transmission line for mechanical waves to travel. Along the process, both linear and non-linear operations happen. The cochlea even acts as a distributed amplifier, adding energy to the traveling waves to boost the response to weaker sounds.

You probably have questions already:

  1. Fluid-filled tubes? What fluids, what's their chemical composition?
  2. Filtering? Amplification? How?

All good questions. But let's finish the general overview first.

Bring back the tuning fork, from Sound I (which I recommend you read before this section), and hit it.


From the point of view of the cochlea, what's happening is that sound waves are reaching the outer ear. Then they're getting transduced into the fluid in the cochlea. This transduction from air to fluid is done by the ossicles. The ossicles are a group of bones (ossified portions of cartilage) in the middle ear, that are among the smallest bones in the human body. They work together like a machine. Their names are malleus, incus, and stapes.

The ossicles mechanically amplify the force of the received vibrations like this: The malleus is joined to, and therefore moved by, the ear drum. The incus is in the middle of the malleus and the stapes. And the stapes (which btw is the smallest bone in the human body) is joined to, and directly pushing and pulling on, the oval window (fenestra vestibuli or fenestra ovalis). The oval window is the membrane separating the air space in the middle ear from the cochlea.

On the other side of the oval window is the scala vestibuli, one of the two fluid-filled, spiralling-up tubes mentioned above. So now you got differential pressure waves propagating through the cochlear fluid of the scala vestibuli, thanks to the stapes. I.e. The stapes conveys the (amplified) energy from the vibrating ear drum to the fluid in the scala vestibuli.

Meanwhile, the other channel, or tube, called the scala tympani, is not being driven by the ossicles. Instead, this one is coupled only to the air in the tympanic cavity of the middle ear.

From studying Pascal's Law, or from using a hydraulic lift, or from strangling a water balloon to death in self-defense, you know that when you push an incompressible fluid, it has to go somewhere.

Well, when the oval window pushes on the essentially incompressible fluid in the scala vestibuli, the round window (fenestra tympani or fenestra rotunda) on the other end bulges out. Pushing in on one end, bulging out on the other, and viceversa. I.e. two membranes at the ends of a tube, vibrating in opposite phases. Just like the top and bottom membranes of a drum. The forces, or pressure, causing this motion, create pressure differences all across the cochlear partitions.

Let's go back to the membrane that separates the two scalae: The basilar membrane (BM).

Being somewhat stiff but springy, the BM gets deflected as well. And not only does it separate the scalae, but also supports the organ of Corti. This organ, sitting on top, and along the edge of the BM, has the assembly of outer hair cells that add energy to the travelling wave. It also has the inner hair cells, that detect sound-induced motion.

The BM is not just being deflected for no reason. As it bends, it too is generating a wave. A displacement wave. So in total, from the ear drum's vibration, we get two coupled waves traveling from the base to the apex of the cochlea: The waves in the scala vestibuli's fluid, and the displacement wave of the BM's motion.

Our friend, Von Békésy was awarded the 1961 Nobel Prize for his pioneering work on what we're talking about: Cochlear mechanics.

He discovered the cochlear mechanical traveling waves. He did the first measurements of the BM's vibrational response to sound, and showed (using his handy cadaver heads) a key part of the mechanics: Frequencies are mapped to longitudinal position along the BM.

He realized this from having observed that the BM's stiffness decreases by 2-4 orders of magnitude as a function of distance from the stapes. So the motion of the basilar membrane allows the cochlea to essentially do Fourier Analysis! (See Fourier Transform I.)

The BM's motion is the effective stimulus that inner hair cells detect and convert to the neurotransmitter release that causes the primary auditory neurons of the spinal ganglion to spike, and send the sound-evoked signals to the brain via the auditory nerve.

The hair cells use their own energy to pump positive potassium and calcium ions out, and achieve a negative internal potential that is 150 mV different from the region immediately outside their end (that holds the cilia, or "hairs," that transduce motion.) This 150 mV is known as the endocochlear potential, or EP, and is the largest potential difference found anywhere in the body. This is what drives the sensitive and fast transduction that these cells achieve.

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