Audition
(or, how we hear things)
April 7, 2009
Dirty Work
• Final interim course reports to turn in.
• Final project report guidelines to hand out...
• On Thursday, we’ll talk about auditory (exemplar) models
of speech perception.
• Recap: categorical perception homework.
How Do We Hear?
• The ear is the organ of hearing. It converts sound waves
into electrical signals in the brain.
• the process of “audition”
• The ear has three parts:
• The Outer Ear
• sound is represented acoustically (in the air)
• The Middle Ear
• sound is represented mechanically (in solid bone)
• The Inner Ear
• sound is represented in a liquid
The Ear
Outer Ear Fun Facts
• The pinna, or auricle, is a bit more receptive to sounds
from the front than sounds from the back.
• It functions primarily as “an earring holder”.
• Sound travels down the ear canal, or auditory meatus.
• Length  2 - 2.5 cm
• Sounds between  3500-4000 Hz resonate in the ear
canal
• The tragus protects the opening to the ear canal.
• Optionally provides loudness protection.
• The outer ear dead ends at the eardrum, or tympanic
membrane.
The Middle Ear
the anvil
(incus)
the hammer
(malleus)
the stirrup
(stapes)
eardrum
The Middle Ear
• The bones of the middle ear are known as the ossicles.
• They function primarily as an amplifier.
• = increase sound pressure by about 30 dB
• Works by focusing sound vibrations into a smaller area
• area of eardrum = .55 cm2
• area of footplate of stapes = .032 cm2
• Think of a thumbtack...
Concentration
• Pressure (on any given area) = Force / Area
• Pushing on a cylinder provides
no gain in force at the other end...
• Areas are equal on both sides.
• Pushing on a thumb tack provides
a gain in force equal to A1 / A2.
• For the middle ear ,
force gain 
• .55 / .032  17
Leverage
• The middle ear also exerts a lever action on the inner
ear.
• Think of a crowbar...
• Force difference is
proportional to ratio of
handle length to end length.
• For the middle ear:
• malleus length /
stapes length
• ratio  1.3
Conversions
• Total amplification of middle ear  17 * 1.3  22
• increases sound pressure by 20 - 24 dB
• Note: people who have lost their middle ear bones can
still hear...
• With a 20-24 dB loss in sensitivity.
• (Fluid in inner ear absorbs 99.9% of acoustic energy)
• For loud sounds (> 85-90 dB), a reflex kicks in to
attenuate the vibrations of the middle ear.
• this helps prevent damage to the inner ear.
The Attenuation Reflex
• Requires 50-100
msec of reaction time.
• Poorly attenuates
sudden loud noises
• Muscles fatigue after
15 minutes or so
• Also triggered by
speaking
tensor
tympani
stapedius
The Inner Ear
• In the inner ear there is a
snail-shaped structure
called the cochlea.
• The cochlea:
• is filled with fluid
• consists of several
different membranes
• terminates in membranes
called the oval window and
the round window.
Cochlea Cross-Section
• The inside of the cochlea is divided into three sections.
• In the middle of them all is the basilar membrane.
Contact
• On top of the
basilar membrane
are rows of hair
cells.
• We have about 3,500 “inner” hair cells...
• and 15,000-20,000 “outer” hair cells.
How does it work?
• On top of each hair cell
is a set of about 100 tiny
hairs (stereocilia).
• Upward motion of the
basilar membrane
pushes these hairs into
the tectorial membrane.
• The deflection of the hairs opens up channels in the hair
cells.
• ...allowing the electrically charged endolymph to flow
into them.
• This sends a neurochemical signal to the brain.
An Auditory Fourier Analysis
• Individual hair cells in
the cochlea respond
best to particular
frequencies.
• General limits:
20 Hz - 20,000 Hz
• Cells at the base
respond to high
frequencies;
tonotopic organization of the
cochlea
• Cells at the apex
respond to low.
How does this work?
• Hermann von Helmholtz (again!) first proposed the place
theory of cochlear organization.
• Original idea: one hair cell for each frequency.
• a.k.a. the “resonance theory”
• But...we can perceive more frequencies than we have
hair cells for.
• The rate theory emerged as an alternative:
• Frequency of cell firing encodes frequencies in the
acoustic signal.
• a.k.a. the “frequency theory”
• Problem: cell firing rate is limited to 1000 Hz...
Synthesis
• The volley theory attempted to salvage the frequency
rate proposal.
• Idea: frequency rates higher than 1000 Hz are “volleyed”
back and forth between individual hair cells.
• There is evidently considerable evidence for this
proposal.
Traveling Waves (in the ear!)
• Last but not least, there is the traveling wave theory.
• Idea: waves of different frequencies travel to a different
extent along the cochlea.
• Like wavelength:
• Higher frequency waves are shorter
• Lower frequency waves are longer
The Traveling Upshot
• Lower frequency waves travel the length of the
cochlea...
• but higher frequencies cut off after a short distance.
• All cells respond to lower frequencies (to some extent),
• but fewer cells respond to high frequency waves.
• Individual hair cells thus function like low-pass filters.
Hair Cell Bandwidth
• Each hair cell responds to a range of frequencies,
centered around an optimal characteristic frequency.
Frequency Perception
• In reality, there is (unfortunately?) more than one truth--
• Place-encoding (traveling wave theory) is probably
more important for frequencies above 1000 Hz;
• Rate-encoding (volley theory) is probably more
important for frequencies below 1000 Hz.
• Interestingly, perception of frequencies above 1000 Hz
is much less precise than perception of frequencies below
1000 Hz.
• Match this tone:
• To the tone that is twice the frequency:
Higher Up
• Now try it with this tone:
• Compared to these tones:
• Idea: listeners interpret pitch differences as (absolute)
distances between hair cells in the cochlea.
• Perceived pitch is expressed in units called mels.
• Twice the number of mels = twice as high of a
perceived pitch.
• Mels = 1127.01048 * ln (1 + F/700)
• where acoustic frequency (F) is expressed in Hertz.
The Mel Scale
Equal Loudness Curves
• Perceived loudness also depends on frequency.
Audiograms
• When an audiologist tests your hearing, they determine
your hearing threshold at several different frequencies.
• They then chart how much your hearing threshold differs
from that of a “normal” listener at those frequencies in an
audiogram.
• Noise-induced
hearing loss tends
to affect higher
frequencies first.
• (especially
around 4000 Hz)
Age
• Sensitivity to higher frequencies also diminishes with
age. (“Presbycusis”)
Note: the
“teen buzz”
Otitis Media
• Kids often get ear infections, which are technically
known as otitis media.
• = fluid fills the middle ear
• This leads to a form of conduction deafness, in which
sound is not transmitted as well to the cochlea.
• Auditorily, frequencies from 500 to 1000 Hz tend to drop
out.
Check out a Praat
demo.
Loudness
• The perceived loudness of a sound is measured in units
called sones.
• The sone scale also exhibits a non-linear relationship
with respect to absolute pressure values.