JedWhittaker on the Ear

7/21/2019 JedWhittaker on the Ear

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The physics of the ear

Comps II Presentation

Jed WhittakerDecember 5, 2006


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Ot!ine

I" #ar anatomy

II" Oter ear resonator

III" $idd!e ear impedance matchin%

I&" Inner ear

a" 'natomy

b" Theories of coch!ear fnction

c" Tra(e!in% )a(e theory

&II" Crrent )ork

a" Physica! mode!

b" $athematica! mode!


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Ot!ine

I" #ar anatomy



I&" Inner ear

a" 'natomy



&II" Crrent )ork

a" Physica! mode!



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#ar anatomy

Oter #ar

*Resonator+http://www.nidcd.nih.gov/StaticReso

urces/health/hearing/images/normal_

ear.asp


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#ar anatomy

Oter #ar

*Resonator+

$idd!e #ar *Impedance

Matching+

http://www.nidcd.nih.gov/StaticReso


ear.asp


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#ar anatomy

Oter #ar

*Resonator+

$idd!e #ar *Impedance

Matching+

Inner #ar*Fourier

Analyzer+

http://www.nidcd.nih.gov/StaticReso


ear.asp


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#ar anatomy sbstrctres

Ossic!es

Coch!ea

#ar Drm

emicirc!ar

Cana!s

*Balance+


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Ot!ine

I" #ar anatomy



I&" Inner ear

a" 'natomy



&II" Crrent )ork

a" Physica! mode!



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The oter ear

The hman ear is

most responsi(e at

abot -,000 ./

$ost speech occrs

at abot -,000 ./


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Partia!!y c!osed pipe resonator

mode!

freency speed ofsond

mode


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Oter ear resonator

The !en%th of the hman

aditory cana! is

This %i(es a

fndamenta! mode of


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Oter ear 1

Oter ear is a !o)1 ca(ity3 other

freencies pass thro%h a!so

W. J. Mullin, W. J. George, J. P. Mestre, and S. L. Velleman, Fundamentals of sound with applicationsto speech and hearing(Allyn and Bacon, Boston, 200!


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Ot!ine

I" #ar anatomy



I&" Inner ear

a" 'natomy



&II" Crrent )ork

a" Physica! mode!



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The midd!e ear

'ir

4!id

There is an impedance

mismatch bet)een the oter and

inner ears

Withot the midd!e ear there )o!d

be !ar%e attenation at the airf!id

bondary


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Transmission and ref!ection

Transmission

Coefficient

ef!ection

Coefficient

". #. Blac$stoc$, Fundamentals of Physical Acoustics(Wiley, %e& 'or$, 2000!


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Po)er transmission

Doin% some math %i(es the po)er

transmission coefficient

P!%%in% in nmbers %i(es the attenation



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Ossic!es as !e(ersi%aments act

as f!crmse(ers increase

force by -07

To o(a! )indo)

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/imgsou/oss3.gif


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tapes footprint

http://www.ssc.education.ed.ac.uk/courses/pictures/hearing.gif

#ar drm

O(a! )indo)


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Impedance match

ince

the sond intensity increases 625

times, or 28 dB

ond intensity


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Ot!ine

I" #ar anatomy



I&" Inner ear

a" 'natomy



&II" Crrent )ork

a" Physica! mode!



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The inner earThe coch!ea transdces

sond into

e!ectrochemica! si%na!s

ond

To brain

The coch!ea is a4orier ana!y/er that

separates freency

information for the brain


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Coch!ear schematic

W. 'ost, Fundamentals of Hearing(Academic Press, San "iego, 2000!


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Wa(es on the basi!ar

membraneWa(e

amp!itde

h(x,t0)8asi!ar

membraneh(x,t1)

W. . )emiln, Speech and Hearing Science(Allyn and Bacon, Boston, *++!


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Coch!ear crosssection

.air ce!! shearin%

re!eases

nerotransmitters

8asi!ar membrane

motion transdces

sond si%na!



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.air ce!! shearin%Tectora! membrane

.air ce!!s

8asi!ar membrane

heared hairs



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.e!mho!t/9s resonance theory

*:;5


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Prob!ems )ith resonance theory

>eeded 6,000? hair ce!!s to e@p!ain

hman hearin%

On!y A-,000 hair ce!!s )ere fond

ater re(isions sed cop!ed membrane

fibers as resonatorsCoch!ear anatomy )as not )e!! kno)n

. G. Weer, Theory of Hearing(Wiley, %e& 'or$, *+5+!


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Competin% theories

Te!ephone theoryreired each hair ce!!to reprodce a!! freencies

tandin% )a(e theoryhad hair ce!!sdetectin% patterns on the basi!armembrane

Tra(e!in% )a(e theorydescribed hair ce!!sas detectin% the amp!itde of a )a(etra(e!in% a!on% the basi!ar membrane

. G. Weer, Theory of Hearing(Wiley, %e& 'or$, *+5+!


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(on 8BkBsy9s physica! mode!

G. on B6$6sy, Experiments in Hearing(McGra&7-ill, %e& 'or$, *+80!

The mode! mimicked

each of the theories

>eed!e


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(on 8BkBsy9s obser(ations

Position of peak depends

on freency

patia! freency

separation

G. on B6$6sy, Experiments in Hearing(McGra&7-ill, %e& 'or$, *+80!

a) tra(e!in% )a(es in

mamma!ian coch!eae


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Ot!ine

I" #ar anatomy



I&" Inner ear

a" 'natomy



&II" Crrent )ork

a" Physica! mode!



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Tra(e!in% )a(e description

re!ati(e pressre

re!ati(e crrent3 indced

by pressre %radients


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Pressrecrrent re!ation

Chan%in% the re!ati(e crrent in time

chan%es the re!ati(e pressre in space

f!id (iscosity

sca!a hei%htf!id density


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Incompressibi!ity

'ssmin% the f!id is incompressib!e

means that a chan%e in re!ati(e crrent

%i(es a chan%e in basi!ar membranedisp!acement h(x,t)

basi!ar membrane

disp!acement


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The )a(e eation

tiffness re!ates pressre and disp!acement

P!% this in to %et the )a(e eation


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tiffness

The stiffness of the basi!ar membrane is

described by

P!% this in to %et

G. /ret,J Acoust Soc Am85, *92 (*+9!#. "u$e and :. J;lic/er, Phys !e" #ett+0, *4*0* (200!


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o!tion

This eation separates into

We can %o no frther ana!ytica!!y

sa!!y the eation is so!(ed nmerica!!y

separation

constant


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>merica!!y %enerated p!ots

#. "u$e and :. J;lic/er, Phys !e" #ett+0, *4*0* (200!


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Ot!ine

I" #ar anatomy



I&" Inner ear

a" 'natomy



&II" Crrent )ork

a" Physica! mode!



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ecent coch!ear mode!

ife si/ei fabrication

$ass

prodcib!e

. ". W/ite and


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Data

. ". W/ite and


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Ot!ine

I" #ar anatomy



I&" Inner ear

a" 'natomy



&II" Crrent )ork

a" Physica! mode!



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ecent math mode!

Why is the coch!ea spira!ed

Data corre!ate nmber of trns to !o)freency sensiti(ity in (arios mamma!s

Pre(ios!y tho%h to ha(e no fnction

3. West,J Acoust Soc Am99, *0+* (*+4!". Manoussa$i, .


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ay!ei%h9s )hisperin% %a!!ery

orce

ond rayond

confined to

bondary

L. ayleig/, The Theory of Sound, ol. == (MacMillan and 3o., %e& 'or$, *+4!


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pira! 8ondary

a E ba

b

http://biomed.brown.edu/"ourses/#$%&/'&&(-%&websites/group%&cochlearimplant/images/greenwood_function.png


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o) freency amp!ification

ond

concentrated

at bondary

o) freencies are

transdced at the ape@

". Manoussa$i, .


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$ath mode!

o!(in% the tra(e!in% )a(e eation

thro%h a spira! coch!ea sho)s that

the sond

concentrates on

the oter )a!! of

the coch!ea

". Manoussa$i, .


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Conc!sion

The ear ses resonance, impedance

matchin%, and 4orier ana!ysis

Tra(e!in% )a(e theory most accrate!ydescribes coch!ear dynamics

Theories of coch!ear fnction are sti!!

ad(ancin% )ith physica! and mathematica!mode!s


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'ppendi@ '

Transmission


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Transmission

Coefficient

ef!ection

Coefficient

". #. Blac$stoc$, Fundamentals of Physical Acoustics(Wiley, %e& 'or$, 2000!


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se

and

to %et


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Po)er

ond intensity is the time a(era%ed

inte%ra! of pressre times (e!ocity

The po)er transmission coefficient is

then


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Po)er transmission coefficient

ince *sin% the definition of T+

the po)er transmission coefficient is


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Impedance (a!es


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Po)er transmission

Doin% some math %i(es the po)er

transmission coefficient

P!%%in% in nmbers %i(es the attenation



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'ppendi@ 8

pira! coch!ea


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Coch!ear eations

tart )ith an irrotationa! f!id of (e!ocity

(e!ocity potentia!

and )hose mass has no sorce or sink


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>a(iertokes

se a !ineari/ed momentm eation

deri(ed from the >a(iertokes eation

for an incompressib!e f!id )ith (iscosity%and ne%!i%ib!e body forces *!ike%ra(ity+


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>a(iertokes

patia!!y inte%rate and se the mass

conser(ation re!ation to %et


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Continity

Chan%e in the (e!ocity potentia! %i(es a

chan%e in the membrane disp!acement

The eation of motion for the membrane is

stiffness

dampin%

mass


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'ppendi@ C

Tra(e!in% )a(e deri(ation


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Tra(e!in% )a(e description

re!ati(e pressre

re!ati(e crrent


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Pressrecrrent re!ation

Chan%in% the re!ati(e crrent in time

chan%es the re!ati(e pressre in space

f!id (iscosity

sca!a hei%htf!id density


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Incompressibi!ity

'ssmin% the f!id is incompressib!e

means that a chan%e in re!ati(e crrent

%i(es a chan%e in basi!ar membranedisp!acement h(x,t)

basi!ar membrane

disp!acement


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Time deri(ati(e

Take the time deri(ati(e

P!% in the pressre crrent re!ation


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The )a(e eation

tiffness re!ates pressre and disp!acement

P!% this in to %et the )a(e eation


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tiffness

The stiffness of the basi!ar membrane is

described by

P!% this in to %et

G. /ret,J Acoust Soc Am85, *92 (*+9!#. "u$e and :. J;lic/er, Phys !e" #ett+0, *4*0* (200!


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o!tion

This eation separates into

We can %o no frther ana!ytica!!y

sa!!y the eation is so!(ed nmerica!!y

separation

constant


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>merica!!y %enerated p!ots

Wa(e

amp!itde

Instantaneos

position h(x,t)

JedWhittaker on the Ear

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