TD 6 : surpression, impédance, application à l`oreille

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45'6'7'-)0.02--+/89'+:.;<=8>29'=..,+>=*+/8'?',@/02+,,2'
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Exercices(encadrés(
(
Exercice(1(:(Relation(déplacement-intensité-surpression(
(8'>/8-+<A02')82'/8<2'-/8/029'.,=829'.0/102--+B29'-+8)-/C<=,29'-2'.0/.=12=8*'<=8-')8':+,+2)D'E2'
<;.,=>2:28*',/>=,'<2-':/,;>),2-'<)':+,+2)'-@;>0+*'-/)-',='F/0:2'7(
𝑢𝑥,𝑡=𝑢!sin(
2𝜋
𝜆(𝑥−𝑐𝑡))'
'
/G')"'2-*',@=:.,+*)<29'H'2-*',=',/81)2)0'<@/8<2'2*'>',='>;,;0+*;'<2',@/8<2D'
ID J=..2,20',='02,=*+/8',+=8*',='>;,;0+*;'<2',@/8<2'>'=B2>'H'2*'F'K,='F0;L)28>2'<2',@/8<2MD'
3D'N=,>),20',='B+*2--2'<2-':/,;>),2-'𝑣𝑥,𝑡'2*'2O.0+:20'-/8'=:.,+*)<2'𝑣!'28'F/8>*+/8'<2'𝑢!'2*'FD'
!D (8'=..2,,2'𝑍=𝜌𝑐',@+:.;<=8>2'=>/)-*+L)2'<)':+,+2)9'/G'P'2-*',=':=--2'B/,):+L)2'<)':+,+2)D'
Q)2,,2'2-*',='<+:28-+/8'<2'Z'R'S8'<;<)+02'-2-')8+*;-D'
TD N=,>),20',@+:.;<=8>2'<2',@2=)'28'-=>U=8*'L)2',='>;,;0+*;'<)'-/8'<=8-',@2=)'2-*''>2=)'V'IW""':D-XI'
KB/)-'<2B2Y'>/88=Z*02',=':=--2'B/,):+L)2'<2',@2=)'[MD'''
WD \=0'=8=,]-2'<+:28-+/882,,29'2O.0+:20',@+8*28-+*;'<2',@/8<2'28'F/8>*+/8'<2',@+:.;<=8>2'Z'2*'<2'
,@=:.,+*)<2'<2',='B+*2--2'<2-'.=0*+>),2-'𝑣!'?')8'F=>*2)0'8):;0+L)2'.0A-D'
E@+8*28-+*;'-/8/02'[email protected]+:2'28'F=+*'<2',='F=^/8'-)+B=8*2'7'
𝐼=
1
2𝑍𝑣!
!'
E='-)0.02--+/8'𝑝(𝑥,𝑡)'>0;;2'.=0',2'<;.,=>2:28*'<2-':/,;>),2-'2-*'.0/./0*+/882,,2'?',='B+*2--2'<2'
>2,,2-X>+'7'
𝑝𝑥,𝑡=𝑍𝑣(𝑥,𝑡)'
6D'SO.0+:20',@+8*28-+*;'-/8/02'_'28'F/8>*+/8'<2'𝑍'2*'<2'𝑝!'=:.,+*)<2'<2',='-)0.02--+/8D'
`D'a'*2:.;0=*)02'=:b+=8*29'c=+0'V'TIW'd1D:X3D-XID'E@=:.,+*)<2'<2'-)0.02--+/8':=O+:=,2'-)../0*=b,2'
.=0',@/02+,,2'U):=+82'2-*'<@28B+0/8'3e'\=D'a'L)2,,2'+8*28-+*;'-/8/02'>2,='>/002-./8<X+,'R'Q)2,'2-*',2'
8+B2=)'-/8/02'=--/>+;'R'
eD' Q)2,,2' 2-*' ,=' B+*2--2' <2' <;.,=>2:28*' <2-' :/,;>),2-' <@=+0'𝑣!R' f' L)2,,2' =:.,+*)<2'𝑢!'<)'
<;.,=>2:28*'<2-':/,;>),2-'>2,='>/002-./8<X+,9'?')82'F0;L)28>2'<2'W'dgY'R''
hD'E@=+02'<)'*]:.=8'2-*'28B+0/8'"9e'>:3D'Q)2,,2'2-*',='F/0>2'2O20>;2'-)0',2'*]:.=8',/0-'<)'.=--=12'
<2'>2**2'/8<2'K82'.=-'/)b,+20'<2'>/8B20*+0',2-'>:3'[M'R'
'
Exercice(2(:(Réflexion/réfraction(d’une(onde(sonore(
E/0-L)i)82'/8<2' -/8/02'*0=B20-2' )82'+8*20F=>2' 28*02'<2)O' :+,+2)O'<2' :=--2'B/,):+L)2' 2*'=B2>'
<2-'>;,;0+*;-'<+FF;028*2-9',i/8<2'B='j*02'.=0*+2,,2:28*'*0=8-:+-2'2*'0;F,;>U+2D''

ID'E2'>/2FF+>+28*'<2'0;F,2O+/8'28'+8*28-+*;'[email protected]+:2'28'F/8>*+/8'<2-'+:.;<=8>2-'=>/)-*+L)2-'<2-'
<2)O':+,+2)O'𝑅=!!
!!
=(!!!!!)!
(!!!!!)!D'S8')*+,+-=8*',='>/8-20B=*+/8'<2',@;8201+29'28'<;<)+02',i2O.02--+/8'<)'
>/2FF+>+28*'<2'*0=8-:+--+/8'28'+8*28-+*;'𝑇=!!
!!
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3D'(8'>/8-+<A02')82'/8<2'-/8/02'-2'.0/.=12=8*'?',i+8*20F=>2'28*02'<2)O':+,+2)OD''
40/)B20')82'2O.02--+/8'=..0/>U;2'<2'4'2*'<2'J'<=8-',2-'*0/+-'>=-'-)+B=8*-7'
X'𝑍!≈𝑍!''
X'𝑍!≫𝑍!''
X'𝑍!≫𝑍!''
N=,>),20'8):;0+L)2:28*'4'2*'J'<=8-',2'>=-'<@)82'+8*20F=>2'28*02',@2=)'2*',@=+0D'
!D'N/8>,)02'-)0',='8;>2--+*;'<i)82'=<=.*=*+/8'<i+:.;<=8>2'-+'/8'B2)*'L)@)82'/8<2'-/+*'*0=8-:+-2'
-=8-'*0/.'<2'.20*2-'=)'.=--=12'=+0X2=)'/)'2=)X=+0D'
TD'SO.,+L)20'./)0L)/+',/0-'<i)82';>U/10=.U+29')8'12,'2-*'.,=>;'28*02',2'*0=8-<)>*2)0'KL)+';:2*'2*'
02^/+*',i/8<2'),*0=-/8/02M'2*',='.2=)'<)'.=*+28*D'
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Exercices(en(autonomie(
(
Exercice(3(:(Comparaison(air/eau(
1. %+',2-'=:.,+*)<2-'<2'-)0.02--+/8'-/8*',2-':j:2-'./)0'<2)O'/8<2-'-/8/02-'-2'.0/.=12=8*',@)82'
<=8-',@=+0'2*',@=)*02'<=8-',@2=)9'L)2,'2-*',2'0=../0*'<2-'+8*28-+*;-'<2'>2-'<2)O'/8<2-'R'
2. %+'<2)O'-/8-'/8*',=':j:2'+8*28-+*;'<=8-',@=+0'2*'<=8-',@2=)9'L)2,'2-*',2'0=../0*'<2-'-)0.02--+/8-'
=--/>+;2-'R''
'
Exercice(4(:(intensité,(surpression(et(déplacement(
E2'<;.,=>2:28*'<2-':/,;>),2-'<@2=)'=--/>+;'?')82'/8<2'-/8/02'-2'.0/.=12=8*'<=8-',@2=)9'=',='
F/0:2'-)+B=8*27'𝑢(𝑥,𝑡)=𝑢!sin !!
! (𝑥−𝑐!"# 𝑡)D'(8'.028<0='𝑢!=1'8:9 𝜆=200'>:'2*'
𝑐!"# =1500 m/sD'
ID'Q)2,,2'2-*',='F0;L)28>2'<)'-/8'R'
3D'Q)2,,2'2-*',i2O.02--+/8'<2',='B+*2--2'<2'<;.,=>2:28*'<i)82':/,;>),2'<i2=)'R'N=,>),20',@=:.,+*)<2'
<2',='B+*2--2D'
!D'N=,>),20',i=:.,+*)<2'<2',='-)0.02--+/8'<2',i/8<2'+8>+<28*2D'
'
Exercice(5(:(Passage(air/eau(
(8'-@+8*;02--2'=)'.=--=12'<)'-/8'<2',@2=)'B20-',@=+0D'
ID N=,>),20',2-'+:.;<=8>2-'<2',@2=)'2*'<2',@=+09'c2=)'2*'c=+0D'
3D S8'<;<)+02',2'./)0>28*=12'<@;8201+2'*0=8-:+-2',/0-'<)'.=--=12'<2',@2=)'?',@=+0D'Q)2'<2B+28*',='
F0=>*+/8'02-*=8*2'<2',@;8201+2'R'
3. N=,>),20',@=**;8)=*+/8'<)'-/8'K28'<#M',/0-'<)'.=--=12'<2',@=+0'?',@2=)D

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Exercices(d’approfondissement(
Exercice(6(:(L’oreille(humaine((
Ei/02+,,2'U):=+82'2-*'F/0:;2'<2'*0/+-'>/:./-=8*2-'7',i/02+,,2'2O*20829',i/02+,,2':/]2882'2*',i/02+,,2'
+8*2082D'k/)-'8/)-'+8*;02--20/8-'<=8-'>2*'2O20>+>2')8+L)2:28*'=)O'<2)O'.02:+A02-'>/:./-=8*2-''
K,2'F/8>*+/882:28*'<2',@/02+,,2'+8*20829'L)+'>/8B20*+*',@/8<2'-/8/02'28'-+18=,';,2>*0+L)29'B/)-'-20='
<;*=+,,;'28'>/)0-MD'
E/0-'<2',='.0/.=1=*+/8'<@)82'/8<2'-/8/02'<=8-',@/02+,,29',@/8<2'.=--2'<2',@=+0'?',@2=)'=)'8+B2=)'<2'
,='F28j*02'/B=,2'<2',='>/>U,;2D'(8'8/*2'_>X',='B=,2)0'<2',@+8*28-+*;'<2',@/8<2'l)-*2'<2B=8*',='F28j*02'
/B=,2'K<=8-',@=+0M'2*'_>m',='B=,2)0'<2',@+8*28-+*;'l)-*2'=.0A-',='F28j*02'/B=,2'K<=8-',@2=)MD'
ID'Q)2,,2'2-*',='B=,2)0'<)'0=../0*'!!!
!c-
',/0-'<)'.=--=12'=+0X2=)'R'
A) L'oreille(externe(''
(8'-)../-2'L)2',2'.=B+,,/8'<2',i/02+,,2'=')82'-)0F=>2'f.D'Ei/02+,,2'2-*'-/):+-2'?')8'-/8'<i+8*28-+*;'_+'
?',i28*0;2'<)'.=B+,,/8D'
3D'SO.0+:20',='.)+--=8>2'=>/)-*+L)2'>/,,2>*;2'.=0',2'.=B+,,/8'𝒫D'
!D' S8' -)../-=8*' L)i+,' 8i]' =' .=-' <2' .20*2' <i;8201+2' ,2' ,/81' <)' >=8=,' =)<+*+F9' 2O.0+:20' ,i+8*28-+*;'
=>/)-*+L)2'_*D=)'8+B2=)'<)'*]:.=89'<2'-)0F=>2'f*'28'F/8>*+/8'<2',i+8*28-+*;'+8>+<28*29'_+D''
TD'SO.0+:20',='-)0.02--+/8'=>/)-*+L)2'=)'8+B2=)'<)'*]:.=8'.*D'
B) L'oreille(moyenne(((
Ei/02+,,2':/]2882'.20:2*'<2'0;=,+-20')82'n'=<=.*=*+/8'<i+:.;<=8>2'o'28*02',@/02+,,2'2O*2082'K=+0M'
2*',@/02+,,2'+8*2082'K2=)MD'52)O':;>=8+-:2-'.20:2**28*'<@=:.,+F+20',='-)0.02--+/89'=B=8*',@28*0;2'
<=8-',@/02+,,2'+8*2082'7''
X')8'b0=-'<2',2B+20'F=+-=8*'+8*20B28+0'*0/+-'/--2,2*-':/b+,2-9',2':=0*2=)9',i28>,):2'2*',i;*0+209'B/+0'
F+1)02' >+X<2--/)-D' f+8-+' ,=' F/0>2' -@2O20^=8*' -)0' ,=' F28j*02' /B=,2' p>' 2-*' .,)-' 10=8<2' L)2' ,=' F/0>2'
-@2O20^=8*'-)0',2'*]:.=8'p*7'p>VIDWp*D'
X')8'0=../0*'<2'-)0F=>2'+:./0*=8*'28*02',2'*]:.=8'2*',='F28j*02'/B=,29'f*qf>V!"D''
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WD' 40/)B20' ,i2O.02--+/8' <2' ,=' -)0.02--+/8' =>/)-*+L)2' -)0' ,=' F28j*02' /B=,2' <2' ,=' >/>U,;2' .>9' 28'
F/8>*+/8'<2',='-)0.02--+/8'=>/)-*+L)2'=)'8+B2=)'<)'*]:.=8'.*9'<2',='-)0F=>2'<)'*]:.=8'f*'2*'<2',='
-)0F=>2'<2',='F28j*02'/B=,2'f>D'
6D'S8'<;<)+02',i2O.02--+/8'<2',i+8*28-+*;'=)'8+B2=)'<2',='F28j*02'/B=,29'_>'28'F/8>*+/8'<2'_+9'+8*28-+*;'
?',i28*0;2'<)'.=B+,,/8D'
`D'N=,>),20'8):;0+L)2:28*',2'0=../0*'<i=:.,+F+>=*+/8'_>q_+9'28'.028=8*7'f.qf*VI"'2*'f*qf>V!"D'
eD'S-*'>2'L)2'>2'1=+8'.20:2*'<2'>/:.28-20',='.20*2'<@=:.,+*)<2'<)2'=)'.=--=12'<2',@/8<2'-/8/02'
<2',@=+0'K<2B=8*',='F28j*02'/B=,2M'?',@2=)'K<200+A02',='F28j*02'/B=,2M'R'