Cnx Physics Ch 17 Physics of Hearing

download Cnx Physics Ch 17 Physics of Hearing

of 27

Transcript of Cnx Physics Ch 17 Physics of Hearing

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    1/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KKV

    !"#$%&' )*+ $",-.!- !" $%&'(!"

    !>"# (%112 68 (6./25 841-.1/*'5 +/2 V+: ;")#=

    -"#/.+"1 j3k

    jWk *.$$# j:5"M _3#/$ +1 B3W#$ 6VD6k

    QD E",1 +"/+ +"# %#' ,B %,3-' )- /). )% KUK *7%H /%

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    2/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KKY

    \D @). +#*./+3.# )- +"# E/"/./ ]#%#.+ */.)-# 48L5 % /B+#. >#)-0 #*)++#'8 ;"/+ )% +"# ')%+/-)()+2 ,B +"# %,-/. %2%+#* +, '#+#

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    3/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KKR

    6^D @ &"2%)/+ 3%#% %,3-' #/+

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    4/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQ^

    W$.;$$1 ,3.,(+1% .($ 45$) 35"/10 .($ 1$,= "5 35"/10 .($ ,($*.I ;(+,( M$31*

    .(3. +. ,"/#0 M+** %53WW+1% +.* 45$)D

    !>"3 (6./2 )/01/()0' +/2 (6./2 ,1

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    5/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQ6

    -"#/.+"1

    6VD E",1 +"/+ /- )-+#-%)+2 ,B )% +"# %/*# /% 8

    -"#/.+"1

    6YD 9/: ;"/+ )% +"# '##( (#A#( ,B / %,3-' +"/+ )% +1):

    ;"/+ )% +"# '##( (#A#( ,B / %,3-' +"/+ )% ,-#GB)B+" /% )-+#-%# /% / P585G'[ %,3-'=

    -"#/.+"1 j3k J5"M B3W#$ 6VDGI

    jWk

    B(/*I

    6RD 9/: ;"/+ )% +"# )-+#-%)+2 ,B / %,3-' +"/+ "/% / (#A#( Q855 '[ (,1#. +"/- /

    %,3-'= 9>: ;"/+ )% +"# )-+#-%)+2 ,B / %,3-' +"/+ )% K855 '[ ")0"#.

    +"/- / %,3-'=

    -"#/.+"1 j3k F*+1% B3W#$ 6VDGI

    jWk

    @^D 9/: ?,1 *3

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    6/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQ@

    Q^D6I +D$D

    jWk B;" 6^[0$,+W$# #"**$* %+_$ .;" :3,."5* ": I "5 3 .".3# :3,."5 ": B($

    5$M3+1+1% G 0$,+W$#* %+_$ 31 300+.+"13# :3,."5 ": D -" .($ 53.+" +* 3 :3,."5 ":

    +D$D

    @6D c#,&(# 1)+" 0,,' "#/.)-0 (# #BB#

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    7/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQG

    @QD CB / %,3-' )-+#-%)+2 (#A#( ,B 5 '[ /+ 4555 ?I 3+ +"# +.3*+ ,-(2 "/%

    /- #BB)

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    8/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQK

    jWk B(+* +1,5$3*$ ": 3445"L+M3.$#) @^ 09 +1,5$3*$* .($ *"/10 ": 3 1"5M3#

    ,"1_$5*3.+"1 ." .(3. ": 3 #"/0 530+" "5 ,#3**5""M #$,./5$ j*$$ B3W#$ 6VD@kD J"5

    *"M$"1$ ;(" ,311". ($35 3. 3##I .(+* ;+## 1". W$ ($#4:/#I W/. :"5 *"M$"1$ ;(" +*

    *.35.+1% ." #"*$ .($+5 3W+#+.) ." ($35I +. M3) ($#4D F1:"5./13.$#)I $35 .5/M4$.* 35$

    _$5) ,/MW$5*"M$I *" $_$1 .("/%( .($) ,"/#0 ($#4I .($ +1,"1_$1+$1,$ M3=$*.($M 53.($5 +M453,.+,3#D

    @YD E,3-' )% *,.# #BB##)-0 (# +, /%%3*# +"/+ %,3-' )% +./-%*)++#' )-+, /

    %+#+",%2 / %+#+",%2 / .%,- 1/+: ;"/+ B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    9/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQQ

    jWk

    G6D 9/: @+ /- /). %",1 / d#+ B()#% ').#%#.A#.%= 9>: ;"/+ B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    10/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQ\

    GKD @ (,1% )+% L55G?I ",.- /% )+ /&&.,/%#.A#. 1/)+)-0 /+ +"#

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    11/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQV

    GVD ;"/+ )% +"# *)-)*3* %#' /+ 1")./%% ",.-% +"/+ /.# %3&&,%#' +, &.,'3#/+ B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    12/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQY

    W$3.* 3W"_$I ;$ 3#*" (3_$A

    K^D ;"/+ >#/+ B.#J3#-,+" #-'%H ,-

    / '/2 1"#- +"# %#' ,B %,3-' )% KUU *7%= 9>: ;"/+ )% +"# B.#J3#-#8:

    Hz77Hz220Hz297;Hz33Hz264Hz297

    ;Hz88=Hz264Hz352=

    ;Hz132=Hz220Hz352=

    A&DB,

    C&DB,

    C&FB,

    A&FB,

    =!=

    =

    !

    =

    !

    !

    ff

    f

    f

    Hz0.3Hz127.8Hz128.1;Hz0.5Hz127.8Hz128.3

    ;Hz0.2Hz128.1Hz128.3

    21B

    =!

    =!

    =!

    != fff

    21

    B

    BHz005.0

    00.2

    11ff

    Tf !====

    Hz256m)2(0.672

    m/s34432,1,=for

    21

    w==!"

    #

    $%&

    '= fn

    L

    vnfn

    Hz512=Hz)(2562=2 1f

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    13/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KQR

    -"#/.+"1

    KKD ;"/+ /.# +"# B).%+ +".## ,A#.+,-#% ,B / >/%%,,- +"/+ "/% / B3-'/*#-+/( B.#J3#-,+" #-'%8 9!"# ,A#.+,-#% ,B / .#/( >/%%,,- /.# *,.# ## )- ,.'#. +, "/A# / B3-'/*#-+/( B.#J3#-,# "/A# +, &.,'3,+" #-'%8

    Hz.32.04

    53,1,=for4

    1

    ww==!"

    #

    $%&

    '= f

    L

    vn

    L

    vnfn

    Hz224Hz)7(32.0overtonethird

    ;Hz160Hz)5(32.0=overtonesecond

    ;Hz96.0Hz)3(32.0=overtonefirst

    7

    5

    3

    ===

    ==

    ==

    f

    f

    f

    Hz90.02

    32,1,=for2

    1 ==!"#$%

    &'= fL

    vn

    L

    vnfn

    Hz360Hz)4(90.0overtonethird

    ;Hz270Hz)3(90.0=overtonesecond

    ;Hz180Hz)2(90.0=overtonefirst

    4

    3

    2

    ===

    ==

    ==

    f

    f

    f

    C0.20

    ....,3,2,1for2

    =!"

    #$%

    &= n

    L

    vnfn

    1

    ww

    1

    22 f

    vL

    L

    vf =!=

    m/s.342.9K273

    K293m/s)(331

    K273

    (K)m/s)(331w ===

    Tv

    cm65.4m0.654Hz)2(262

    m/s342.9===L

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    14/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\^

    -"#/.+"1

    KVD ;"/+ )% +"# (#-0+" ,B / +3># +"/+ "/% / B3-'/*#-+/( B.#J3#-: ;"/+ )% )+% B3-'/*#-+/(

    B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    15/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\6

    -"#/.+"1

    Q^D !"# #/. #

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    16/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\@

    -"#/.+"1

    C$L.I *" .(3.A

    B($ $35 +* 1". 435.+,/#35#) *$1*+.+_$ ." .(+* :5$T/$1,)I *" ;$ 0"1]. ($35 "_$5."1$* 0/$

    ." .($ $35 ,313#D

    Q@D @ # )% 58LU5G* (,-0H >2 +/6)-0 /). +#*./+3.# +, >#

    = 9>: ;"/+ 1,3(' +")% B.#J3#-#: @+ 1"/+ (#-0+" 1)(( +"#2 ,>%#.A# +"#

    %#

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    17/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\G

    -"#/.+"1j3k

    J+5*. 5$*"131,$ +* 3. .($ :/103M$1.3#I *" I 310

    jWk B($ *$,"10 5$*"131,$ ",,/5* 3. .(5$$ .+M$* .($ :+5*. 5$*"131,$A

    QKD ;"/+ B.#J3#-# &.,'3# )% : C+ )% ,- /+ >,+" #-'%=

    -"#/.+"1j3k

    -+1,$ M/*. W$ 31 "00 1/MW$5I +* K6R "5 K@6 j0$4$10+1% "1 .($

    +10+_+0/3#kD

    jWk

    !>"X &1+4)/7

    QQD !"# B/#=

    Hz2564

    .....5,3,1for4

    w

    1

    w==!="

    #

    $%&

    '=

    L

    vfn

    L

    vnfn

    K273

    (K)m/s)(3314 1w

    TLfv ==

    C22.0K295m/s)(331

    K)(273Hz)(256m)(16)(0.336

    m/s)(331

    K)(273162

    22

    2

    2

    1

    2

    ==== fL

    T

    ( ) m01.1m336.033 ==L

    C0.20

    9.419Hz47.63

    Hz20,000

    ...1,3,forHz)(47.63m)4(1.80

    m/s342.9

    4

    m/s.342.9K273

    K293m/s)(331

    K273

    (K)m/s)(331

    max

    w

    w

    ==

    ==!!"

    #$$%

    &=!

    "

    #$%

    &=

    ===

    n

    nnnL

    vnf

    Tv

    n

    nmax

    n

    21097.209Hz95.25

    Hz20,000

    ...3,1,2,forHz)(95.25m)2(1.80

    m/s342.9

    2

    max

    w

    ===

    ==!!"

    #$$%

    &=!

    "

    #$%

    &=

    n

    nnnL

    vnfn

    1210

    !

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    18/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\K

    -"#/.+"1

    Q\D !"# B.#J3#-2 +"# %/*# B/# +"# %(,1#%+ -,-I#., %#' )+

    #)-0 ')BB#.#-+ )- B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    19/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\Q

    \6D [/%#' ,- +"# 0./&" )- \)03.# 4Q8KOH 1"/+ )% +"# +".#%",(' ,B "#/.)-0 )- '##(% B,.

    B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    20/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\\

    -"#/.+"1 j3k J5"M J+%/5$ 6VDG\I

    jWk J5"M J+%/5$ 6VDG\I

    j,k J5"M J+%/5$ 6VDG\I

    \QD E3&&,%# / .%,- "/% / N5G'[ "#/.)-0 (,%% /+ /(( B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    21/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\V

    -"#/.+"1 n :+_$ :3,."5* ": 6^ 4#/* "1$ :3,."5 ": QD ?1 0$,+W$#*I .(+* +*

    j*$$ B3W#$ 6VDGkD

    \VD 9/: ;"/+ )% +"# )-+#-%)+2 )- 1/++% . *#+#. %J3/.#' ,B / d3%+ >/.#(2 /3')>(# L55G?I%,3-'= 9>: ;"/+ )% +"# )-+#-%)+2 )- 1/++% . *#+#. %J3/.#' ,B / >/.#(2 /3')>(# U555G

    ?I %,3-'=

    -"#/.+"1 j3k H. @^^ ceI

    F*+1% B3W#$ 6VDGI @G 09 +* .;+,$ j@D^^k .($ +1.$1*+.) ": @^ 09D J5"M B3W#$ 6VD@I

    !"

    !" ! !!!"!!"!"!!!B(/*I ! ! !!!"!"!"!! !!!! !!!!"!"!"!!

    jWk H. K^^^ ceI

    fV 09 +* .($ +1.$1*+.) ": ^ 09D B(/*I

    ! !!!!"

    !!"!"!!

    !!!!!!!!"!!"!"!!

    \YD 9/: \)-' +"# )-+#-%)+2 )- 1/++% . *#+#. %J3/.#' ,B / O585G?I %,3-' "/A)-0 / (,3'-#%%

    ,B O5 &",-%8 9>: \)-' +"# )-+#-%)+2 )- 1/++% . *#+#. %J3/.#' ,B / 45H555G?I %,3-'

    "/A)-0 / (,3'-#%% ,B O5 &",-%8

    -"#/.+"1 j3k F*+1% J+%/5$ 6VDG\I 3 \^D^ ce *"/10 3. \^ 4("1* (3* 3 *"/10 #$_$# ":

    QD^^ .+M$* .($ +1.$1*+.) ": V^ 09D

    jWk F*+1% J+%/5$ 6VDG\I .+M$* .($ +1.$1*+.) ": V^ 09D

    \RD @ .%,- "/% / "#/.)-0 +".#%",(' 45 '[ />,A# -,.*/( /+ 455 ?I /-' N5 '[ />,A#-,.*/( /+ U555 ?I8 ?,1 *3/.#(2 /3')>(# +, +")% .%,-=

    -"#/.+"1 J5"M J+%/5$ 6VDG\I .($ ^ 4("1* #+1$ +* 1"5M3# ($35+1%D -"I .(+* 4$5*"1 ,31 W35$#) ($35

    3 6^^ ce *"/10 3. 6^ 09 3W"_$ 1"5M3#I 5$T/+5+1% 3 KV 09 *"/10 #$_$# j kD J"5 3 K^^^

    5100.5 !

    dB57dB7dB50 =+

    dB23phons0 =

    dB7phons0 !=

    !"

    #$%

    &

    00.5

    1

    5

    1

    =!= IdB77"

    2525 W/m105.00)W/m10(15.00 !! "=""=I

    2dB72 !"= I#

    2525 W/m102)W/m10(12 !! "=""=I

    1!

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    22/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    K\Y

    ce *"/10I .(+* 4$5*"1 5$T/+5$* Q^ 09 3W"_$ 1"5M3#I "5 3 KG 09 *"/10 #$_$# j k ." W$

    3/0+W#$D -"I .($ 6^^ ce ."1$ M/*. W$ K 09 (+%($5 .(31 .($ K^^^ ce *"/10D B"

    ,3#,/#3.$ .($ 0+::$5$1,$ +1 +1.$1*+.)I /*$ .($ $T/3.+"1

    310 ,"1_$5. .($ 0+::$5$1,$ +1 0$,+W$#* ." 3 53.+" ":

    +1.$1*+.+$*D

    -" .($ 6^^ ce ."1$ M/*. W$ @DQ .+M$* M"5$ +1.$1*$ .(31 .($ K^^^ ce *"/10 ." W$

    3/0+W#$ W) .(+* 4$5*"1D

    V^D @ ,+" >/.#(2 /3')>(# +, +"# .,04+(6./2

    2!

    !!"

    #

    $$%

    &'

    !!"

    #

    $$%

    &='

    0

    2

    0

    1

    21

    log10log10I

    I

    I

    I((

    2.510ordB,4dB43dB47

    log10log10log10

    4/10

    2

    1

    2

    1

    0

    2

    0

    121

    ===!=

    ""#

    $%%&

    '=""

    #

    $%%&

    '!""

    #

    $%%&

    '=!

    I

    I

    I

    I

    I

    I

    I

    I((

    1!

    2!

    445/10

    2

    1

    2

    1

    0

    2

    0

    1

    21

    103.1610

    thatso,log10log10log10451055

    !==

    ""#

    $

    %%&

    '=

    ""#

    $

    %%&

    '(

    ""#

    $

    %%&

    '==(=(

    I

    I

    I

    I

    I

    I

    I

    I))

    26.110log10log10log101 10/1

    2

    1

    2

    1

    0

    2

    0

    121 ==!""

    #

    $%%&

    '=""

    #

    $%%&

    '(""#

    $%%&

    '==(

    I

    I

    I

    I

    I

    I

    I

    I))

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    23/27

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    24/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KV^

    -"#/.+"1F*$ B3W#$ 6VDQ:"5 _3#/$* 310 .($ $T/3.+"1 :"5 D

    j3k I *" 6^^m 5$:#$,.$0D

    jWk

    j,k Z$# +* /*$0 ." :3,+#+.3.$ .($ .531*M+**+"1 ": .($ /#.53*"/10 W$.;$$1 .($ .531*0/,$5

    310 .($ 43.+$1.p* W"0)D

    VVD 9/: W/(,3+ K855

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    25/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KV6

    VRD 9/: S2 = 9>: ;"/+ *)-)*3* B.#J3#-

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    26/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KV@

    -"#/.+"1j3k H**/M$ 310 .($5$:"5$ *+1,$

    jWk C"I *+1,$ 0""5* 35$ ;+0$5 .(31 6V ,MI .(+* 0"$* 1". $L4#3+1 ;() W3.* ,311". %$.

    "/. ": ("/*$* *+1,$ .($+5 5$*"#/.+"1 +* %5$3. $1"/%( ." :+10 .($ "4$1+1%D

    Y@D @ ',(&")- )% />(# +, +#(( )- +"# '/.6 +"/+ +"# 3(+./%,3-' #2 K8N5 *H

    ,-# >#)-0 +"/+ *32 )+% 1/A#(#-0+"8 9>: CB +")%

    />)()+2 )% '3# +, +"# ',(&")-T% />)()+2 +, '#+#

  • 8/9/2019 Cnx Physics Ch 17 Physics of Hearing

    27/27

    !"##$%$ '()*+,* ?1*.5/,."5 -"#/.+"1* 231/3# !(34.$5 6V

    KVG

    3445"3,(+1%k %+_$* .($ :5$T/$1,) 5$,$+_$0 W) .($ *,311$5A

    -"#_+1% :"5 .($ *4$$0 ": W#""0 %+_$*A

    YKD Y(+./%,3-' .#B(#