Content uploaded by David Olson
Author content
All content in this area was uploaded by David Olson on Dec 13, 2019
Content may be subject to copyright.
!
!
!
!
"#$%&'()#*!#+!,(++-'-*.!.-/0*(12-)!#+!
.0-'$&3!$#,(+(/&.(#*4!!
'-5&',(*5!.0-!($%'#6-$-*.!#+!!
&/#2).(/&3!%'#%-'.(-)!#+!!
'-)#*&*.!)#2*,7#&',!$&.-'(&3!
!
!
8/(-*.(+(/!9-%#'.!!
!
7:!#',-'!#+!;&/(+(/!9($!<#*-=##,)!>*/?!
!
!
!
!
!
!
!
!
!
!
!
!
@-'7).!A?4!"3&2,-'!B?4!8&**-!C?4!;+'(-$!D?!EFGHI!
!
J(.0!)%-/(&3!.0&*K)!.#!F#'7-3.!G?!EC;>I!
!
!
! !
!
L!
Abstract(
!
>*!.0-!%'-)-*.!=#'K!,(++-'-*.!.-/0*(/)!#+!.0-'$&3!$#,(+(/&.(#*!E<CI!=-'-!/#$%&'-,?!>.!
=&)! '-6(-=-,! 0#=! .0-! .0-'$&3! .'-&.$-*.! (*+32-*/-)! .0-! )#2*,! %'#%-'.(-)! #+! 8(.K&!
)%'2/-!)&$%3-)!+#'!52(.&'!)#2*,7#&',)?!<0-'-+#'-!*&.2'&3!+'-12-*/(-)!&*,!,&$%(*5!=&)!
$-&)2'-,! 7:! &/#2).(/! '-)#*&*/-! &*&3:)()?! J(.0! .0()! ,&.&! -3&).(/! /#*).&*.)! =-'-!
/&3/23&.-,!(*!.0-!3#*5(.2,(*&3! &*,!'&,(&3!,($-*)(#*?!D33!.'-&.$-*.)!(*/'-&)-,!.0-!)#2*,!
12&3(.:4! ,-+(*-,! &)! &! 0(50-'! '&.(#! #+! ).(++*-))! &*,! ,-*)(.:?! D.! .0-! )&$-! .($-! )#$-!
.'-&.$-*.)! &/0(-6-,! &! 3#=-'! ,&$%(*5?! J(.0(*! &! '&*K(*5! .0-! $-.0#,! #+! .'-&.$-*.! L!
&/0(-6-,!.0-!7-).!'-)23.)?!
!
!
1.(Introduction(
!
<C!&7#6-!MNOP"!/&2)-)!%&'.(&3!,-5'&,&.(#*)!#+!/-33!=&33!/#$%#*-*.)4!=0(/0!&'-!%'($&':!
0-$(/-3323#)-)?! <0()! -++-/.)! 3#=-'! =&.-'! )#'%.(#*! &*,! ($%'#6-)! ,($-*)(#*&3! ).&7(3(.:!
&*,! 7(#3#5(/&3! ,2'&7(3(.:!EF(33! LOOQI?! H&'3:! -6&32&.(#*)! #+! .0-'$&3! .'-&.$-*.)! EMLOR
MSOP"I!+#'!$2)(/&3!(*).'2$-*.)!=-'-!&))-))-,!&)!2*)2(.&73-!ET&,,4!,UD'/:!MVWQI?!B&.-'4!
-X.-*)(6-!).2,(-)!=(.0!0(50-'!.-$%-'&.2'-)!&.!<Y!A'-),-*!)0#=-,!/3-&'!>$%'#6-$-*.)!
#+! .0-! )#2*,! 12&3(.:4! -)%-/(&33:! +#'! '-)#*&*/-! )#2*,7#&',)4! /#$%&'-,! .#! 2*.'-&.-,!
=##,!E;+'(-$! LOOQ4!H(/0-37-'5-'! LOON4!T'#.0-! LOONI?!<0-)-! =#'K)!%'#%#)-,! .0-'$&3!
.'-&.$-*.)!7-.=--*!MWOP"!&*,!LLOP"!+#'!&*!&,Z2).$-*.!#+!7-..-'!'&.(#!#+!.0-!$#,232)!#+!
-3&).(/(.:!EC[HI!&*,!.0-!,-*)(.:4!/&2)-,!7:!.0-!,-*)(.:!'-,2/.(#*?!D!$&))!3#))!(*!.2'*4!7:!
*#.!.#2/0(*5!.0-!).(++*-))4!=&3K)!&3#*5!=(.0!&!7-..-'!.'&*)$())(#*!#+!.0-!6(7'&.(#*!-*-'5:!
\! .0-! ,&$%(*5?! [*! .0-! #.0-'! 0&*,! .0-! '-)23.)!)0#=-,! .0&.! .0-! 7-*,(*5! ).'-*5.0!
,-/'-&)-)! =(.0! 0(50-'! 5'&,-)! #+! $#,(+(/&.(#*! E@&2-'4! ;+'(-$! LOMOI?! 8-6-'&3!&*&3:)()!
,()/#6-'-,!&*!(*/'-&)(*5!C[H!&.!'-3&.(6-3:!$(3,!.'-&.$-*.)! &'#2*,!MQORMWOP"! E;+'(-$!
LOO]4!^27#Z($&!et#al.!ELOOOI4!J&5-*+_0'!et#al.!LOON4!@&2-'! et#al.!LOMQI?![`D<DaD!et#al!
ELOOOI!/'-&.-,! &! $#,-3! +#'! .0-! 7-..-'! 2*,-').&*,(*5! #+! .0-! '-3&.(#*)0(%! 7-.=--*! .0-!
+(7-'R$&.'(X!).'2/.2'-!&*,!.0-!6(7'&.(#*&3!%'#%-'.(-)?!`&)-,!#*!.0&.!$#,-3!.0-:!&))2$-!
.0&.!3#=R5'&,-!=##,!/&**#.!7-!/#*6-'.-,!.#! 0(50R5'&,-! #*-4! 7-/&2)-!#+!&!'-,2/.(#*!#+!
.0-!&*()#.'#%(/!%'#%-'.(-)!,2-!.#!/0-$(/&3!.'-&.$-*.)?!JDTHGbcF9!ELOONI!/#*+('$-,!
.0&.! .0-'$&3! $#,(+(/&.(#*! 5(6-)! 0(50-'! &/#2).(/&3! ($%'#6-$-*.)! +#'! 5##,! 12&3(.:!
'-)#*&*/-! $&.-'(&3?! H$7-,,-,! (*! .0&.! /#*.-X.! (*! .0()! ).2,:! 0(50! 12&3(.:! $&.-'(&3! +#'!
)#2*,7#&',)! =&)! $#,(+(-,! 7:! $(3,! .'-&.$-*.)! &.! '-3&.(6-3:! 3#=! .-$%-'&.2'-)! EMQOPR
M]NPI!.#! &/0(-6-! &*! ($%'#6-,! '&.(#! #+! ).(++*-))! &*,! ,-*)(.:! &*,! &! 3#=-'! ,&$%(*5?! D!
/#$%&'()#*! #+! $#,(+(/&.(#*)4! '&*! 7:! +#2'! $&*2+&/.2'-')4! =&)! $&,-! 7:! $-&)2'(*5! .0-!
&/#2).(/&3!%-'+#'$&*/-!7-+#'-!&*,!&+.-'!.0-!.'-&.$-*.)?!
!
!
2.(Materials(and(methods((
!
L?M!<'-&.$-*.)!
!
<0-! &($! #+! .0()! ).2,:! ()! .#! +(*,! .0-! '(50.! .'-&.$-*.! &*,! .-/0*#3#5:! #+! .0-'$&3!
$#,(+(/&.(#*!+#'! ($%'#6(*5! )#2*,!%'#%-'.(-)! #+!=##,! +#'! 52(.&'!)#2*,7#&',)?! b#'!.0()!
/#$%&'()#*4! .=#! /#$%&*(-)! &*,! .=#! )/(-*.(+(/! (*).(.2.(#*)! =(.0! '-)-&'/0! K(3*)!
%-'+#'$-,!.0-'$&3!.'-&.$-*.)!#*!=##,!)&$%3-)!(*!&!Z#(*.!'-)-&'/0!%'#Z-/.?!<0-)-!=-'-d!!
!
!
S!
!
• %'#/-))!eMd!f&'.-K!>*6-).![:!Eb(*3&*,I!
!
• %'#/-))!eLd!b('$#B(*!<-/0*#3#5(-)!`?g?!EG-.0-'3&*,)I!
!
• %'#/-))!eSd!"G9R>gDB8D!<'--)!&*,!<($7-'!>*).(.2.-!E>.&3:I!
!
• %'#/-))! ehieNd! Y*(6-')(.:! +#'! 82).&(*&73-! A-6-3#%$-*.! EFGHI4! H7-')=&3,-!
ET-'$&*:Ij!
!
b#'! &! '-,2/.(#*! #+! ,-*)(.:!&*,! &! 3#=! &++-/.(#*! #+! .0-! C[H4! &! '-/(%-! =(.0! $&X($2$!
.-$%-'&.2'-)! &'#2*,! M]NP"! &*,! .-$%-'&.2'-! $&(*.-*&*/-! %0&)-)! #+! LRh! 0#2')! =&)!
/0#)-*!+#'! &33! .-/0*(12-)?! >*! &,,(.(#*! .#! .0&.! &! .'-&.$-*.! =(.0! MQOP"! &*,! ML! 0#2')!
$&(*.-*&*/-! =&)! '2*! &.! FGH! &)! %'#%#)-,! (*! @DYH9! et# al.!ELOMQI!E+(5?MRNI?! <0-!
.'-&.$-*.!).&'.-,!&+.-'!&!,':(*5!%0&)-!2*.(3!MOOP"!
!
!
!
+(52'-!Md!%'#/-))!M!
!
!
+(52'-!Ld!%'#/-))!L(
!
!
+(52'-!Sd!%'#/-))!S!
!
!
+(52'-!hd!%'#/-))!N!
!
!"
#!"
$!"
%!"
&!"
'!!"
'#!"
'$!"
'%!"
'&!"
#!!"
()" !" )" '!" ')" #!"
*+,-+./01.+"2345"
*6,+"275"
!"
#!"
$!"
%!"
&!"
'!!"
'#!"
'$!"
'%!"
'&!"
()" !" )" '!" ')" #!" #)"
*+,-+./01.+"2345"
*6,+"275"
!"
#!"
$!"
%!"
&!"
'!!"
'#!"
'$!"
'%!"
'&!"
#!!"
(#!" (')" ('!" ()" !" )" '!" ')" #!"
*+,-+./01.+"2345"
*6,+"275"
!"
#!"
$!"
%!"
&!"
'!!"
'#!"
'$!"
'%!"
'&!"
#!!"
()" !" )" '!" ')" #!" #)"
*+,-+./01.+"2345"
*6,+"275"
!
h!
!
+(52'-!Nd!;'#/-))!h!
!
!
L?L!8&$%3-!$&.-'(&3!!
!
<0-!.-).-,!$&.-'(&3!+#'!.0-!6(7'&.(#*&3!$-&)2'-$-*.)!=&)!8(.K&!)%'2/-!=(.0!,($-*)(#*)!
#+! NhOXLOOXSO$$S?! <0-! 7#&',)! =-'-! %'#,2/-,! 7:! ;9<! )&=$(33! &*,! /&*! 3&.-'! 7-! /2.!
,#=*!.#!T2(.&'!)#2*,7#&',)?!<0-!)%-/($-*)!=-'-!/2.!=(.0!-,5-)!&//2'&.-3:!%&'&33-3!.#!
.0-! 5'&(*?! <0-! 0(50! 12&3(.:! #+! .0-! =##,! =&)! ,()%3&:-,! =(.0! 6-':! ).'&(50.! &*,! '-523&'!
5'#=.0!&*,!5'&(*?!J(.0!-&/0!%'#/-))!MM!#+!.0-)-!7#&',)!=-'-!$#,(+(-,!&*,!$-&)2'-,?!!
!
!
L?S!;'-3($(*&':!).'2/.2'&3!&*&3:)()!
!
b#'!&*! ($%'-))(#*!#+!.0-! 6-':!0(50! 7&)(/!12&3(.:!#+! .0-!*&.2'&3! .#*-=##,4!2)-,!(*! .0()!
).2,:4! )#$-! ).'2/.2'&3! '-/#',(*5)! =-'-! $&,-! &.! C&X! ;3&*K! >*).(.2.-! #+! "#33#(,)! &*,!
>*.-'+&/-)!EC;>I?! ;(/.2'-)! #+! /'#))! )-/.(#*)! +'#$! &*! -*6('#*$-*.&3! )/&**(*5! -3-/.'#*!
$(/'#)/#%-! EH8HCI! )0#=-,! .0-! 0(50! #',-'! #+! .0-! +(7-')4! -)%-/(&33:! (*! .0-! -&'3:! =##,4!
=0-'-!.0-!/-33!=&33)!#//2'!&3$#).!12&,'&.(/?!
!"
#!"
$!"
%!"
&!"
'!!"
'#!"
'$!"
'%!"
'&!"
#!!"
()" !" )" '!" ')" #!" #)" 8!" 8)" $!" $)"
*+,-+./01.+"2345"
*6,+"275"
!
N!
!
+(52'-!Qd!H8H8C!%(/.2'-!#+!3&.-!&*,!-&'3:!=##,!/-33)!(*!
/'#))!)-/.(#*?!
!
!
+(52'-!]d!H8HC!%(/.2'-!#+!-&'3:!=##,!/-33)!(*!/'#))!)-/.(#*!
!
<0-!).(++*-))!#+!=##,!()!.'&/-,!7&/K!.#!.0-!23.'&).'2/.2'-!&*,!(*!%&'.(/23&'!.#!.0-!$(/'#!
+(7'(3!&*53-!ECbDI!#+!.0-!8L!3&:-'!EB(/0.-*-55-'!et#al.!MVVV4!9-(.-'-'!et#al.!LOOWI?!`-/&2)-!
#+!.0&.!(.!/#23,!7-!0:%#.0-)(k-,!.0&.!.0-!'-&)#*!+#'!.0-!-++(/(-*/:!#+!0(50!C[H!&.!)&$%3-)!
=(.0!3#=!,-*)(.:!)0#23,!7-!+#2*,!(*!.0-!23.'&).'2/.2'-?!<0-!CbD!=&)!$-&)2'-,!#*!.0(*!
)-/.(#*)! #+! #*-! )&$%3-! 7:! &*! lR'&:! )#2'/-! &.! C;>! &*,! =(.0! ):*/0'#.'#*! '&,(&.(#*! &.!
`H88a!>>!EF-3$0#3.kR@-*.'2$!`-'3(*I?!!
8-.2%!3&7#'&.#':!lR9&:!)#2'/-!E`'2K-'!G&*#).&'Id!
• `-&$!+#/2)d!NOO!m$!
• 8&$%3-!.0(/K*-))d!MNO!m$!
• C-&)2'-$-*.!.($-d!M0!
8-.2%!`H88a!>>d!
• `-&$!+#/2)d!MO!m$!!
• 8&$%3-!.0(/K*-))d!MNO!m$!
• C-&)2'-$-*.!.($-d!MLO!)!
>.! ()! =-33! K*#=*! .0&.! 3#=-'! CbD! %'#,2/-)! 0(50-'! C[H! &3#*5! .0-! 5'&(*?! "[JA9Ha4!
;9H8<[G!EMVQQI!+#2*,!&!)(XR+#3,!(*/'-&)-!#+!).(++*-))!7-.=--*!&*!CbD!+'#$!hOP!.#!MOP!
&.!8(.K&!8%'2/-?!<9HD"a!et#al!ELOOOI!/#$%&'-)!CbD!#+!8(.K&!+'#$!,(++-'-*.!%'#6-*&*/-)!
(*!.0-!Y8D?!<0#)-!$-&)2'-$-*.)!=(.0!%#3&'(k-,!3(50.!$(/'#)/#%:!'-)23.)!(*!$-&*!CbDU)!
+'#$!LLP!+'#$!/-33!=&33)!#+!&!5'#=.0!'(*5!*-&'!.0-!%(.04!.#!VP!#+!&*!-X.-'*&3!5'#=.0!'(*5?!
bD`>8>D^! et# al.# ELOMLI! -X%3&(*-,! .0&.! 3#=-'! CbD! /#''-3&.-)! 3(*-&'3:! =(.0! (*/'-&)(*5!
.'&/0-(,! 3-*5.0!#*! '-)#*&*.! =##,?! <0-! 0(50R'-)#32.(#*! ):*/0'#.'#*! )/&..-'(*5! )(5*&3!
,-3(6-'-,!&*!CbD!#+!MM?MP!n!M?SP?!"#*)(,-'(*5!.0&.!.0()!6&32-!'-%'-)-*.)!Z2).!&!6-':!)$&33!
)-/.(#*!#+!&7#2.! hRN!/-33)4!.0()!&*53-!&%%-&')!12(.-!*#'$&3!&*,!()!*#.!-X/-%.(#*&33:!3#=?!
F#=-6-'!.0-!7&/K!)/&..-'(*5!($&5-)!E+(5?]I!5(6-!6-':!/3-&'!)(5*&3)!=(.0!3#=!,().'(72.(#*?!
<0-!3&7#'&.#':!lR9&:!$-&)2'-$-*.)!#+!&!=(,-'!'&*5-!E&!+-=!02*,'-,!/-33)I!'-)23.-,!(*!&!
$-&*!CbD! #+! ML?OP!n! L?MP?!`#.0!$-&)2'-$-*.)! ,-3(6-'-,!*-&'3:! .0-! )&$-!'-)23.)! =(.0!
6-':!3#=!,().'(72.(#*?!<0()!2*,-'3(*-)!.0-!0(50!0#$#5-*-(.:!#+!.0-!5'&(*)?!!
!
Q!
G-6-'.0-3-))! &*! &7#6-R&6-'&5-! ).(++*-))! /&**#.! 7-! ,-'(6-,! +'#$! &! 3#=! CbD! (*! .0-)-!
$-&)2'-$-*.)4!&)!(.!$(50.!7-!%'-)2$-,?!
!
!
+(52'-!Wd!8/&.-''(*5!($&5-!#+!`H88a!>>!!
!
L?h!C#,&3!&*&3:)()!
!
<0-!$-&)2'-$-*.! #+! .0-!)#2*,! %'#%-'.(-)! =&)!,#*-! =(.0! .0-!$-.0#,! #+!-X%-'($-*.&3!
$#,&3! &*&3:)()! &*,! -)%-/(&33:! &*! ($%&/.! .-).4! 7&)-,! #*! .0-! ,-)/'(%.(#*)! #+! Co8H9!
ELOMOI?!b#'!.0&.!6(7'&.(#*)! =-'-! -X/(.-,!7:!0(.)!#+!&*!($%&/.! 0&$$-'! E;"`!COWQ"OMI!
#6-'!-6-*3:! ,().'(72.-,!%#(*.)! #*! .0-!)&$%3-! E+(5?MOI?!<0-! ($%&/.!)/&..-'! /#*)().)! #+!N!
'#=)!=(.0!V!($%&/.!%#(*.)?!H6-':!%#(*.!=&)!0(.!S!.($-)!.#!5-.!&*!&6-'&5-,!$-&)2'-$-*.!
&*,!.#!'-,2/-!(*&//2'&/(-)!#+!.0-!0(.)?!<0-!)&$%3-!'-&/.)!#*!&*!-3&).(/!,-+#'$&.(#*!=(.0!
&! .'&*)(-*.! #)/(33&.(#*! (*! (.)! '-).(*5! +#'$?! D*! &//-3-'&.(#*! )-*)#'! E;"`! CSNL"QNI!
&..&/0-,! .#! .0-! 7&/K! #+! .0-! )&$%3-)! '-/#',-,!.0#)-!6(7'&.(#*)?! <0-! >*%2.! \! E>$%&/.!
0&$$-'I!&*,![2.%2.R)(5*&3!E&//-3-'&.(#*!)-*)#'I!=&)!,-3(6-'-,!.#!&!b'#*.-*,!Eg(7;(3#.R
hI!&*,! .0-*!,-3(6-'-,! .#! .0-! &*&3:k(*5! )#+.=&'-! ECp;! >*.-'*&.(#*&34! 8$&'.! [++(/-!
D*&3:k-'4!g-')(#*!hI?!<0-'-!.0-!.($-!,-%-*,-*.!)(5*&3)!=-'-!.2'*-,!(*.#! )%-/.'&3! ,&.&?!
<0()! ,&.&! 5(6-)! .0-!+'-12-*/:! '-)%#*)-! +2*/.(#*! Eb9bI4! =0(/0!'-%'-)-*.)! .0-!
/0&'&/.-'().(/4!$-/0&*(/&3!'-)%#*)-!7-0&6(#'!#+!.0-!).'2/.2'-?!!
!
]!
D$%3(.2,-!%-&K)!&%%-&'(*5!(*!.0-)-!)%-/.'2$)!&'-!*&.2'&3!6(7'&.(#*)!#+!.0-!):).-$!\!.0-!
'-)#*&*/-)!#'!-(5-*+'-12-*/(-)!E+(5?VI?!<0#)-!&'-!5-*-'&.-,!+'#$!.0-!3&=)!#+!.'&*)6-')&3!
=&6-!%'#%&5&.(#*!(*!)#3(,)?!H6-':!!-(5-*+'-12-*/:!0&)!&!/0&'&/.-'().(/!$#,-!)0&%-!=(.0!
&!/-'.&(*! ,&$%(*5?! <0()!,&.&!()! #7.&(*-,!7:!/2'6-! +(..(*5!.0-!)-.! #+!b9b!$-&)2'-$-*.)!
+'#$!.0-!hN!($%&/.!%#(*.)!EC23.(%3-!A-5'--!#+!b'--,#$!D*&3:)()I?!!
!
!
+(52'-!Vd!b9b!=(.0!'-)#*&*/-)!&*,!/0&'&/.-'().(/!$#,-!)0&%-)!
!
<0-!-(5-*+'-12-*/(-)!&'-!,('-/.3:!,-%-*,-*.!#+!.0-!$&.-'(&3)!%'#%-'.(-)!3(K-!,-*)(.:!&*,!
-3&).(/(.:! &*,! .0-! )&$%3-)! 5-#$-.':?! `-/&2)-! #+! .0&.4! -3&).(/! /#*).&*.)! /&*! 7-! ,-'(6-,!
+'#$! .0-! 6(7'&.(#*&3! 7-0&6(#'! E-1?LI?! >*! .0-! %'-)-*.! $-&)2'-$-*.! )-.2%! .0-! )&$%3-)!
=-'-!02*5!2%!=(.0!-3&).(/!'277-'!7&*,!&*,!)$&33!%(*)?!<0()!)2)%-*)(#*!52&'&*.--,!.0&.!
.0-!).'2/.2'-!/#23,!+'--3:!#)/(33&.-4!&*,!.0&.!.0-'-!=&)!&*!&%%'#X($&.-3:!+'--!).#'&5-!&)!
7#2*,&':!/#*,(.(#*!+#'!.0-!/&3/23&.(#*?!!
(
!
(
+(52'-!MOd!C-&)2'-$-*.!)-.2%d!>$%&/.!0&$$-'!EMI4!)-*)#'!ELI4!)&$%3-!ESI!+'#*.-*,!EhI4!/#$%2.-'!ENI?!
!
W!
!
L?N!"&3/23&.(#*!#+!-3&).(/!/#*).&*.)!EC[HI!
!
b#'!.0-!(,-*.(+(/&.(#*!#+!.0-!-3&).(/!/#*).&*.)!(*!.0-!3#*5(.2,(*&3!&*,!.0-!'&,(&3!,('-/.(#*!
.0-!-(5-*+'-12-*/(-)!#+!.0-!#',(*&':!7-*,(*5!$#,-!)0&%-)!=-'-!&*&3:k-,!EC#,-!L!&*,!h!
E+(5?VII?!<0-!/&3/23&.(#*!=&)!$&,-!&*&3#52-!.#!@DYH9!et#al.#ELOMQI!&*,!()!7&)-,!#*!.0-!
-12&.(#*)!+#'! &*&3:.(/&3! .-'$(*&.(#*! #+! +3-X2'&3!6(7'&.(#*)! #+!7-&$)! EA&*K-'.4!A&*K-'.!
LOMSI?!<0-'-&+.-'!.0-!'&,(&*!+'-12-*/:!EωI!/&*!7-!)#36-,!=(.0!.0-!7-*,(*5!).(++*-))!EI4!
.0-! $&))! ,().'(72.(#*! ρA! &*,! .0-! ).'2/.2'-)! 3-*5.0!L?! qL! ()! 5(6-*! +'#$! .0-! 7#2*,&':!
/#*,(.(#*!&*,!.0-!#',-'!#+!.0-!6(7'&.(#*?!b#'!.0()!/#*).&*.!LL4h!=&)!/0#)-*!+#'!#',(*&':!
7-*,(*5!$#,-)?!
!
𝜔=
𝜆!
𝐿!
𝐸𝐼
𝜌𝐴!!!!!!!!!!!!!!!!!!!!!!!!(1)!
!
<0-! '&,(&*! +'-12-*/:! &*,! .0-!-(5-*+'-12-*/:! &'-! /#**-/.-,! .0'#250!.0-! '-3&.(#*d!
ω=2πf?! J(.0! .0()! &*,! &+.-'! .'&*)%#)(*5! .0-! -12&.(#*! .0-! /&3/23&.(#*! #+! .0-! ,:*&$(/!
$#,232)!#+!-3&).(/(.:!'-)23.)!.#d!
!
𝐸!/!=
4𝜋!𝑓!𝐿!𝜌𝐴
(𝜆!)!𝐼10!!!!!(2)!
!
𝐸!/!!A:*&$(/!C[H!rGi$$Ls!
𝜔!9&,(&*!+'-12-*/:!r)RMs!
f!-(5-*+'-12-*/:!r)RMs!
L!B-*5.0!#+!.0-!)&$%3-!r$s!
𝜌!A-*)(.:!rK5i$Ss!
𝐴!"'#))!)-/.(#*!r$Ls!
𝜆!
!!"#*).&*.4!,-%-*,(*5!#*!.0-!#',-'!#+!.0-!$#,-!rRs!
𝐼!T-#$-.'(/&3!$#$-*.!#+!(*-'.(&!𝐼=!∗!!
!" !r$hs!
!
"DBAH98C><F4! 9[88>GT! EMVWhI! ,-+(*-,! .0-!/#2%3(*5! #+! ;#())#*U)! '&.(#! 7-.=--*!
6(7'&.(#*&3! 7-*,(*5! $#,-! %&(')4! &)! .0-:! &'-! #7)-'6-,! (*! .0-! %'-)-*.! =#'K!.##4! &*,!
,-'(6-,!-12&.(#*)!+#'! /&3/23&.(*5! -3&).(/!/#*).&*.)! #+!'-/.&*523&'! #'.0#.'#%(/! %3&.-)?! D!
'-,2/-,!+#'$! #+!.0#)-! +#'$23&)4! 5(6-*!7:! T[9H4!T>BH<!ELOMMI4! =&)!2)-,! +#'! 6-'(+:(*5!
.0-! /&3/23&.(#*)! #+! -12&.(#*! L?! `#.0! /&3/23&.(#*! %&.0=&:)! ,-3(6-'-,! &3$#).! .0-! )&$-!
'-)23.!E,(++-'-*/-!O?StI?!
!
𝐸!/!=0.94625 𝜌𝐿!𝑓!
ℎ!!!!!!(3)!
!
C&*:!%273(/&.(#*)!)0#=-,!.0&.!,:*&$(/!$-&)2'-$-*.)!#+!-3&).(/!/#*).&*.)!.-*,!0(50-'!
6&32-)!.0&*!).&.(/!7-*,(*5!.-).)!ETu'3&/0-'!MVWh4!C&/0-K!et#al.!LOOM4!T'(*,&!&*,!Tu33-'!
LOON4! D3+'-,)-*! et# al.! LOOQI?! b#'! &! 6-'(+(/&.(#*! #+! .0-! ,:*&$(/! $-&)2'-$-*.)! )#$-!
&,,(.(#*&3!).&.(/!7-*,(*5!.-).)!=-'-!$&,-!#*!.0'--!.-).!)&$%3-)?!D)!-X%-/.-,4!.0-!).&.(/!
6&32-)!=-'-!$2/0!3#=-'4!.0&*!.0-!6&32-)!#+!.0-!6(7'&.(#*&3!$-&)2'-$-*.)!E+(5?MMiMLI?!
!
!
V!
!
+(52'-!MMd!).&.(/!E5'-:I!&*,!,:*&$(/!E73&/KI!
$-&)2'-$-*.)!!#+!C[H!E3#*5(.2,2*&3I!#*!.0'--!
)&$%3-)?!
!
!
+(52'-!MLd!).&.(/!E5'-:I!&*,!,:*&$(/!E73&/KI!$-&)2'-$-*.)!!
#+!C[H!E'&,(&3I!#*!.0'--!)&$%3-)?!
!
L?Q!"&3/23&.(#*!#+!,&$%(*5!
!
<0-! %&'&$-.-'! #+! ,&$%(*5! EtanδI! ,-)/'(7-)! .0-! $&.-'(&3)! 7-0&6(#'! #+! '-+3-/.(*5!
6(7'&.(#*&3!-*-'5:?!>.!()!.0-!'&.(#!#+!.0-!(*,2/-,!&*,!.0-!&7)#'7-,!-*-'5:!,2-!.#!(*.-'*&3!
+'(/.(#*?! >*! .0-! &*&3:)()! )#+.=&'-! .0-! '-)#*&*/-! ,&$%(*5! =&)! /&3/23&.-,! 7:! .0-! CA[b!
$-.0#,!=(.0!.0-!+'-12-*/:!=(,.0!'&*5-!EvfI#&*,!.0-!-(5-*+'-12-*/:!EfI!#+!.0-!#',(*&':!
7-*,(*5!$#,-)4!7&)-,!#*!.0-!,-+(*(.(#*d!
!
2𝜋!𝑡𝑎𝑛𝛿 =2𝜋
∆𝑓
𝑓!!!!!!!!!!!!!(4)!
!
!
L?]!"&3/23&.(#*!#+!HC"!&*,!$&))!3#))!
!
<0-! -12(3(7'(2$! $#().2'-! /#*.-*.! EHC"I! =&)! ,-.-'$(*-,! 7:! .0-! ,':(*5! $-.0#,4! 7:!
,':(*5!.0-!)&$%3-)!=(.0!MOSP"!2*.(3!/#*).&*.!=-(50.?!`-+#'-!.0-!.'-&.$-*.!.0-!HC"!=&)!
$-&)2'-,!#*! )$&33-'!)-/.(#*)4! =0(/0! &//'2-,!7:! +#'$&..(*5!.0-! )&$%3-)?!<0-! HC"!+#'!
.0-!$#,(+(-,!)&$%3-)!=&)!.&K-*!#*!.0-!6(7'&.(#*!)%-/($-*)!(.)-3+?!`-/&2)-!#+!.0-!3($(.-,!
)%&/-!(*!.0-! ,':(*5! K(3*!&*,!.0-!'-3&.(6-3:! 7(5! )%-/($-*)4!.0-!$#,(+(-,!HC"! =&)!.&K-*!
#*3:!+#'!.0'--!)&$%3-)!(*!-6-':!.'-&.$-*.?!b#'!/&3/23&.(*5!.0-!3#))!#+!=##,!%23%4!.0-!,':!
$&))! EmdryI! #+! .0-! )&$%3-! 0&,! .#! 7-! -).($&.-,! 7:! .'&*)+-''(*5!.0-!HC"! #+! (.U)! )&=*!
)-/.(#*! #*! .0-! =0#3-! )&$%3-! E-1?QI?! <0()4! &*,! .0-! +&/.! #+! #*3:! .0'--! 6&32-)! $-&)2'-,4!
$&K-)!.0()!%&'&$-.-'!2*/-'.&(*?!G-6-'.0-3-))!(.!5(6-)!&*!($%'-))(#*!#+!.0-!$#,(+(/&.(#*!
,-5'--?!
!
𝐸𝑀𝐶%=
𝑚!"#$% −𝑚!"#
𝑚!"#
∗100%!!!!(5)!
!
!
𝑚𝑎𝑠𝑠!𝑙𝑜𝑠𝑠%=
𝑚!"!!"# −𝑚!"!!"#
𝑚!"!!"#
∗100%!
!
=
𝑚!"#$!!"# −
𝑚!"#$!!"#
100 ∗𝐸𝑀𝐶!"# −𝑚!"!!"#
𝑚!"#$!!"# −
𝑚!"#$!!"#
100 ∗𝐸𝑀𝐶!"#
∗100%!!(6)!
)!!!"
9!!!"
'8!!!"
:0/;<"=">:"?@A/,6<"="2BC,,#5"
!"
8!!"
%!!"
9!!"
:0/;<"=">:"?@A/,6<"="2BC,,#5"
!
MO!
!
!
L?W!H6&32&.(#*!#+!)#2*,!12&3(.:!E9-)#*&*/-!+&/.#'I!
!
D! /0&'&/.-'(k&.(#*! #+! .0-! &/#2).(/! %'#%-'.(-)! =&)! $&,-4! 7:! 2)(*5! .0-! 9R+&/.#'4! &)!
%'#%#)-,! 7:![G[4! G[9>C[<[! EMVWSI! &*,! FD>GH8! ELOOOI?! <0()! +&/.#'! 7&)-)! #*! .0-!
%'-,(/.(#*!#+!5##,!)#2*,!12&3(.:!+#'!&!0(50!'&.(#!#+!)#2*,!6-3#/(.:!EcI!&*,!,-*)(.:?!!
!
𝑅=
𝑐
𝜌⇔𝑅=
𝐸
𝜌!!!!!!!!!!!!!!!(7)!
!
!
!
3(Results(
!
S?M!;'-)-*.&.(#*!#+!.0-!'-)23.)!
!
b#'!+#33#=(*5!=0-.0-'!&!/0&*5-!.0'#250!.0-!$#,(+(/&.(#*!=&)!)(5*(+(/&*.4!&!%&('-,!.R.-).!
=&)! /&''(-,! #2.?! <0()! ()! &! 0:%#.0-)()R.-).4! =(.0! .R,().'(72.-,! .-).! 6&32-4! +#'! %&('=()-4!
/&2)&3!'-3&.-,!)&$%3-)?!b#'! &! /0#)-*!)(5*(+(/&*/-!3-6-3!#+! Nt! .0-!.R6&32-M!+#'!&!,#273-R
)(,-,! .R.-).! =&)! .&K-*?!<0-*! .0-! <R6&32-L!#+! .0-! .-).! ,().'(72.(#*! =&)! /&3/23&.-,?! D!
)(5*(+(/&*.!,(++-'-*/-!7-.=--*! .0-! .=#!$-&*)!7-+#'-! &*,!&+.-'!.0-!.'-&.$-*.! #//2')4!(+!
<wp.!&*,!<xR.!E)--!.&73-)I?! >*! &,,(.(#*!.#!.0&.!.0-!/#*+(,-*/-!(*.-'6&3)!=-'-!/&3/23&.-,!
&*,!,()%3&:-,?!b#'!.0-! '-)23.)! (*.-'%'-.&.(#*!&*,!.#!)0#=!0#=! ).'#*5! &!/0&*5-!#//2')4!
.0-! 6&32-! #+!-++-/.! )(k-! ECohen´s# dI! ()! 2)-,?! <0()! ()! &!2*(.R(*,-%-*,-*.! 6&32-4! =0(/0!
,-)/'(7-)!.0-!5'&,-!#+!.0-!(*.-'&/.(#*!7:!&!.'-&.$-*.!(*!&!%'-R%#).R$-&)2'-$-*.?!J(.0!
.0()!6&32-!(.!()!&3)#!%#))(73-!.#!/#$%&'-!-++-/.R3-6-3)!7-.=--*!,(++-'-*.!%&'&$-.-')?!b#'!
-X&$%3-!#*-!/&*!)&:!.0&.!&!.'-&.$-*.!0&)!&!7(55-'!-++-/.!#*!.0-!,-*)(.:!.0&*!#*!.0-!C[H?!
Cohen´s# d!-X%'-))-)! ,(++-'-*/-)! 7-.=--*! $-&*! 6&32-)! ExI! (*! *2$7-')! #+! ).&*,&',!
,-6(&.(#*)!EsI?!!
!
𝑑!"!!" =
𝑥!−𝑥!
(𝑠!
!+𝑠!
!)/2
!!!!!!!!!!!(8)!
!
b#'!/0-/K(*5!=0-.0-'!&!/0&*5-!#+!&!%&'&$-.-'!()!(*+32-*/-,!7:!.0-!(*(.(&3!0-(50.!#+!.0-!
6&32-! 7-+#'-! .0-! .'-&.$-*.4! .0#)-! 6&32-)! =-'-! /#''-3&.-,! &5&(*).! .0-! /0&*5-!
$-&)2'-$-*.!&+.-'!.0-!$#,(+(/&.(#*!E+(5?MSiMhI?!<0-'-+#'!*#!,-%-*,-*/-!=&)!&))-'.-,?!
[*3:!+#'!.0-!/0&*5-!#+!.0-!C[H!(*!%'#/-))!L!&!=-&K!/#''-3&.(#*!#+!0(50-'!/0&*5-)!(*!C[H!
=(.0!0(50-'! (*(.(&3!C[H!/#23,! 7-!)%-/23&.-,! E+(5?MhI?!F#=-6-'!.0()! /&*!7-! /#*).'2/.-,!
+#'!#*3:!#*-!%'#/-))!&*,!7-/&2)-!#+!.0-!'-3&.(6-3:!)$&33!)&$%3-!)(k-!.0-!&2.0#')!'-Z-/.-,!
.0()!0:%#.0-)()?!<0-!/0&*5-)!%'#/--,!6-':!0#$#5-*-#2)!=0(/0!()!&3)#!,-$#*).'&.-,!7:!
/#*)(,-'(*5!-&/0!)%-/($-*!7-+#'-!&*,!&+.-'!.0-!.'-&.$-*.!E+(5?MNiMQI?!`-/&2)-!#+!.0&.!(.!
()! )2%%#)-,! .0&.! /0&*5-)! &'-! -X/32)(6-3:! (*+32-*/-,! 7:! .0-! ,(++-'-*.! .'-&.$-*.)?! <0()!
&33#=)!.0-!(*.-'%'-.&.(#*!#+!.0-!'-)23.)!7:!'-5&',(*5!.0-!$-&*!6&32-)4!(*!.0-!+#33#=(*5?!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
M!.R6&32-d!b'#$!.0-!.R,().'(72.(#*!=(.0!&!,-5'--!#+!+'--,#$!#+!MO!&*,!&!)(5*(+(/&*/-!3-6-3!#+!VNt!
L!<R6&32-d!"&3/23&.-,!6&32-!+'#$!.0-!12&*.(.:!.-).-,!
!
MM!
!
!
+(52'-!MSd!"#''-3&.(#*!7-.=--*!(*(.(&3!,-*)(.:!&*,!,-*)(.:!/0&*5-!&)!'-)23.!#+!.0-!.'-&.$-*.?!
!
+(52'-!Mhd!"#''-3&.(#*!7-.=--*!(*(.(&3!C[H!&*,!C[H!/0&*5-!&)!'-)23.!#+!.0-!.'-&.$-*.?!
($!"
(8)"
(8!"
(#)"
(#!"
(')"
('!"
()"
!"
8!!" 8#!" 8$!" 8%!" 8&!" $!!" $#!" $$!" $%!"
DE"2FGC,85"
"
EA/0"2FGC,85"
'"
#"
8"
$"
)"
(&!!"
(%!!"
($!!"
(#!!"
!"
#!!"
$!!"
%!!"
&!!"
&!!!" 9!!!" '!!!!" ''!!!" '#!!!" '8!!!" '$!!!" ')!!!"
D=H"2BC,,#5"
=HIA/0"2BC,,#5"
"
'"
#"
8"
$"
)"
!
ML!
!
+(52'-!MNd!"0&*5-!#+!A-*)(.:4!-X-$%3&'(3:!#*!.'-&.$-*.!
N?!C-&*!6&32-)!(*!'-,!
!
!
+(52'-!MQd!"0&*5-!#+!C[H4!-X-$%3&'(3:!#*!.'-&.$-*.!L?!
C-&*!6&32-)!(*!'-,!
!
b#'!&*#.0-'!&%%'&()&3!#+!.0-!-++-/.)!3-6-3!.0-!'-)23.)!=-'-!%'-)-*.-,!(*!%-'/-*.?!F-'-!.0-!
&6-'&5-! /0&*5-)! =(.0(*! &! 5'#2%! =-'-! '-3&.-,! .#! .0-! &6-'&5-! (*(.(&3! %&'&$-.-'! #+! .0-!
5'#2%! -*.('-.:!E-1?VI?! D3.0#250! )$&33! -''#')! /#23,! #//2'4! .0()! %'#/--,(*5! $&K-)! .0-!
'-)23.)! $#'-! /#$%&'&73-! &*,! 7&)-)! &3)#! #*! .0-! &))2$%.(#*! .0&.! &33! /0&*5-)! &'-!
-X/32)(6-3:!(*+32-*/-,!7:!.0-!.'-&.$-*.?!!
!
∆𝑥%=
𝑥!"#_!"#$% −𝑥!"#$_!"#$%
𝑥!"#_!"!#$
∗100%!!!!!!!!!!(9)!
!
!
S?L!B#*5(.2,(*&3!C[H!
!
J##,!+#'!0(50!12&3(.:!)#2*,7#&',)!'-12('-)!0(50!-3&).(/!).(++*-))!&*,!3#=!,-*)(.:!&.!.0-!
)&$-!.($-?!b#'! .0-!a#2*5U)!$#,232)!(*! .0-!3#*5(.2,(*&3!,('-/.(#*!`Y"Y9! ELOOQI! 5(6-)!
MSOOO!Gi$$L!+#'!8(.K&!)%'2/-?!>*!.0()!%'#Z-/.!&!$-&*!3#*5(.2,(*&3!C[H!#+!MOWOO!n!MMOO!
Gi$$L!=&)!/&3/23&.-,?! 9-5&',(*5!.0-! 3#=!,-*)(.:! .0()! 6&32-! ()! /#*)(,-'&73:! 0(50!E)--!
/0&%.-'!S?hI?!<0-!)&$%3-)!#+!.0-!%'#/-))-)!h!&*,!N!)2++-'-,!'-,2/.(#*)!#+!.0-!C[H!,2-!
.#! .0-! .'-&.$-*.4! =0-'-7:! .0-! /0&*5-)! #+! .'-&.$-*.! h! &'-! *#.! )(5*(+(/&*.! 2*,-'! &!
/#*+(,-*/-! 3-6-3! #+! VNt!E.&7?MI?! 8(5*(+(/&*.! (*/'-&)-!#+! .0-! C[H! =&)! +#2*,! +#'! .0-!
%'#/-))-)!M4!L!&*,!S?!<0-!7(55-).!-3-6&.(#*!#+!.0-!).(++*-))!=&)!&/0(-6-,!7:!.'-&.$-*.!L!
E+(5?M]I?!!
!
.&73-!Md!H3&).(/!/#*).&*.)!(*!.0-!3#*5(.2,(*&3!,('-/.(#*!
!
!
#)!"
#J!"
#9!"
8'!"
88!"
8)!"
8J!"
89!"
$'!"
$8!"
$)!"
A/01./K"
,L?6M+?"
"N+A:60@"2FGC,85"
""
&)!!"
9)!!"
'!)!!"
'')!!"
'#)!!"
'8)!!"
'$)!!"
A/01./K"
,L?6M+?"
=H"2BC,,#5"
!
MS!
!
!
+(52'-!M]d!"0&*5-)!#+!3#*5(.2,(*&3!-3&).(/!/#*).&*.)!,2-!.#!.0-!
.'-&.$-*.)!=(.0!/#*+(,-*/-!(*.-'6&3)?!
!
!
+(52'-!MWd!;-'/-*.&5-!/0&*5-)!#+!3#*5(.2,(*&3!-3&).(/!
/#*).&*.)?!
!
S?S!9&,(&3!C[H!
!
8#$-! &2.0#')! $-*.(#*-,! .0-! ($%#'.&*/-! #+! &! 0(50! &*()#.'#%:! #+! =##,! +#'! .0-! )#2*,!
12&3(.:! E[*#! MVVQ4! `2/2'! LOOQI?! <02)! (.! /#23,! 7-! /#*/32,-,4! /#*)(,-'(*5! .0&.! +#'!.0-!
3#*5(.2,(*&3! 6(7'&.(#*)! &*!(*/'-&)-! #+! .0-! ).(++*-))! ()! 7-*-+(/(&34! .0&.! &! ,-/'-&)-! #+! .0-!
'&,(&3!-3&).(/!/#*).&*.)! /#23,! 7-!-6&32&.-,!&)!%#)(.(6-?! [`D<DaD!-.!&3!ELOOOI!,-/3&'-,!
.0&.! &*! (*/'-&)-! #+! &*()#.'#%:! =(.0! /0-$(/&3! .'-&.$-*.)! ()! *#.! %#))(73-?!>*,--,! .0-!
'-)23.)!#+!.0-!'&,(&3!-3&).(/!$#,232)!)0#=-,!$#'-!#'!3-))!.0-!)&$-!%-'+#'$&*/-!.0'#250!
.0-! $#,(+(/&.(#*! &)! .0-! 3#*5(.2,(*&3?! J0(3-! %'#/-))! *2$7-'! h! ,(,! *#.! /&2)-! &*:!
)(5*(+(/&*.!/0&*5-)4!=(.0!VNt!/#*+(,-*/-4!%'#/-))!h!'-,2/-,!.0-!).(++*-))!&*,!M4!L!&*,!S!
(*/'-&)-,!E+(5?MVI?!
!
.&73-!Ld!H3&).(/!/#*).&*.)!(*!.0-!'&,(&3!,('-/.(#*!
!
!
(&!!" (%!!" ($!!" (#!!" !" #!!" $!!" %!!" &!!"
'"
#"
8"
$"
)"
D=H"2BC,,#5"
#"
)"
'"
('"
($"
1" 2" 3" 4" 5"
D=H"2O5"
!
Mh!
!
+(52'-!MVd!"0&*5-)!#+!'&,(&3!-3&).(/!/#*).&*.)!,2-!.#!.0-!
.'-&.$-*.)!=(.0!/#*+(,-*/-!(*.-'6&3)?!
!
!
+(52'-!LOd!;-'/-*.&5-!/0&*5-)!#+!'&,(&3!-3&).(/!/#*).&*.)!
!
S?h!A-*)(.:!
!
<0-!$-&*!,-*)(.:!#+!8(.K&!)%'2/-!()!5(6-*!7:!`Y"Y9!ELOOQI!=(.0!hWO!K5i$S?!A-*)(.(-)!#+!
.0-! )&$%3-)! 2)-,! (*! .0()! ).2,:! 6&'(-,! &'#2*,! SWO! n! SO! K5i$S4! &.! *#'$&3! /3($&.-!
/#*,(.(#*)4!=0(/0!2*,-'3(*-)! .0-!-X/-33-*.! 12&3(.:!#+! .0-! *&.2'&3! )#2*,7#&',!$&.-'(&3?!
`&)(/&33:! &33! %'#/-))-)! '-,2/-,! .0-! ,-*)(.:! )(5*(+(/&*.3:?! Cohen´s# d!(*,(/&.-)! .0&.! .0-!
.'-&.$-*.)! (*+32-*/-,! .0-! ,-*)(.:! $#'-! .0&*! .0-! #.0-'! %&'&$-.-')! E.&7?SI?! <0()!
'-,2/.(#*!()!/#*)-12-*/-!#+!.0-!=##,!$&))!3#))!&*,!.0-!'-,2/-,!)#'%.(#*!/&%&/(.:!E)--!
/0&%.-'!S?]I?!J(.0(*!&!'&*K(*5!#+!,-*)(.:!'-,2/.(#*4!/#*)(,-'(*5!.0&.!3#=!,-*)(.:!/&2)-)!
0(50-'! &/#2).(/! 12&3(.:4!%'#/-))! *2$7-'! N! $&,-! .0-! 7-).! )2//-))! +#33#=-,! 7:! .0-!
%'#/-))-)! h4L4M! &*,! S?! 9-).'(/.(6-3:! (.! 0&)! .#! 7-! '-+-''-,! .0&.! .0-! 0(50-'! '-,2/.(#*! #+!
,-*)(.:!#+!.'-&.$-*.!N!/#''-3&.-)!.#!C[H!'-,2/.(#*)!E+(5?!LSI?!>.!)0#23,!&3)#!7-!*#.-,!.0&.!
+#'!.0-! C[H!&*,! .0-!,-*)(.:! .0-!.'-&.$-*.)! h! &*,! N!%'#,2/-,! 0(50-'!).&*,&',! -''#')!
E+(5?M]iMViLMI?!<0()! /#23,!7-!.'&/-,!7&/K! .#!.0-!+&/.! .0&.!.0-!'-)-&'/0! *(.'#5-*!K(3*!()!
*#.!-12(%%-,!=(.0!&*!&('!/('/23&.(#*!):).-$?!b#'!.0&.!'-&)#*!.0-!0-&.!$(50.!7-!2*-12&33:!
,().'(72.-,?!
!
.&73-!Sd!A-*)(.:!
!
!
($!" (8!" (#!" ('!" !" '!" #!" 8!" $!" )!"
'"
#"
8"
$"
)"
D=P"2BC,,#5"
J" J" J"
#"
()"
1" 2" 3" 4" 5"
D=P"2O5"
!
MN!
!
+(52'-! LMd! 9-,2/.(#*)! #+! ,-*)(.:! ,2-! .#! .0-! .'-&.$-*.)! =(.0!
/#*+(,-*/-!(*.-'6&3)!
!
!
+(52'-!LLd!;-'/-*.&5-!'-,2/.(#*)!#+!,-*)(.:!
!
!
+(52'-!LSd!"#''-3&.(#*!#+!/0&*5-!#+!-3&).(/!/#*).&*.)!E3#*5(.2,(*&3I!&*,!,-*)(.:!'-,2/.(#*)?!
!
S?N!9-)#*&*/-R+&/.#'!E3#*5(.2,(*&3i'&,(&3I!
!
9-5&',(*5! Cohen´s# d!(*! 5-*-'&3!.0-! 9R+&/.#'! ()! 6-':! 0(50! &++-/.-,! 7:! .0-! .'-&.$-*.)!
E.&7?hiNI?! H12&.(#*! ]! )0#=)! .0&.! -)%-/(&33:! .0-! ,-*)(.:!(*+32-*/-)! .0()! 6&32-! =(.0! .0-!
.0(',!%#=-'!2*,-'!.0-!)12&'-!'##.?!>.!$(50.!7-!(''(.&.(*5!.0&.!.0-'-!()!&*#.0-'!#',-'!#+!9R
(*/'-&)-)!=(.0!.0-!%&'&$-.-'!#+!Cohen´s#d!.0&*!+#'!.0-!&7)#32.-!6&32-)!E.&7?hI?!!
($!" (8)" (8!" (#)" (#!" (')" ('!" ()"
'"
#"
8"
$"
)"
DE"2FGC,85"
($"
(%"
(8"
(%"
(9"
1" 2" 3" 4" 5"
Δρ"[%]"
('!!!"
(&!!"
(%!!"
($!!"
(#!!"
!"
#!!"
$!!"
%!!"
&!!"
($!" (8)" (8!" (#)" (#!" (')" ('!" ()" !"
DE"2FGC,85"
DQR="2BC,,#5"
'"
#"
8"
$"
)"
!
MQ!
`-/&2)-!#+!.0-!0(50-'!).&*,&',! -''#'! (*! .0-!)&$%3-)!,().'(72.(#*!#+!.'-&.$-*.!L! &*,! N4!
.0-!-++-/.!)(k-!E,I!()!)$&33-'!#*!.0-)-!)&$%3-)4!&3.0#250!.0-!&7)#32.-!,(++-'-*/-!7-.=--*!
.0-!%'-R%#).!$-&*)!Ev9I!()!7(55-'!0-'-?!D!=&:!.#!-12&3(k-!.0()!%'#73-$!/#23,!7-!.#!'-3&.-!
.0-! ,().&*/-! 7-.=--*! .0-! %'-R%#).R$-&*)! #*! .0-! ).&*,&',! ,-6(&.(#*! #+! .0-! =0#3-!
%#%23&.(#*! #+! .0-! *&.2'&3! )&$%3-)4! (*).-&,! #+! .0-! ).&*,&',! ,-6(&.(#*! =(.0(*! 5'#2%)?!
F#=-6-'4!&)! -X%3&(*-,! (*! /0&%.-'! S?M!.0-!/0&*5-)! &'-!6-':! 0#$#5-*-#2)!&*,! .0-'-!()!
*-&'3:!*#!)0(+.!(*!.0-!,().'(72.(#*!+'#$!.0-!$-&)2'-$-*.)!#+!.0-!*&.2'&3!)&$%3-)!.#!.0-!
$#,(+(-,!#*-)?!`-/&2)-!#+!.0()!+&/.!.0-!+#/2)!()!$#'-!#*!.0-!&7)#32.-!$-&*!/0&*5-)!#+!9?!!
!
D)! )&(,! .0-! $&(*! (*+32-*/-! #*! .0-! 9R+&/.#'! ()! +'#$! .0-! ,-*)(.:?! b#'! .0&.! '-&)#*!&*,!
7-/&2)-! #+! )($(3&'! /0&*5-)! #+! .0-! C[H!7#.0! .0-! 3#*5(.2,(*&3! &*,! .0-! '&,(&3! 9R+&/.#'!
/0&*5-,!$#'-!#'!3-))!)&$-!=&:)?!<'-&.$-*.)!=(.0!0(50-'!'-,2/.(#*!#+!,-*)(.:!&/0(-6-,!
7-..-'!9R6&32-)?!>.!()!0&',3:!%#))(73-!.#!-6&32&.-!.0-!)#2*,!12&3(.:!($%'#6-$-*.)!#+!.0-!
,(++-'-*.!%'#/-))-)!7&)-,!#*!9!&*,!.#!%2.!.0-$! (*! &*! #',-'4! (*!.0()!).2,:?!b#'!-X&$%3-!
%'#/-))!*2$7-'!N!&/0(-6-,!6-':!0(50!94!72.!.0-!0(50!,-*)(.:R'-,2/.(#*!=-*.!&3#*5!=(.0!
&! ,-/'-&)(*5! C[H?! >.! ()! &))2$-,! .0&.! +#'! '-)#*&*/-! $&.-'(&3! .0-! ).(++*-))! )0#23,! ).&:!
).&73-!#'!-6-*!(*/'-&)-4! ,2-!.#!.0-!.'-&.$-*.?!D%&'.!+'#$!.0&.4!%'#/-))!*2$7-'!L!$&,-!
.0-! 7-).! )2//-))! #+! (*/'-&)(*5! .0-! 9-)#*&*/-R+&/.#'?! <0()! %'#/-))! (*/'-&)-,! C[H! &*,!
'-,2/-,!.0-!,-*)(.:!&.!.0-!)&$-!.($-!E+(5?LhiLQI?!
(
.&73-!hd!9-)#*&*/-!+&/.#'!E3#*5(.2,(*&3I!
!
!
.&73-!Nd!9-)#*&*/-!+&/.#'!E'&,(&3I!
!
!
M]!
!
+(52'-!Lhd!>*/'-&)-)!#+!9!+&/.#'!E3#*5(.2,(*&3I!#+!,2-!.#!
.0-!.'-&.$-*.)!=(.0!/#*+(,-*/-!(*.-'6&3)!
!
!
+(52'-!LNd!;-'/-*.&5-!(*/'-&)-)!#+!9!+&/.#')!E3#*5(.2,(*&3I!
!
!
!
+(52'-!LQd!>*/'-&)-)!#+!9!+&/.#'!E'&,(&3I!#+!,2-!.#!.0-!
.'-&.$-*.)!=(.0!/#*+(,-*/-!(*.-'6&3)!
!
!
+(52'-!L]d!;-'/-*.&5-!(*/'-&)-)!#+!9!+&/.#')!E'&,(&3I!
!
S?Q!A&$%(*5!
The damping constants of the first bending modes changed differently for the
longitudinal (mode2) and the radial (mode4) motion. In general there were small
changes for the damping and the variation was very high, although significant shifts
were detected. For a longer sound fade out and a higher reflection of the induced
energy at the guitar, a lower damping is requested. For the longitudinal bending mode,
this could be achieved from the treatments 2 and 3. Process 1 did not change
significantly and 4 and 5 increased the damping slightly. The radial bending vibration
was stronger affected (fig.29/31). All treatments decreased the damping. The highest
reduction of vibration energy absorption was measured on samples of treatment
number 3 in both directions.
!" !S)" '" 'S)" #" #S)"
'"
#"
8"
$"
)"
DPH"
&"
'8"
%"
&"
'#"
1" 2" 3" 4" 5"
DPH"2O5"
!S!" !S'" !S#" !S8" !S$" !S)"
'"
#"
8"
$"
)"
DPP"
''"
'8"
9"
'!"
''"
1" 2" 3" 4" 5"
DPP"2O5"
!
MW!
For all samples could be suggested that there is a weak correlation between the change
of the damping and the MOE (fig. 32/33). It seems logical that samples with stiffness
reductions caused increased damping at the same time,.
.&73-!Qd!G&.2'&3!+'-12-*/(-)!&*,!,&$%(*5!#+!$#,-!L?!
!
!
.&73-!]d!G&.2'&3!+'-12-*/(-)!&*,!,&$%(*5!#+!$#,-!h!
!
!
!
!
!
+(52'-!LWd!"0&*5-)!#+!,&$%(*5!EC#,-LI!,2-!.#!.0-!
.'-&.$-*.)!=(.0!/#*+(,-*/-!(*.-'6&3)?!
!
!
+(52'-!LVd!!;-'/-*.&5-!/0&*5-!#+!,&$%(*5!EC#,-LI?!
!
!
!
(!S!&" (!S!%" (!S!$" (!S!#" !" !S!#" !S!$" !S!%" !S!&"
'"
#"
8"
$"
)"
DNQL?+#"2O5"
O!
RN!
RV!
V!
N!
1" 2" 3" 4" 5"
DNQL?+#"2O5"
!
MV!
!
+(52'-!SOd!"0&*5-)!#+!,&$%(*5!EC#,-hI!,2-!.#!.0-!.'-&.$-*.)!
=(.0!/#*+(,-*/-!(*.-'6&3)?!
!
!
+(52'-!SMd!;-'/-*.&5-!/0&*5-!#+!,&$%(*5!EC#,-hI?!
!
!
+(52'-!SLd!"#''-3&.(#*!#+!/0&*5-!#+!-3&).(/!/#*).&*.)!E3#*5(.2,(*&3I!&*,!,&$%(*5!#+!$#,-L?!
!
(!S#)" (!S#" (!S')" (!S'" (!S!)" !"
'"
#"
8"
$"
)"
DNQL?+$"2O5"
RV!
RMS!
RMN!
RW!
RN!
1" 2" 3" 4" 5"
DNQL?+$"2O5"
(!S'"
(!S!&"
(!S!%"
(!S!$"
(!S!#"
!"
!S!#"
!S!$"
!S!%"
!S!&"
!S'"
('!!!" (&!!" (%!!" ($!!" (#!!" !" #!!" $!!" %!!" &!!"
DN"TQL?+#U"2O5"
D=H"2BC,,#5""
'"
#"
8"
$"
)"
!
LO!
!
+(52'-!SSd!"#''-3&.(#*!#+!/0&*5-!#+!-3&).(/!/#*).&*.)!E'&,(&3I!&*,!,&$%(*5!#+!$#,-h?!
(
S?]!HC"i!3#))!#+!=##,!%23%!
!
<0-! ,-/'-&)-,! /&%&/(.:! #+! =&.-'! 2%.&K-! ()! &! /#*)-12-*/-! #+! .0-! ,-5'&,&.(#*! #+!
0:,'#%0(3(/!/#$%#*-*.)!#+!.0-!/-33!=&33!Eb-*5-34!J-5-*-'!LOOSI?!<0()!()!(*,(/&.-,!7:!&!
3#))! #+! =##,-*! %23%! $&))?! `-/&2)-! &2+! .0-! )$&33! )&$%3-! )(k-! =(.0!#*3:! .0'--! %-'!
.'-&.$-*.4!.0-'-! =-'-!*#! ).&.().(/)!,#*-! +#'! .0-! HC"! &*,!.0-! $&))!3#))! #+!=##,! %23%?!
D3.0#250!-''#')!/#23,!7-!(*/32,-,!+#'!7#.0!#+!.0-)-!%&'&$-.-')4!.0-:!/#''-3&.-!6-':!=-33!
=(.0!.0-!'-,2/.(#*!#+!.0-!,-*)(.:!E.&7?WiSI?!<0-!3#))!#+!=##,!%23%!()!(*!.0-!)&$-!#',-'!#+!
$#,(+(/&.(#*!%'#/-))-)!&)!.0-!,-*)(.:!'-,2/.(#*?!`&)-,!#*!.0&.4!&*,!&)!)0#=*!(*!;b9>HC!
ELOOQI4!.0-!=##,-*!$&))!3#))!(*,(/&.-)!.0-!,-5'--!#+!$#,(+(/&.(#*!6-':!=-33!<0&.!$-&*)!
.0&.!)&$%3-)!#+!.0-!.'-&.$-*.)!L4!h!&*,!N!'-/-(6-,!&!).'#*5-'!$#,(+(/&.(#*!&)!M!&*,!S?!
!
.&73-!Wd!HC"!&*,!3#))!#+!=##,-*!%23%?!
!
!
!
(!S8"
(!S#)"
(!S#"
(!S')"
(!S'"
(!S!)"
!"
!S!)"
(%!" ($!" (#!" !" #!" $!" %!"
DN"TQL?+$U"2O5"
D=P"2BC,,#5" '"
#"
8"
$"
)"
!
LM!
4(Summary(
`&)(/&33:!,2-!.#!,(++-'-*.!.-/0*(12-)!&*,!)3(50.3:!,(++-'-*.!'-/(%-)!&33!.0-'$&3!.'-&.$-*.)!
/#6-'!&! 3&'5-! '&*5-! .#! )--! ,(++-'-*.! -++-/.)! #*! .0-! '-)#*&*/-! 7-0&6(#'! #+! .0-! )&$%3-)?!
82$$&'(k-,4! .0-! &2.0#')! &))2$-! &*! ($%'#6-$-*.! #+! .0-! )#2*,! 12&3(.:! +#'! &33! #+! .0-!
%'#/-))-)4! /#*)(,-'(*5! .0&.! )#$-! *-5&.(6-! -++-/.)4! 3(K-! ,-/'-&)-,! C[H! #'! (*/'-&)(*5!
,&$%(*54!=-'-!'&.0-'!)$&33?!F#=-6-'!&!/3&))(+(/&.(#*!7&)-,!#*!94!3(K-!(.!()!,#*-!7:!$&*:!
%'-6(#2)3:! /(.-,! %273(/&.(#*)4! )0#23,! 7-! %-'/-(6-,! =(.0! 5'-&.! /&'-!>.! ()! #76(#2)! .0&.!
0(50-'! ,-5'--)! #+! $#,(+(/&.(#*)4! 3(K-! +#2*,! +#'! .'-&.$-*.)! h! &*,! N4! 5(6-)! 0(50-'!
'-)#*&*/-!+&/.#')4!7-/&2)-!#+!.0-!0(50-'!=-(50.(*5!#+!.0-!,-*)(.:!(*!.0-!-12&.(#*!E]I?!b#'!
.0#)-!.'-&.$-*.)!.0-!C[H!,-/'-&)-,!)3(50.3:!&*,!.0()!=#'K!/#23,!)0#=!.0&.!&!,-/'-&)(*5!
).(++*-))!=-*.!&3#*5!=(.0!&*!(*/'-&)-!#+!.0-!,&$%(*5?!<0()!'-3&.(#*!()!)2%%#'.-,!7:!.0-!
+&/.4!.0&.!.'-&.$-*.! S!/&2)-,!.0-! 3#=-).!$#,(+(/&.(#*!,-5'--4! '-5&',(*5! .0-!/0&*5-)!#+!
,-*)(.:!&*,!C[H!&*,!.0-!$&))!3#))4!72.!&/0(-6-,!.0-!0(50-).!,-/'-&)-!#+!.0-!,&$%(*5?!
<0-)-! +(*,(*5)! )255-).4! .0&.! &! 3#=-'! ,-5'--! #+! $#,(+(/&.(#*! ()! %'-+-'&73-! +#'! )#2*,!
12&3(.:! ($%'#6-$-*.)?! >.! )--$)! .0&.! .'-&.$-*.! L! 0(.)! -X&/.3:! .0&.! =(*,#=!7-.=--*!
$&X($2$! ,-*)(.:! '-,2/.(#*4! $&X($2$! C[H! (*/'-&)-! &*,! ,&$%(*5! '-,2/.(#*?! <0()!
.'-&.$-*.!'&*!.0-!7-).!'-/(%-!E0-&.(*5!'&.-d!MMP"i$&X!.-$%-'&.2'-d!M]OP"i$&(*.-*&*/-!
%0&)-d! S?W0I! +#'! ($%'#6(*5! .0-! '-)#*&*/-! %-'+#'$&*/-! #+! 8(.K&! )%'2/-!)#2*,7#&',)?!
b2.2'-! 3().-*(*5! -X%-'($-*.)! =(.0! 52(.&')! 72(3,! =(.0! .0-! .-).-,! $&.-'(&3! =#23,! 7-! &!
5'-&.!#%%#'.2*(.:!.#!6-'(+:!.0-!$-&)2'-$-*.)!#+! .0()! ).2,:?! b2'.0-'!9-)-&'/0!/#23,!7-!
,#*-!#*!.0-!12-).(#*!#+!.0-!)2).&(*&7(3(.:!#+!.0-!$#,(+(/&.(#*)?!B#*5R.-'$!(*6-).(5&.(#*)!
&7#2.! .0-! ).&7(3(.:! #+! C[H! (*/'-&)-)! #'! ,-/'-&)-)! #+! .0-! ,&$%(*5! =#23,! 7-!
'-/#$$-*,&73-?!
!
! !
!
LL!
5(References(
!
F(33!"D8!ELOOQI!=##,!$#,(+(/&.(#*?!"0-$(/&34!<0-'$&3!&*,!#.0-'!%'#/-))-)4!f#0*!J(3-:!&*,!8#*)!B.,?!
!
T&,,!"04!AyD'/:!f!EMVWQI![*!.0-!-++-/.!#+!0-&.!.'-&.$-*.!2%#*!&/#2).(/!%'#%-'.(-)!#+!)%'2/-?!f#2'*&3!#+!.0-!
g(#3(*!8#/(-.:!#+!D$-'(/&!]dMN]\MQQ!!
;+'(-$!D!ELOOQI!Y*.-')2/02*5-*!k2$!C&.-'(&36-'0&3.-*!.0-'$()/0!$#,(+(k(-'.-'!Fu3k-'!+_'!,-'-*!
g-'=-*,2*5!($!C2)(K(*).'2$-*.-*7&2?!A())-'.&.(#*4!<Y!A'-),-*!!
H(/0-37-'5-'!^!ELOONI!H(*)&.k!6#*!,2'/0!.0-'$()/0-!2*,!.0-'$#$-/0&*()/0-!g-'+&0'-*!6-'7-))-'.-!
Fu3k-'!($!C2)(K(*).'2$-*.-*7&2?!D7)/032))7-'(/0.!>*).(.2.!+_'!C2)(K(*).'2$-*.-*7&2!@=#.&!&*!,-'!<Y!
A'-),-*!!
T'#.0-!<!ELOONI!Y*.-')2/02*5-*!k2'!"0&'&K.-'()(-'2*5!6#*!.0-'$()/0!6-'5_.-.-$!F#3k!+_'!,-*!H(*)&.k!
($!C2)(K(*).'2$-*.-*7&2?!T'#z-'!`-3-5!<-/0*()/0-!Y*(6-')(.{.!A'-),-*!!
@&2-'!C4!;+'(-$!D!ELOMOI!9-(*+#'/-$-*.!#+!.0-'$&33:!$#,(+(-,!=##,!+#'!2)-!(*!0(503:!).'-))-,!
/#$%#*-*.)!#+!$2)(/&3!(*).'2$-*.)?!>*d!;'#/--,(*5)!#+!.0-!b(+.0!H2'#%-&*!"#*+-'-*/-!#*!J##,!
C#,(+(/&.(#*?!9(5&d!SM\SW!!
^27#Z($&!a4![K&*#!<4![0.&!C!ELOOOI?!g(7'&.(#*&3!%'#%-'.(-)!#+!0-&.R.'-&.-,!=##,?!f#2'*&3!#+!J##,!
8/(-*/-4!hQEMId!QSRQ]!
J&5-*+_0'!D4!;+'(-$!D4!T'#.0-!<4!H(/0-37-'5-'!^!ELOONI!Y*.-')2/02*5-*!k2'!6-'53-(/0-*,-*!
"0&'&K.-'()(-'2*5!6#*!.0-'$()/0!$#,(+(k(-'.-'!b(/0.-!+_'!9-)#*&*k,-/K-*!6#*!T(.&''-*?!F#3k!&3)!9#0R!2*,!
J-'K).#++!!QhEhId!SMSRSMQ!
@&2-'!C4!^#=&3-=)K(!D4!8%'#z$&**!94!8.#*Z-K!F4!J&5-*+_0'!D!ELOMQI!<0-'$&3!$#,(+(/&.(#*!#+!H2'#%-&*!
7--/0!&.!'-3&.(6-3:!$(3,!.-$%-'&.2'-)!+#'!.0-!2)-!(*!-3-/.'(/!7&))!52(.&')!?H2'#%-&*!f#2'*&3!#+!J##,!&*,!
J##,!;'#,2/.)4!]hEMId!hSRhW!
B(/0.-*-55-'!F4!9-(.-'-'!D4!8.&*k3R<)/0-55!8H4!b'&.k3!;!EMVVVI?!g&'(&.(#*!#+!"-3323#)-!C(/'#+(7'(3!D*53-)!(*!
8#+.=##,)!&*,!F&',=##,)|!D!;#))(73-!8.'&.-5:!#+!C-/0&*(/&3![%.($(k&.(#*?!f#2'*&3!#+!8.'2/.2'&3!
`(#3#5:!MLWd!LN]RLQV!
D?!9-(.-'-'4!F?!B(/0.-*-55-'4!8?!<)/0-55!}!;?!b'&.k3!EMVVVId!HX%-'($-*.&3!-6(,-*/-!+#'!&!$-/0&*(/&3!
+2*/.(#*!#+!.0-!/-3323#)-!$(/'#+(7'(3!&*53-!(*!=##,!/-33!=&33)4!;0(3#)#%0(/&3!C&5&k(*-!D4!]VEVId!LM]SRLMWh!!
[7&.&:&!H4![*#!<4!G#'($#.#!C!ELOOOI!g(7'&.(#*&3!%'#%-'.(-)!#+!=##,!&3#*5!.0-!5'&(*?!f#2'*&3!#+!C&.-'(&3)!
8/(-*/-!SNd!LVVSRSOOM!
Cu)-'!C!ELOMOI!C-)).-/0*(K!,-'!DK2).(K4!ED/#2).(/!$-&)2'-$-*.!!
.-/0*(12-I!8%'(*5-'Rg-'3&54!`-'3(*!!
!
A&*K-'.!f4!A&*K-'.!F!ELOMSI!<-/0*()/0-!C-/0&*(Kd!8.&.(K4!b-).(5K-(.)3-0'-4!^(*-$&.(K!^(*-.(K4!]?!8%'(*5-'!
!
"&3,-')$(.0!T4!9#))(*5!<A!EMVWhI!A-.-'$(*&.(#*!#+!C#,&3!"#2%3(*5!(*!g(7'&.(*5!9-/.&*523&'!;3&.-)?!
D%%3(-,!D/#2).(/)!M]d!SSRSh!
!
T#'-!<4!T(3-.!T!ELOMMI!"#*.-$%#'&':!D/#2).(/!T2(.&'!A-)(5*!&*,!`2(3,d!A-)(5*!
!
[*#!2*,!G#'($#.#!EMVWSI!8.2,:!#*!a#2*5U)!C#,232)!&*,!>*.-'*&3!b'(/.(#*!#+!J##,!(*!9-3&.(#*!.#!.0-!
H6&32&.(#*!#+!J##,!+#'!C2)(/&3!>*).'2$-*.)?!f&%&*-)-!f#2'*&3!#+!D%%3(-,!;0:)(/)!LLd!QMMRQMh!
!
F&(*-)!AJ!ELOOOI!<0-!-))-*.(&3!$-/0&*(/&3!%'#%-'.(-)!#+!=##,!+#'!$2)(/&3!(*).'2$-*.)?!<0-!"&.52.!
D/#2).(/&3!8#/(-.:!f#2'*&3!hELI!
!
`2/2'!g!ELOOQI!D/#2).(/)!#+!J##,4!8%'(*5-'!
!
LS!
!
Alfredsen G, Larnøy E, Militz H (2006) Dynamic MOE Testing of Wood: the Influence of Wood Protecting
Agents and Moisture Content on Ultrasonic Pulse and Resonant Vibration. Holzforschung 51: 11-20
Machek, L, Militz H, Sierra-Alvares R (2001) The use of an acoustic technique to assess !wood decay in
laboratory soil-bed tests. Wood Sci. Technol. 34(1): 467-472 !
Grinda M, Göller S (2005) Some experiments with stake tests at BAM test field and in the BAM fungus cellar.
Part 2: Comparison of static and dynamic moduli of elasticity (MOE). !International Research Group on Wood
Protection IRG/WP 05-20320 !
Görlacher, R. (1984) Ein neues Messverfahren zur Bestimmung des Elastizitätsmodulus von !Holz. Holz als Roh-
und Werkst. 42: 219-222 !
Ono T (1996). Frequency responses of wood for musical instruments in relation tot he vibrational properties.
Journal of the Acoustic Society of Japan 17: 183 !
Fengel D, Wegener G (2003) Wood. Chemistry, Ultrastructure, Reactions. Verlag Kessel!
"#=,'-:!A94;'-).#*!9A!EMVQQI?!H3&).(/(.:!&*,!$(/'#+(7'(33&'!&*53-!(*!.0-!=##,!#+!8(.K&!)%'2/-?!
;'#/--,(*5)!#+!.0-!9#:&3!8#/(-.:!#+!B#*,#*!MQQ`!EMOOhId!LhNRL]L?!!
!
<'-&/:!C4!H6-'.)#*!f4!A0270~(*!DG!ELOOOI!D!/#$%&'()#*!#+!.0-!$-/0&*(/&3!&*,!%0:)(/&3!=##,!%'#%-'.(-)!
#+!&!'&*5-!#+!8(.K&!)%'2/-!%'#6-*&*/-)!!
!
b&7()(&K!H4!C#3(*)K(!J4!^2,-3&!f4!C&*(&!;!ELOMLI!D!).2,:!#*!.0-!,-%-*,-*/-!7-.=--*!.'&/0-(,!3-*5.0)!&*,!
$(/'#+(7'(3!&*53-!(*!'-)#*&*.!=##,!#+!)%'2/-!E;(/-&!&7(-)!B?I!D**&3)!#+!J&')&=!Y*(6-')(.:!#+!B(+-!8/(-*/-)!
\!8TTJ!b#'-).':!&*,!J##,!<-/0*#3#5:!]]d!LLLRLLQ!
!