2P1-5( $ % %$ '*"' #'$( )(*'( %''%$%*$ (%'&) %$
%#$

26A.*.A.;./2I"686F.B76A..;1 2;76(@B?BA.$8.F.:.);6CI

!  '  '& " $)'%*) %$

'<B;1./@<?=A6<; 6;@B9.A6<;5.C2/22;<;2<3
A5282FA205;<9<462@6;12C29<=6;4;2EA42;2?.A6<;
.?056A20AB?2@ .;1 .BA<:</692@ <;C2;A6<;.9 @<B;1./@<?/2?@ 5.C2 ?2>B6?21 A5608;2@@2@ 0<:=.?./92 A<
A52D.C292;45A5<3.B16/92@<B;1@92.16;4A<9.?42
:.@@D560596:6A@A526?2336062;0F;A56@@AB1FD2
3<0B@ <; A52 20<?.A21 "2:/?.;2 &2@<;.A<?
"& , - D5605 6@ <;2 <3 A52 .0<B@A60
:2A.@B?3.02@A5.A.?2@B336062;A9F@:.992?6;@6G2A5.;
A52D.C292;4A5<3@<B;1D.C2@.;12E56/6AB;6>B2
.0<B@A60 ?2@=<;@2@ @B05 .@ 6;0612;AD.C2
?23920A6<; 1633?.0A6<;A<.?/6A?.?F16?20A6<;@  A5.@
/22;@5<D;A5.AA52"&0.;.0562C2;2.?9F
@<B;1 ./@<?=A6<; .A A52 ?2@<;.;02 3?2>B2;0F
<D2C2?A52@5.?==2.8.A A52 ?2@<;.;A 3?2>B2;0F
5.:=2?@ A< BA696G2 A52 @A?B0AB?2 6; =?.0A60.9
.==960.A6<;@A5.A5.C2.:/62;A@<B;12;C6?<;:2;A@
D6A5 ?29.A6C29F D612 3?2>B2;0F @=20A?. *2 5.C2
=?2C6<B@9F=?<=<@21.@A?B0AB?2A5.A0<:/6;2@"&.;129:5<9AG?2@<;.A<?@A?B0AB?2, -.;1.@A?B0AB?2
A5.A.6:@.A@B=2?=<@6;4@<B;1./@<?=A6<;=2.8@/F.??.;46;4 :B9A6=92 "&@ D6A5 16332?2;A 16.:2A2?@, - ; A52 =?2@2;A @AB1F D2 =?<=<@2 . ;2D@A?B0AB?2D6A5.D612/.;1/F05.;46;4<;9F@5.=2
<3 A52 :2:/?.;2 6; . @6;492 @A?B0AB?2 )@6;4 A5?22
16:2;@6<;.936;6A2292:2;A.;.9F@6@D236;1<=A6:.9
@A?B0AB?2 3<? 2336062;A ./@<?=A6<; <3 @<B;1 D6A5 .
3?2>B2;0F@=20A?.D6A56;   GA.?42AA6;4A<.;6;C256092;<6@2 #*") %$#)%
      @2?62@ <3 ;B:2?60.9 @6:B9.A6<;@ <; A52
:2A.@B?3.02:<129D.@=2?3<?:21B@6;4$"'$!
"B9A6=5F@60@J,-.0<::2?06.9 36;6A2292:2;A:2A5<1"@<3AD.?212C29<=21/F$"'$! (< 2C.9B.A2 A52 ./@<?=A6<; 05.?.0A2?6@A60@ D2
0.90B9.A21 A52 ./@<?=A6<; 0<2336062;A /.@21 <; A52A?.;@32?3B;0A6<;:2A5<1,-(56@:2A5<1;221@A<:2.@B?2A52@<B;1=?2@@B?2.AAD<9<0.A6<;@D6A5.
:60?<=5<;2 D5605 6@ @6:B9.A21 /F :2.@B?6;4
=?2@@B?2 .A AD< 16332?2;A =<6;A@ 6; A52 "0.90B9.A6<;@*") &"'(%$$##'$()'*)*'(52"&<?646;.99F=?<=<@216;&23, -5.@ A@B?BA.20<8.F.:.B.07=A52 06?0B9.? :2:/?.;2 .;1 A52 2E06A21 :<12@ .?2@6:=920<;02;A?6092.16;4A<A52@5.?=./@<?=A6<;.A
. ?2@<;.;02 3?2>B2;0F 2?2 D2 2E.:6;21 A52
:2:/?.;2@5.=2 12=2;12;02 <; A52 @<B;1
'=206360.99F D2./@<?=A6<; 05.?.0A2?6@A60@
6;C2@A64.A21 A52 :B9A6=92E6;4 <3 ?2@<;.;02
0<;16A6<;@D6A5.@A?B0AB?2A5.A/?2.8@A52@F::2A?F<3A52:2:/?.;2N@@5.=2 12=60A@A52@A?B0AB?2@A</2@AB162164
.@5<D@.AD<:2:/?.;2@@A?B0AB?26;D5605
AD<06?092@<3A52@.:2?.16B@.?2.??.;421D6A5A526?
02;A2? :BAB.99F @563A21 64 / @5<D@ . A5?22
:2:/?.;2@ @A?B0AB?2 6; D5605 A5?22 06?092@ .?2@6:69.?9F.??.;421#<A2A5.AA52:2:/?.;2@.?2;<A
<C2?9.==21D6A56;A521<AA2196;2.;1A52?23<?2A52
A5608;2@@6@B;63<?:2C2?FD52?26;A52:2:/?.;2@
*2 .1<=A =<9F=?<=F92;2 3<? 3./?60.A6;4 A52 2;A6?2
@A?B0AB?2 6;09B16;4 :2:/?.;2 6; <?12? A< ?21B02
A<A.9D2645A<3A52@A?B0AB?2





.

 /
64 .(D<:2:/?.;2@@A?B0AB?2       /(5?22:2:/?.;2@@A?B0AB?2
&) # ,) %$%()'*)*'

2?2 D2 .@@B:2 @<B;1 @=20A?B: <3 A52;<6@2 @<B?02 0.; /2 ?2=?2@2;A21 /F . @6:=92
.B@@6.;3<?:D6A5=2.8.?<B;1G.@@5<D;
6; *2A52;@2.?053<?A52<=A6:B:@A?B0AB?2
A5.A ./@<?/@ A52 @<B;1 :<@A 2336062;A9F F
05.;46;4 A5202;A2?16@A.;026;64 D2</A.6;
A52@<B;1./@<?=A6<;=2?3<?:.;02 2C.9B.A21/F

 .A 2.05 02;A2? 16@A.;02 2?2  6@ . @<B;1./@<?=A6<; 0<2336062;A 2C.9B.A21 /F ;B:2?60.9
@6:B9.A6<;12@0?6/216;'2 .;16@A52@=20A?B:
<3A52;<6@2@<B?0212=60A216;64 Proceedings of Symposium on Ultrasonic Electronics, Vol. 40 (2019)25-27 November, 2019















64 :<129@=20A?B:3<?;<6@2@<B?02(*")

   . @5<D@ A52 @<B;1 ./@<?=A6<;
@=20A?B:<3A52<=A6:6G21AD<:2:/?.;2@@A?B0AB?2F/?2.86;4A52@F::2A?FD2@B002@@3B99F</A.6;21
D612?./@<?=A6<;@=20A?B:C6.@2=.?.A6;4A52@6;492=2.8 6; A52 <?646;.9 "& 6;A< A5?22 D5692
:.6;A.6;6;4.5645C.9B23<?.99A52=2.8@42;2?.A21
(52.;.9F@6@@5<D@A5.AA52@2=2.8@,-,-.;1,-.?2 1B2 A< ;<;0<;02;A?60 :<12@ 64  / @5<D@A52 @<B;1 ./@<?=A6<; 0<2336062;A 3<? A52 <=A6:6G21
A5?22:2:/?.;2@ @A?B0AB?2 A 5.@ . 5645 @<B;1./@<?=A6<; 0<2336062;A 6; A52 /.;1D61A5 <3   G.;1A5?22@<B;1./@<?=A6<;=2.8@.?23<?:21
@6:69.?9FA<A520.@2<3A52AD<:2:/?.;2@@A?B0AB?2
(52 =2.8@ ,- .;1 ,- 3<?: . 0<;02;A?60
16@=9.02:2;A 16@A?6/BA6<; :<12 .@ 6; A520<;C2;A6<;.9"&D5692A52=2.8,-6@.;2D:<12
6;D56052.05:2:/?.;2?2@<;.A2@@6:B9A.;2<B@9F
















.AD<:2:/?.;2@@A?B0AB?2




















/A5?22:2:/5/?.;2 @AA?B0AB?2
/A5?22:2:/?.;2@A?B0AB?2

64 /@<?=A6<;@=20A?.3<?<=A6:6G21"&@A?B0AB?2@
%$"*( %$  *2 =?<=<@21 . 0<:=<@6A2 @A?B0AB?2 D6A5
:B9A6=9206?0B9.?:2:/?.;2@<=A6:6G21A52@A?B0AB?2
3<?5645@<B;1./@<?=A6<;=2?3<?:.;02.;1C2?63621
A52 =<@@6/696AF <3 D612/.;1 @<B;1 ./@<?=A6<; /F
;B:2?60.9 .;.9F@6@ @ . ?2@B9A D2 @B0022121 6;
12@64;6;4 . 5645 @<B;1 ./@<?=A6<; 23320A 3<? .
D612/.;1 ;<6@2 @<B?02 /2AD22;   .;1   G (56@5.@/22;?2.96G21/F:B9A6=92E6;4A52?2@<;.;A
:<12@ A5?<B45 /?2.86;4 A52 @F::2A?F <3
:2:/?.;2N@ @5.=2 D5692 822=6;4 . 5645 @<B;1./@<?=A6<; 0<2336062;A .A 2.05 :<12 0AB.9
3./?60.A6<; B@6;4 .  =?6;A2? .;1 . @<B;1./@<?/.;02:2.@B?2:2;A<3A52=?<=<@21@A?B0AB?2@.?26;=?<4?2@@
!$%+"#$)
(56@ D<?8 D.@ @B==<?A21 6; =.?A /F A52 '%' #?.;A#B:/2?   '$(".L0<B@A60:2A.@B?3.02D6A55F/?61
?2@<;.;02@M#.AB?2".A2?6.9@ = H 
+BA. </.F.@56 2;76 (@B?BA. .;1 A@B@56
@568.D.     %    "B76A. ".;./2 (@B?BA.(.1..;1 #+<?<GB      %   
5AA= DDD0<:@<90<:'$    L0<B@A60@K2A2?:6;.A6<; of sound absorption coefficient andimpedance in impedance tubes – Part2:
Transfer-function method”.
#2C699292A052?.;1(5<:.@&<@@6;4L(52%5F@60@<3"B@60.9;@A?B:2;A@M 