Please use this identifier to cite or link to this item: https://er.chdtu.edu.ua/handle/ChSTU/8362
Title: Автоматизована система керування імпульсного гідроакустичного вимірювання
Authors: Базіло, Костянтин Вікторович
Перкін, Денис Олексійович
Keywords: ультразвукова кавітація;швидкість звуку в рідинах;автоматизована система керування вимірюванням;імпульсне гідроакустичне вимірювання;цифрова обробка сигналів;багаточастотний метод
Issue Date: 15-Dec-2025
Abstract: У роботі розробляється автоматизована система керування імпульсним гідроакустичним вимірюванням для надійного визначення швидкості звуку в рідинах в умовах інтенсивних акустичних завад із використанням багаточастотного методу та цифрової обробки сигналів.
The work develops an automated control system for pulsed hydroacoustic measurement to reliably determine the sound velocity in liquids under intense acoustic interference using a multi-frequency method and digital signal processing.
URI: https://er.chdtu.edu.ua/handle/ChSTU/8362
Appears in Collections:174 Автоматизація, комп'ютерно-інтегровані технології та робототехніка (Робототехнічні системи та автоматизація)

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. 
 5 
 1.        
  8 
1.1.       
      8 
1.2.     11 
1.2.1.    ( )  14 
1.3.2.     15 
   1  20 
 2.      23 
2.1       25 
2.2.      29 
2.3.       
  30 
2.3.1.       30 
2.3.2. '        31 
2.3.3.     (   )  32 
2.3.4.       
  34 
2.4.        37 
   2  39 
 3.       
   40 
3.1.        44 
3.2.      46 
3.2.1.      47 
3.2.2.      48 
3.2.3.     (DDS)  49 
4 
 
3.2.4.       54 
3.3. -    66 
3.4.     68 
   3  70 
 4.      
  71 
4.1.       
  71 
4.2.         
  74 
4.3.       80 
4.4.         83 
   4 .. 85 
   86 
    88 
  
  
  
5 
 
 
 
 
        
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      . 
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7 
 
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  . 
    
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   ,      «  » 
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      ’ . 
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 :     
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AD9833,          2%. 
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   . 
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 1 
     
   
 
 
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9 
 
K = −V dP ,                                                                 (1.1)  
dV
 P —  ( ), V — ’  ( 3). 
       (c)  
     : 
 
c = K ,                                                         (1.2)  
ρ
 
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        : 
 
c fluid = 1 ,                                                      (1.3)  
βρ
 
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       : 
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 ,       . 
 ,        
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  .      : 
 
Z = ρ ⋅ c,                                                                (1.4)  
 
  1.1     ,  
    . 
 
 
10 
 
 1.1 
    
  ,    
/ 3   c, Z 10 3, /  
/  
 1,29 331 0,0004 
 1000 1483 1,48 
 789 1143 0,90 
(C_2H_5OH) 
 
      
 (I, / ^2),      ( Pa )   
: 
I =                                                                    (1.5) 
 
  ,  ,      , 
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 P  = cA                                                    (1.6) 
 
      : 
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 ,         
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. 
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11 
 
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 ,    . 
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 . 
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. 
 
 
1.2.    
 
         
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   .   ,   
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 ),   . 
    
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        : 
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   . 
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12 
 
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 (   ,   ),  ,  
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 .       
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     —  ( ) — 
     . 
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  ,      : 
•     ,    
 '   (  ). 
•       , 
       . 
13 
 
    
      
 —   ( χ ): 
 
χ  =                                                                  (1.7) 
 
  —  , —   ,  —  
 . 
       
 (I)     ( ρc ): 
                                                                   (1.8) 
 
 (1.8)  (1.7),   : 
 =   
                                                        (1.9) 
 
     χ     χk  
 (1.9) ,        
 ,     ( ρ,c )  
    . 
  
        
    .      
 ( nf )   ( f / 2, f / 3 )  ,   
    .     
14 
 
    ,     (  
   . 1.1). 
 
 
.1.1.   
 
    1.3.    :   
  ,       .  
 — ,       
. 
 
1.2.1.    ( ) 
        .  
   '     ,   
   (   ),    .  
       
     ( )   ( ).  
        . 
        
    c = 2l  f   : 
                                                    (1.10) 
 l —    , f —   
. 
15 
 
  ,    , 
    ,    .   
   =     ( :  )                                                         (1.11) 
    —   ,   (m - n)  
     . 
       
   ( ),      
(  1.2). 
 
 1.2.        
 
   (     )   
     .   
        ,  
      . 
 
1.2.2.    
   ,     
          
  (Time-of-Flight). 
      
’  ,     ’  
       (  1.3). 
16 
 
 
 
 1.3.       
 
        
( ).        (  FS),  
  ,        
 (  B1).      
  -  B2 , B3   (  1.4). 
 
 1.4.   
 
       t  
   d: 
 =                                                            (1.12) 
17 
 
 
 ,        
         180°.  
         
   .     
     . 
     ,    
   .        
. 
.   (Sing-Around) 
 ,      ,   
 (  1.5).      
        . 
 
 1.5. -     
 
    ,     
       .  
         
   ,     . 
.    (PulseSuperposition) 
    .    
    ,    (  1.6). 
18 
 
 
 
 1.6. -     
 
 
 1.7.      
.   -  (Echo-Overlap) 
 
   ,      
     -    .   
        (  
1.7).          
   . 
19 
 
         
 (  1.8).         
    ( ,    ). 
 
 
 
 1.8. -       
-  
 
      
   (  1.9).     
     ,    . 
           , 
   ,       
(«cycle-to-cyclematching»). 
 
20 
 
 
 
 1.9.    -  (  –  
;  –  - ;  –  ) 
 
 
   1 
       
   ,     
 ,         
. 
       : 
1.   (  ): 
o       
 (10–40 ),     . 
21 
 
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o        
 ,    . 
o        
. 
2.   (  ): 
o         
      . 
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o     : -    
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 :        
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22 
 
         
          
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1.       
. 
2.       
 . 
3. ,      
  . 
  
23 
 
 2.    
 
 
 
         
      .     
    . 
 1:   ( - )     
          
  (  2.1).    
 '  ,    (  )  
 . 
 
 
 2.1.      -
 
 
         
 .        
 :       
       ,     
   (  ).      
 , ,   ,     
      ( ). 
24 
 
 2:   (  )   
    :    
 ,  —    (  2.2). 
 
 
 
 2.2.       
 
 
          . 
        (  
),        
  '  . 
         
  ,        
 .       
     . 
      ' ,     
: 
1.  . 
2.   (  ). 
3.  . 
       , 
    .   
          
,          '  
  . 
 
25 
 
2.1      
       
  .        
     : 
 + K = 0                                                     (2.1) 
 
:  —   (  ,  ); 
η  —     ; 
t —  ; 
K — ,       (  
 E,   σ ,  ρ   2h ). 
'         : 
 (r, , t) = Y(r, )e                                       (2.2) 
 
  (2.2)  (2.1)   ,    
         Y:  
 (  ) Y = 0  ( +  )Y = 0                              (2.3)  
 
 γ  —    . 
   ' ,     
  ( r,φ ).  '     
    Jm  (   )   
  Im  (   ): 
 Y (r) = [A J ( r) + B I ( r)] (m )                  (2.4) 
26 
 
 m = 0,1,2,…—    (  ); 
Am , Bm —  ,    . 
     
         
.       (r = a).  ,  
     ,     .   
   , '       
(  ). 
   =      ( fmn ): 
(  )                                (2.5) 
 βmn  —   ,       
(n)   (m). 
 (2.5)       
   .    30  
    -19    2.1. 
   
     '  (2.4)  
      . 
1.   (m=0).     n  
  .       
  ,      
 .         
. 
 
 
 
 
 
27 
 
 2.1 
 
      
 ,  ,  , 
      
1 13,1 11 1584,7 21 5775,7 
2 52,4 12 1885,9 22 6338,8 
3 117,9 13 2213,4 23 6928,2 
4 209,5 14 2567,0 24 7543,8 
5 327,4 15 2946,8 25 8185,5 
6 471,5 16 3352,8 26 8853,0 
7 641,7 17 3785,0 27 9548,0 
8 838,2 18 4243,4 28 10268,0 
9 1068,0 19 4727,9 29 11014,0 
10 1309,7 20 5238,7 30 11787,0 
 
 
 2.1.      m = 0, n = 4 
 
28 
 
2.   ( m ≠ 0 ).    
,    .      
           . 
   
     '  (2.4)  
      . 
3.   (m=0).     n  
  .       
  ,      
 .         
. 
4.   ( m ≠ 0 ).    
,    .      
           . 
 
 
 2.2.      m = 4, n = 3  
 
 
29 
 
2.2.     
      
’       .     
     . 
    ( fn )   
         : 
 =                                                      (2.6) 
 
: n = 1, 3, 5, … —   ; 
 —     ’ ; 
h —  . 
   20     
    2.2. 
 
 2.2  
    ’  
 ,  ,  , 
      
1 2,439 8 19,515 15 36,590 
2 4,879 9 21,954 16 39,030 
3 7,318 10 24,393 17 41,469 
4 9,757 11 26,833 18 43,908 
5 12,197 12 29,272 19 46,348 
6 14,636 13 31,712 20 48,787 
  
7 17,075 14 34,151 
 
 ,        
,     (   . 2.1.1) —  .    
30 
 
        
. 
 
 
2.3.       
 
2.3.1.      
        , 
    .   
    '      
 Φ(r,φ, z,t) .       
 :   = 0                                                      (2.7) 
 
 c —     . 
   '      
  .        : 
1.  ’  :       (P=0), 
   Φ = 0 2. 
2.   :     
     ( vn = 0 ).  ,     
    . 
     ,  
      .  
     : 
 ( )                                                 (2.8) 
,                                                  (2.9) 
31 
 
2.3.2. '       
   (2.7)   ’  (  ). 
        , 
       : 
 ( , , , ) = ( ) ( ) ( ) ( )                               (2.10) 
 
 (2.10)    (2.7)     
   , '     
 (   kr ,kφ ,kz ,k ). 
       : 
 =  +                                                 (2.11) 
 
   
    R(r)   .   
'      ( Jm )   ( Nm ,  ) 
: 
 
R(r) = A ( ) + ( )                                      (2.12) 
 
     (   )  
r → 0 ,          , 
 A'   . ,    
: ( ) = ( )                                                       (2.13) 
   
     (2.8)   ' , 
        : 
32 
 
  [ ( )]                                                 (2.14) 
 
         
 .          
2.3. 
 
 2.3  
     (  Jm′ (x) ) 
   1  2  3  4 
(m) (i=1) (i=2) (i=3) (i=4) 
0 0 3,8317 7,0156 10,1735 
1 1,8412 5,3314 8,5363 11,7060 
2 3,0542 6,7061 9,9695 13,1704 
3 4,2012 8,0152 11,3459 14,5858 
 
 
2.3.3.     (   ) 
        
   ,     z.   
 ,        ,    
. 
        , 
 kz → 0 ,   k  . 
      2.3 (  m=1, i=1)  
1,8412.     : 
 = 1.8412                                        (2.15) 
33 
 
 '      ( k = 2π f / c ),  
      ,    
  : 
1.    ( ): 
 =  .     
                                              (2.16) 
 
2.   ( ): =  .       
                                           (2.17) 
 
     (     dmax ),   
   ,     ,   
     . 
        
   2.4. 
 2.4  
   (  ) 
  (amax),    (fcr),  
5 86,7 
10 43,4 
25 17,3 
50 8,7 
100 4,3 
  (  2.4) ,      
"  "       . 
 
 
 
34 
 
2.3.4.       
    (m=0),    
   .     
  ( kz = 0 )      
: (r) ~ J  ( , r)                                             (2.18) 
 
   MATLAB    
        . 
 
 
 
 2..3-    
 
35 
 
 
 
 2.4.       
   i=2 
 
 2.5.       
   i=3 
36 
 
 
 
 2.6.       
   i=4 
 
 
 2.7.       
   i=5 
37 
 
  (  2.4–2.7)      
,       . 
 
 
2.4.       
 
      
        
    .    
       . 
         
 ,       
  ,      . ,  
   (   )   
 ,     : 
1.    .   (2.6), 
         
’ . 
2.    .    
 ,   (2.9)     ( fcr ), 
       . 
3.   .    
 :        
,      . 
  
         
: 
• ’  :  -19,  10 ,  1 . 
•  :     
 7  (  R=3,5 ). 
38 
 
  :  =  7.5   10 /   =0.37 E = 5.4   10   
 
        fcr = 62  
. 
        (  2.5), 
   . 
 
 2.5.  
    
    ,   
1 12  ( < fcr ) 
2 47  ( < fcr ) 
3 106  ( > fcr ) 
4 188  
5 294  
6 423  
7 576  
8 753  
9 953  
10 1176  
 
 
 ,         
   (12   47 )      
(  ).         
   ,        
    . 
 
 
39 
 
   2 
 
        
    .     
 : 
1.   .   
      
’     :    (  
 )     (   
).        
. 
2.   .     
,         
'         .  
           . 
3.   .     
    .    
         
 ,       
. 
  
40 
 
 3. 
     
  
 
       
   (  2.2),    
     . 
       
  ( t1 ).      ( ) 
 :         
 ,        
,       . 
      —   t2 , 
        .  
          
 ( t3 )     ( tc ): 
 =  +                                                    (3.1) 
 
    (    l, 
   : 
 =  =                                                       (3.2) 
 
      :  — 
 ( H2O ),   l = 7 .       
    (Trep ).     
41 
 
 ( )   ,    (
Frep = 1/ Trep )   :  
                                                       (3.3) 
 
,          
    (   5 ),   
      -  . 
   :    
(  )    ’  
,   ,       
2,      (  )   (  
). 
       ( ). 
 
 
 
 3.1.       
 
 
   (  3.1)   , : 
42 
 
•      ’  (  
2.1, 2.2, 2.4),    . 
•   ( )    ( , 100 
),    (3.3)  . 
     ,     
 t3.      —  
      . 
     
      :  
  . 
1.    
 (  3.2)      
,       . 
 
 
 
 3.2.      
 
        : 
•  :       
    .  
43 
 
       
     . 
•  :      
     ,   
     . 
•  :      
      ,    
     . 
2.   
     .  
      ( )  fg , 
      ( fIF ): 
 = |  |                                         (3.4) 
 
 
 
 
 
 3.3.     
 
   (  3.3): 
44 
 
•         
 ( , 450 ),      
    . 
•        
 (    ). 
•       ,  
     . 
 ,      , 
         
    . 
 
 
3.1.       
 
    (  3.4)   
      . 
        
 .        
  ( fc ),     ( .  2.1, 2.2, 
2.4).     ,        
    ( fIF ). 
      : 
1.   .    ( fc ) 
    (  ). ,   
  ,    
   .   (   
)  ,      (3.3). 
2.  .   
    ’   (1). 
45 
 
  ’       
,      . 
3.  .     ,  
  ( t3 ),        . 
4.    .    
   ,    .  
     ,    
:          
 ’     . 
5.  .     
    . 
        (  
3.5),     ( )    —   
( fIF ),      . 
6. .       
,     ( ). 
 
 
 
 
 
 
 
 
 
 
 3.4.        
          
     . 
 
46 
 
 
 
 
 
 
 
 3.5.    
 
    
     .    
 : 
1. :    -   
          (3.2). 
2. :        
(    ),       
  . 
   (  ,  ) 
     . 
 
 
3.2.     
 
        
     (   )  
     ,     (
fIF ). 
    ,   
      ( ).  
    450     Q ≈ 22,5 , 
   (B) : 
47 
 
 =   20                                                 (3.5) 
 
       :   
        . 
 
3.2.1.     
     LC-    
         
 ,      
 . 
     ’  
.       LTM450EW,  
     . 
  LTM450EW: 
•  : 450 ±1.5$ ; 
•     :   2 ; 
•     (   ±15 ):  50 
; 
• /  : 1500 . 
 
    (  3.6)    
       . 
 
 
 
 
 
 
48 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.6. -     
 
 
 
3.2.2.     
       
 ,      (  3.7). 
 
 
 
 
 
 
 
 
 
 
 3.7.       
49 
 
 
 
 
 3.8.       
 
      ,   
     .   
  RC-  ( =  ).     
     ,     
       .  
          
   .      
  . 
 
3.2.3.     (DDS) 
      
     (DirectDigitalSynthesis — DDS). 
  
50 
 
 DDS        
       .  
 (  3.9) : 
1.  : ,      ( ) 
      —   (). 
2.  « - »:  ( ),    
 ,        ' . 
3. :      . 
 
 
 
 
 
 
 
 
 
 
 3.9.      
 
 " "   (  3.10),     
 ,       M (  
). 
 
 
 
 
 
 
 
51 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.10.      
 
  ( fout )  : 
 =     
                                           (3.6) 
 
 —  , n —   . 
         , 
        . 
  
      AD9833  AnalogDevices.  
   ,   , 
  . 
 : 
52 
 
•   : 28 .    25   
    0.1 . 
•  : 3-  SPI. 
•  : 2.3...5.5 . 
      3.11. 
 
 
 
 
 3.11.   AD9833     
  
 
53 
 
      DA1 (KXO-V97) 
 12 .        
 (  5-6 ), ,    - , 
      
 
 =   
 
      SPI 
    (  3.12, 3.13)     (  
3.1). 
 
 
 
 
 
 
 3.12.     
 
 
 
 
 
 
 
 
 3.13.      AD9833 
 
 
 
54 
 
 3.1. 
     
 .,   
t  40    (MCLK) 
1
t 25   (SCLK) 
4  
t 5   FSYNC  SCLK 
7  
t 5    (SDATA) 
10  
 
 DDS    : 
      ( M1     M 2  
),     450 ,      
. 
 
 
3.2.4.      
  
  ,     
     ,   
( ).         
. 
    : 
1.       ( ),  
   . 
2.        . 
3.        ,  
     . 
4.     ,   
 (ttotal),           . 
55 
 
5.        
 (3.1)  (3.2). 
     MSP430G2553  
TexasInstruments.     : 
• :       
      . 
• : 16-  RISC-      
 (DCO)         1 . 
• :  16-   /  
(Timer_A)         . 
 10-        
. 
      3.14. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.14.      
MSP430G2553 
56 
 
      Spy-Bi-Wire 
( '  X1). RC-  (R2, C11)    (Reset)   
.    -      
(  3.15),      . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.15.    ,  
 
 
-   
       
(  )     WH1602 
(2   16 ).     4-    
(DB4-DB7),     .   
     3.16. 
 
 
 
57 
 
 
 
 3.16.      WH1602 
 
        (P1-
P6),     (  3.17).   : 
  ,    DDS,    
 .  R1      
 . 
 
 
 
 
 
 
 
 
 
 
 
 3.17.       
 
58 
 
   (  ) 
   DDS-  AD9833  
’        
.     200 ,   ’   
  (1 )     (1...10 )  
 : =   15 … 150                                (3.7) 
 
 
 
 3.18.      
 
 
       
 ,        
 . 
         
 CD4011 (   2 - ).     : 
1.  :   -    
  . 
2.  :     
 (  DDS)    (  )    
(  3.19). 
 
 
59 
 
 
 
 3.19.       CD4011 
 
     Tina-TI (  3.20) , 
      ,    
 (3 ),     (   100 ). 
 
 
 
 
 
 
 
 
 
 
 3.20.      
60 
 
    
        
/ . ’         
 ,     . 
      (    
 )         
("  ").      ,   
     (  3.21). 
 
 
 
 
 3.21.        
 
 
           
2N3904.       ( Rin )    
  . 
      ( Ie ): 
                                             (3.10) 
 
61 
 
   (  3.22)    
  50 .    (VD1, VD2)  
       (3.3 ). 
 
 
 
 
 
 
 
 
 
 
 
 3.22.      
 
  (  ,  3.23)   
 32     10      2 ,   
  . 
 
 
 
 
 
 
 
 
 
 3.23. -   -   
 
62 
 
 
 
 3.24.        
 
     
    ( , , ) 
   TA2003,     -
. 
 
 
 
 
 
 
 
 
 
 
 
 
 3.25.  -   TA2003 
63 
 
         (  
16 TA2003),     .   
  ’  (450 )      (  
3.27),         . 
 
 3.26.      
 
64 
 
 
 
 3.27.      
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.28.      
 
    (  11)  . 
       ("  "),  
         
 TLC272CP (  3.29). 
65 
 
 
 
 
 
 
 
 
 
 3.29.    ( ) 
 
  R1-R2    (0.9 ),    
        (  3.30), 
    . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.30.      
 
 
66 
 
3.3. -    
 
        
(Mixed-SignalDesign)      
 ( ). 
     
       
.        
  ("GroundBounce"),       
. 
      « » (Single-
PointGrounding).  (AGND)   (DGND)    
 '     —    . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.31.   : )  ( ); ) 
 " " ( ) 
 
67 
 
        
SMD- ,       
.          
. 
     AltiumDesigner. 3D-   
   3.32–3.34. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.32. 3D-    (  ) 
 
 
 
 
 
 
 
 
 3.33. 3D-    (  ) 
68 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.34. 3D-    ( ) 
 
 
3.4.    
 
   (  3.35)    
  FR-4  1,5    . 
     : 
1.   (1):   ,  DDS  
 . 
2.   (4):   TI LaunchPad  
 MSP430,       . 
3.   (2):  ,      
     ’ . 
 
 
 
 
69 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3.35.      
 
 
  (  1-6)     
   .    '   
      (  3.37). 
 
 
 
 
 
 
 
 
 3.36.      
 
70 
 
 
 
 
 
 
 
 
 
 3.37.      ’  
 
 
   3 
 
      : 
1.         
 DDS-  ,      
  . 
2.      (   
 )       . 
3.         
     . 
4.    ,    
     . 
 
  
71 
 
 4. 
   
  
 
 
4.1.      
 
 
      ,  
         
  ’ .       
:    (    )     
(    ). 
        
     ,   
   . 
 
 
 
 
 
 
 
 
 4.1.        
   
 
       '  
(    . 3.4),     ’  
72 
 
.       
 : 
1.  :    '  
    (   1 ).    
 . 
2.  :      
     (50 ).     
. 
       
,       ( ).  
-   : 
•   : 10 ; 
•  : 100  – 1 ; 
•  : 1 ; 
•  : 10 . 
 
 
 
 
 
 
 
 
 
 
 
 4.2.       (  
) 
73 
 
        
 ,      -  
 ( )  . 
       
 4.2,    —   4.3. 
 
 
 
 
 
 
 
 
 
 
 
 
 4.3.        
R_{ } = 50\  (  ) 
 
  
       
   .  ,    
   (  4.2),    
 .     ,   
   "  " (crosstalk) —  
          
 ' ,   .      
         . 
74 
 
,     (  4.3) 
     .   
     - - . 
:        
 ,      
         (   
).      , 
   3. 
 
 
4.2.        
 
 
'       
      
'   (  Tina-TI).     
       
  . 
      ,   
 ’     ,  
      (  " ").   
: 
•  : 20 ; 
•   : 2,407 . 
1.     
       (  
 CD4011).     (  4.4)  
  ( .  3.20)   . 
 
 
75 
 
 
 
 
 
 
 
 
 
 
 
 
 4.4.      
 
 
 
     ,   
 .    ( )   
       ,   
     ’ . 
2.     
        
 (    ),      
 TA2003 (  4.5). 
      (  16 
):         
    .      
       . 
 
 
 
76 
 
 
 
 
 
 
 
 
 
 
 
 
 4.5.     TA2003 
 
3.     
     .  
     (2,407 )   450 .  
        
(  4),      4.6. 
 
 
 
 
 
 
 
 
 
 
 4.6.       
 
77 
 
4.    
        
’  .     (  4.7)  
    :   
   (      
 ). 
 
 
 
 
 
 
 
 
 
 
 
 4.7.      ( ) 
 
       ,   
          
. 
5.    
       (  
4.8). 
 
 
 
 
 
78 
 
 
 
 
 
 
 
 
 
 
 
 
 4.8.     
 
     : 
1.  :        
. 
2.   :      
 ,    ,   
 .        . 
        
(  4.9). 
 
 
 
 
 
 
 
 4.9.     
  
79 
 
   ,      
   (  4.10),    
. 
 
 
 
 
 
 
 
 
 
 
 
 4.10.     
 
    
   (  4.4 – 4.10)   
    ( tc )   : 
1.       (  ). 
2.   . 
3.     (  ). 
 ,      
 ,       (   
),      72 .     
       
 . 
 
 
 
80 
 
4.3.      
 
       
      .  
    : 
1.   :    
 '    . 
2.   '    (  
  ). 
3.  :    
’    . 
4.  :      (t_{total}) 
     . 
5.  :      
     . 
 : 
•   (     ): L = 53 
. 
•    (   . 4.2): t_c = 72 . 
  (c)   : 
 =                                             (4.1) 
 
 1:   (H O) 
       . 
    :  (152.4 )   (22.407 
, 34.814 ),     . 
   (    )   
 4.1. 
81 
 
 4.1. 
      
 /      
 (ttotal),  (tacoust),  (c), /  
  
   
 
152.4  
1 112 40 1325,0 
2 102 30 1766,7 
3 110 38 1394,7 
... ... ... ... 
   
 
22.407  
1 106 34 1558,8 
2 110 38 1394,7 
... ... ... ... 
 
 « »  (  4.1)    
 ,         . 
       . 
   ( tacoust )     
  : 
 
N
t 1
acoust = (t
N total ,i − tc )  
i=1
 
     36 . 
,   : 
82 
 
53 ⋅10−3
cH O = −6 ≈1472 /
2 36 ⋅10  
 
  (1472 / )      
     20°C  (1481 / ).    
 1%,     . 
 2:    (C H OH) 
      .  
   4.2. 
 4.2. 
      
 /       
 (ttotal), (tacoust),   (c), /  
 
1 109 37 1432,4 
2 119 47 1127,7 
3 114 42 1261,9 
... ... ... ... 
 117 45 1177,8 
 
      (45 )   
: 
−3
ceth = 53 ⋅10
45 ⋅10−6 ≈1178 /  
 
     1180 /  2.   
        . 
    (  ) 
83 
 
          
" "  — ,       ( fcr ),  
      ’ . 
    : 
1.    ( tacoust )     
. 
2.        
 . 
 :      
  .   f > f cr       
,    ,    
   L.       
 . 
:        
'       : 
•       (  ); 
•     ,   
 ,       3. 
 
 
4.4.        
 
       
        
 .       
,      , 
" "    . 
      ,   
     . ,   
84 
 
   ,        
     (  22, 44  
66 ). 
  ( - ) 
       
  .     
    ’ ,    
        . 
 : 
•    (  ): 2…5  . 
•   :   0  1000 . 
 
  ,     
         
 ,   1000 .  ,     
    '   /  (  
      40-50 ). 
      : 
1.  :       
   . 
2.  :     
   ,       (\pm 7.5 
),    . 
 ,         
       
 ,       
,         
. 
 
 
85 
 
   4 
 
      
 : 
1.        
   (    ),    
  . 
2.         
  (    2%),    
 . 
3.        ' : 
       ,    
 ,    ,     
. 
4.    ,    
     . 
 
  
86 
 
  
 
 
     -   
—          
,      . 
        : 
1.  .        
 ,    ( , 
)        
,    .    
  . 
2.  .    
  ,      ’   
      .   
      . 
3.  .     
    . ,    
 20       62,1 .   
       . 
4.  .      
,      . 
       
   . 
5.  .   ,  
  ,    (    ), 
      .    
 «  »      
    2% (    1472 / ,   — 1178 / ). 
87 
 
6.  . ,    
       72  (40  — , 
32  —  ).        
 50     30 . 
7. .      
      /   -40 ,  
        
  . 
  
88 
 
   
 
 
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7.  . .,  . .     
   FPGA.   . 2024. . 8,  1. . 55–61. 
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(    ). 
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18. 
10.         
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89 
 
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