8/13/2019 Bab 4 stts

1/29

1

CHAPTER 4

LINES WITH REFLECTIONS

4.1. V E F AC S S.

I S. 2.2

E =(4.1)

I =

(4.2)

W A ,

. T , , :

= =

W

; ,

:

= +

T , E. (4.1) (4.2)

2 . T, =

2R

T

/, S. 2.4. S,

. T

, . I ,

.I S. 1.6

. A ,

: . T

8/13/2019 Bab 4 stts

2/29

2

(4.1) (4.2). T , .W E. (4.1)

.

T . T E = +

(4.3)

I ,

, , , I =

+

(4.4)

C E. (4.1) (4.2)

= (4.5)

= (4.6)

T . H, , 180 . W . P, E.

(4.6) S. 1.5 F. 1.7:

,

.

N, (4.1) (4.2). T , . T

( . 4.1): ; ; , , . O ( = . 4.1).

T , E = I = =0 . (4.1) (4.2).

8/13/2019 Bab 4 stts

3/29

3

S , = =

E =

(4.7)

I =

(4.8)

I

. F , . (4.1) (4.2) E = I = = . , , = =

S E. (4.1) (4.2) = ,

E =

(4.9)

A

E =

(4.10)

T , . 4.1.

T , , E = = 0 = = , .

8/13/2019 Bab 4 stts

4/29

4

I ,

( ) , ( ). O (4.5) (4.6) .

T

. . (4.9)

==

=

(4.11)

T , , . A

==

(4.12)

T . 1.6 . T

(4.11) (4.12): = =

(4.13)

I . (4.10)

, .., ,

= = (4.14)

T E I

. D . (4.9) (4.10),

=

(4.15)

A = 0 , , . , , = .

T

. U . (4.9) E =

= ,

8/13/2019 Bab 4 stts

5/29

5

12 4.16

T .

(4.10)

2

(4.17)

I ,

sin W ( = ), . 2.3, . F,

(4.15) = , = . T (4.7) (4.8) E = . = , (4.17)

.A . 4.1,

. F ,

. 4.2. , . (4.15) = , , , . T (4.7) (4.8) , (4.16) (4.17)

.

E. G 100 , = 685 92 , =0.00497 /, = 0.0352 / 1,000 . T = 2,000 +

0 . T 10 700

. F , , , ,

, , .

F , = 3.52 = 202. T, .. ./2021.64 cos202 sin 202

1.520.615

./

202= 0.566 + 0.229

U . (4.15),

8/13/2019 Bab 4 stts

6/29

6

68592 2,68592 1,315922,68592 1,31592691/7.65) ,/../. 919/20.7

861 325 A

. 5, , ,

.

T . 4.2.

,

||

10

700861325

101596 6.26 10 T

|| ||. || 6.26 10 919 5.75 T ||,

. T,

6.26 10 861 33.8 10T . (4.7) (4.8).

(4.16) (4.17).

,

6.26 10|| 3,8102 691I . T,

|| 2.28 T 2000 ,

|| 4.56 , 10.4 4.2. S , , .

T E I , , = = . (4.1) (4.2). H, . 1.6

. I . S

8/13/2019 Bab 4 stts

7/29

7

,

.

W , . T,

/ . T , ,

(4.18)A , .

(1.25) (4.12):

(4.19)

A . T

, (4.18) =

, , = . T

(4.20)

T = 0

(4.21)

T ;, , :

(4.22)

C , , .

T . T

8/13/2019 Bab 4 stts

8/29

8

1

T 1 + + + , 1/(1 ) < 1. T,

1 (4.23)

T ,

. T

, , . T + , , . T / . (4.11) , . T , . I

= ( ) /( ), . A . (4.23),

( . 14 . 2).

I . (4.23)

, ,

8/13/2019 Bab 4 stts

9/29

9

1 (4.24)

T . (4.24) .(4.5) (4.6): .T

1 (4.25)

T .

4.3. H .

I

, .

E

c o s s i n (4.26)

c o s s i n A , :

(4.27)

A , ,

. 4.3.

T , ,

2A/, A . 4.3.I

8/13/2019 Bab 4 stts

10/29

8/13/2019 Bab 4 stts

11/29

11

sinhcosh coshsinh (4.31)

ta

F, . F

,

(4.32)

(4.33)

(4.34)

C . (4.27) (4.28)

, ,

(4.35)

,

(4.36)

8/13/2019 Bab 4 stts

12/29

12

F = , (4.28) ,

= , = (4.33)

(4.34), (4.35).

sinh sinh cosh j cosh sinh

(4.37)

cosh cosh cosh j sinh sinh 4.4. H F S.

T

. T . H,

,

,

2.

E (4.7) (4.8)

2 2

2

S A.E. K. T C H C F, H U P,C, M., 1927; , C A C H C F, H U

P, C, M, 1924.

8/13/2019 Bab 4 stts

13/29

13

2 2

T ,

, = + . H,

cosh sinh (4.38)

I cosh sinh (4.39) .

S, . (4.9) (4.10)

cosh sinh (4.40)

I cosh sinh (4.41) .

T E I.

tanh tanhW , , .

T (4.16)

cosh sinh(4.43)

T (4.17):

cosh sinh(4.44)

8/13/2019 Bab 4 stts

14/29

14

T , . T (4.37)

.

E. C . 4.1,

:

100 1,000 685 92

0.00497 0.0352 2,000 0

10

700 0 F , ,

, .

F, . M . (4.37), = (0.497 + 3.52) = 0.497 3.52 + 0.497 3.52 , 3.52

202,

sinh 0.518 0.927 1.126 0.375

0.4800.422A, (4.37)

coshcosh0.497cos3.52sinh0.497sin3.52 1.126 0.9270.518 0.375 1.0420.194

W

tanh sinhcosh 0.4800.4221.0420.1940.5230.311

T . (4.42), = . ,

68592 2,000 685920.5230.31168592 2,0000.5230.311

859325

8/13/2019 Bab 4 stts

15/29

15

T

(861 325 ).

T

|| 10|700859325| 6.26 10T . (4.44):

6.26 10|| 1.0420.194 2,000685920.4800.422

|| 2.27 10T

|| ||. || 2.27 10 2,000 4.54

4.5. I S P.

T

. I . 2 ,

,

. H, ,

. T

,

T . 4.6 4.8

; ..,

. T

; .., , ,

. F 4.6

. B ;

, , ,

. T

, .

O , .F 4.7

. O ,

. F,

, ,

8/13/2019 Bab 4 stts

16/29

16

( ). T . T

. T . A

180 . A ,

. T

.

F 4.8

. T ,

, . 4.7, 2. W , ,

.

T

. 4.6 4.8 . A

. T

8/13/2019 Bab 4 stts

17/29

17

. 4.9.

, ( .

4.12):

T

. T , , . T . 4.9 = 0.6 /45, : =1.251.66

T .

F . (4.5),

T, .

I . 4.9 10, . I

T (4.6),

8/13/2019 Bab 4 stts

18/29

18

T + , .

T . A

,

360 . I ,

, ,

,

T . 4.9 =/8 = /4, 0.4

, 3.47 . T

.

8/13/2019 Bab 4 stts

19/29

19

T

. 4.9. S E I ,

. I ,

|| ||(4.45)

W = = ( .10).R . 4.9,

; , , , : = (1.25 1.66) = /S /4

. F

, , . T

8/13/2019 Bab 4 stts

20/29

20

. B ,

.4.6 T C D.

I , . 4.13. T

. 4.9 : (1)

8/13/2019 Bab 4 stts

21/29

21

T E ( I)

. , 0 ( ). I ,

, = 1, . B ,

. I

:

1 2 cos2

4.46 . T .

4.7 M C L.

A

.

T

: , .

T (4.42) = . T,

,

tanh

(4.47)

,

tanh(4.48)

I

(4.49)

T ; ,

,

. T , , 0. T, (4.37),

8/13/2019 Bab 4 stts

22/29

22

sin, cos, tan. T :

tan(4.50)

tan(4.51)

I , /2 ; . T . O , , . I ,

, 1/tan. T . I , ,

.

I . (4.47) . (4.48), :

tanh (4.52)

(4.53)

T (4.53). A

12 log 1 1 (4.54)

:

2 (4.55)

8/13/2019 Bab 4 stts

23/29

23

W A , , . S ,

. T ; , ,

.

I .

T R, L, G, C

. F 1 . U (4.47) , ,

(4.56)

T

.

S, (4.48) , ,

1 (4.57)

A, ,

, .

T , , .

4.8. E F N

I

. W

8/13/2019 Bab 4 stts

24/29

24

,

; ,

. A . I ,

,

. W , ,

T .

F 4.14 T , , . S

,

. W

. T

,

.

I ,

(4.58)

(4.59)

T , . (4.39) = .

(4.41) = . T,

cosh sinh(4.60)

cosh sinh (4.61)

T (4.58) (4.59) . T

coth (4.62)

8/13/2019 Bab 4 stts

25/29

25

coth (4.63)B . (4.58) (4.59),

(4.64)

coth (4.65)E (4.64) (4.65) cosh1 /sinhtanh/2, :

tanh (4.66)

R . 4.14 . (4.64) (4.66), .

4.15. I

, .

T T

T , , . T

. 4.16.

8/13/2019 Bab 4 stts

26/29

26

2 (4.67)

1 (4.68)

T . 4.17.

, . 1

( . 1,3). A 60

. A

, , , , . I ,

. A

,

. I

,

.

4.9. I R I L.

Q

( ) ,

. C . 4.18 ,

, . O , . 4.18, . W

(4.69)

S ,

,

. T , ,

(4.69).

8/13/2019 Bab 4 stts

27/29

27

T

, ..,

(4.70)

20

R . 4.18,

4.71

T .

(4.24) = 0. T

1 1 (4.72)

(4.73)

(4.74)

D (4.71) (4.72),

,

1 1

(4.75)

8/13/2019 Bab 4 stts

28/29

28

T

, . S .(4.73) . (4.74) ,

1 1

1 1

U ,

. (4.75) 1/1 ,

11 1 (4.76)

T . F,

,

, .., T (4.76)

R

T (1.77), , ,

1 1 (4.78)

T

8.686 201 201 (4.79)

T . I , 8.686.

8/13/2019 Bab 4 stts

29/29