1. SchoolDD.com
11
www.schoolDD.com

2. 11
F
F F F F
F
F F
F
- F F F F F F
- S.H.M.
y = A sin t
y= y
A=
=
t= F
FF F F y = A sin t F S.H.M
y F
r y = r sin
r=A = t
F y = A sin t
– F F www.schoolDD.com 1

3. F F
t=0
A
t = T/4
t = T/2
t = 3T/4
A
t=T
F F F
y
y = A sin t
A
0 t
T/4 T/2 3T/4 T
-A
11.1
1. F F
F
2. F F F
F 2
1.
F
F
2.
F
– F F www.schoolDD.com 2

4. 11.2
F F
A A’
O
P
B F B’ F
- F F F O, P
- F
F F A B
- F F F A A
- F F F F B B
- F F F F
F AA , BB F F F F 2
F F (m)
F F
F ( ) F 1
– F F www.schoolDD.com 3

5. 0
t=0
λ/4
t = T/4
λ/2
t = T/2
3λ/4
t = 3T/4
λ
t=T
11.3
F F F /
(1)
= v=
t s F F
F T
(2)
v= = = f
v=f
v =
f = F F F
F / F (Hz)
T= F F F F
F
= F
- F F
– F F www.schoolDD.com 4

6. F F F F F F
A 0°
B B 90°
A C 180°
C E
D 270°
D
E 360° 2
- F F F 360˚ 2
2 F
1. F 2 ,4 ,6 ,
2. F ,2 ,3 ,
3. F T, 2T, 3T,
B F J A,E,I M
P R B,F,J
A C G K
Q
E
S
I M C,G,K
D H L D,H,L
P,R
Q,S
F 2 F F F
F
1. F ,3 ,5 ,
2. F /2, 3 /2, 5 /2,
3. F T/2, 3T/2, 5T/2,
C,G,K F A
D,H,L F B
A,E,I,M F C
Q,S F P
– F F www.schoolDD.com 5

7. F 1
F F
(cm)
+10
0
a b (cm)
5 10 15 20
-10
.
. A
. a b
. =?
= 10 cm = 0.10 m Ans
.
= 10 cm = 0.10 m Ans
.
a = Ans
b =2 Ans
F 2
F F F F F 30
10 F F 4 cm
4 cm 30 / 10
f= =
f = 3.0 Hz Ans
v = f = 3.0 x 0.04
v = 0.12 m/s Ans
– F F www.schoolDD.com 6

8. T= =
T = 0.33 s Ans
F 3
A B F 2
cm
A 3
1 2 4 5 6
cm
B 1 2 3 4 5 6
F A B
s = 6-3 = 3 cm
F t=2 s
v= = = 1.5 m/s Ans
f v=f
= 4 cm
f= = = 0.375 Hz Ans
F 4
F F 20 cm/s 5 / F
F F 1.0 m F F F
1.0
F F v = 20 cm/s , f = 5 Hz
v=f
– F F www.schoolDD.com 7

9. = = = 4.0 cm = 0.04 m Ans
F F
s = 1.0 +
= 1.03 m
v=
t= = = 5.15 s Ans
F 5
F 100 / F 0.5 F /4
0.50
0 /4
F /4 F F
0.5
F 2 F F
0.5x2 /( /4) = 4.0
= 4.0 m Ans
v v = f = 100x4.0
v = 400 m/s Ans
11.4
F F
F F F
– F F www.schoolDD.com 8

10. - F F ( - F )
- F F
11.5 F
F F F
1 F F
F F F
F F
- F F
11.5 F
F F F
F
F
F F F
F F
11.6 F
F F
F F F F F F F
F
– F F www.schoolDD.com 9

11. F
F
F 6
2 F F 1 cm/s F F
F
cm
+1
cm
1 2 3 4 5 6
-1
F 2 cm
cm
+2
+1
cm
1 2 3 4 5 6
-1
-2
F s = 2 cm
t F s= vt
t= = = 2.0 s Ans
= 1.0 + 1.0 = 2.0 m Ans
– F F www.schoolDD.com 10

12. 11.7
4 F
- F F F
F
11.8 F
1. F F
F F F F
F F F
F F
F F F
F
F
F 7
F F 1 cm/s F F
F F F 2 cm
– F F www.schoolDD.com 11

13. F F
F
F
F F
F F 2 cm
t F s= vt
t= = = 2.0 s Ans
2. F
F F F F F F F
F F F F F
F
F
F F
F
1
1 2
2
F
1 = F 2 F
1 , 2 = F F F
F = F F
- F F F
F 8
F F F
50°
120°
– F F www.schoolDD.com 12

14. 11.9
F F
F
F
F F F
C 1 B
2
1
1 1
2
A 2 2
D
= = ------
= = ------
/ , = = =
= =
F f1 = f2
1 =
= F
2 =
- F F F F
F
v >v
=
>
F 1 > 2 ( F )
F 1
F F F F
2
- F F
– F F www.schoolDD.com 13

15. F 9
F 1 m/s F F F
0.50 m 1.0 m
1
v1 = 1 m/s 2 v2 = ?
1 = 0.5 m 2 = 1.0 m
=
F F =
v2 = 2 m/s Ans
f v=f
f= = = = 2.0 Hz Ans
F 10
F 2.0 cm 3 Hz 1 F 2 F
16˚ 2
2.0 cm
1
53° 2
16°
1 = 53°
2 = 53° - 16° = 37°
=
=
F F =
– F F www.schoolDD.com 14

16. = 1.5 m Ans
v2 v=f
v2 = 3x1.5 = 4.5 m/s Ans
11.10
F2 F F ( F
)
F F
N1 A0 N1
A1 A1
N2 N2
A2 A2
N3 N3
F
A3 A3
s1 s2
s1 s2 F F
F ( )
F F F ( )
F F ( )
(Antinode) F
(Node) F F F
F A0 , A1 , A2 , , An F F F F
F N1 , N2 , N3 , , Nn F F F F
– F F www.schoolDD.com 15

17. F F F s1 , s2 F F
A0
A1 N1 N1 A1
N2 N2
Q
P
s1 + + s2
d
n = 0, 1, 2, 3,
| s 1P – s 2P | = n P F F n ( An )
n=0 F ( A0 )
n = 1, 2, 3,
| s 1Q – s 2Q | = ( n - ) Q F F n ( Nn )
n= 1 F
F F
N1 A0 N1
A1 A1
N2 N2
A2 P1 A2
Q1
P2 N3
N3
F
Q3
P3
A3 Q2 A3
+ +
s1 s2
– F F www.schoolDD.com 16

18. F P1 , | s1P1 s2P1 | = | 5 - 5 | = 0 n=0
F P1 F F (A0)
F P2 , | s1P2 s2P2 | = | 5 - 4 | = 1 n=1
F P2 F F 1 (A1)
F P3 , | s1P3 s2P3 | = | 1.5 3.5 | = 2 n=2
F P3 F F 2 (A2)
F Q1 , | s1Q1 s2Q1 | = | 4.5 - 5 | = 0.5 n-1/2 = 0.5 n=1
F Q1 F F F 1 (N1)
F Q2 , | s1Q2 s2Q2 | = | 1.5 - 4 | = 2.5 n-1/2 = 2.5 n=3
F Q2 F F F 3 (N3)
F Q3 , | s1Q3 s2Q3 | = | 4 2.5 | = 1.5 n-1/2 = 1.5 n=2
F Q3 F F F 2 (N2)
F X , | s1X s2X | = | 5 2.5 | = n= .
F X F ................... F ............ .......( ..)
F F F s1 s2 ,
F
d=n d = ( n- )
N1 A0 N1
A1 A1
N2 N2
A2 A2
N3 N3
An An
+ +
s1 s2
d F
– F F www.schoolDD.com 17

19. 1. F An F n d=n
2. F F n (n = 0, 1, 2, ) F F
3. F F n F ( n = 0.5, 1.5, 2.5, ) F F Nn F F n F
F d = (n - )
F
- d=n d = (n - ) F P Q F F s2 F
s1P s2P = d s1Q s2Q = d F
- F n F F F F
s1 s2 A0 FF d F F
F 11
s1 s2 F F F F 10 cm F 2 cm
F F F F F 8 cm 13 cm
F F
P, Q
8 cm 13 cm
= 2 cm
+ +
s1 d = 10 cm s2
F F F F
F n F | s1P s2P | = n ( F F n )
| 8 13 | = n (2)
n = 2.5
F n F F F F F F F
F n F F | s1Q s2Q | = (n - )
| 8 13 | = (n - ) (2)
n = 3.0
F F F F 3 (N3 ) Ans
– F F www.schoolDD.com 18

20. F
F F An
F n F d=n (F F n )
10 = n (2)
n = 5 (n F )
F 5 (A5 )
A0 N1 A1
N2
A2
N3
A3
N4 11
A4
N5
10 Ans
A5
F F ”
+ + F
s1 d s2
F 12
F F s1 , s2 F F 7 cm F F 2 cm
F F s1 s2
A0
= 2 cm
+ +
s1 d =7 cm s2
F F F s1 s2
F n F d=n (F F n )
7 = n (2)
n = 3.5 ( n F )
F F F F
– F F www.schoolDD.com 19

21. F n d = (n - )
7 = (n - ) (2)
n=4
F F F s1 s2 4 (N4 )
F F s1 s2 F F
F 13
F F s1 , s2 F F 6 cm 1 cm M F F s1 s2
12 cm 8 cm F F s2 M
A0
M
12 cm 8 cm
= 1 cm
+ +
s1 d =6 cm s2
F F F M s2
F M
F n F | s1M s2M | = n ( F F n )
| 12 8 | = n (1)
n = 4 (n F )
F M F F 4 (A4 )
F s2
F n F d=n (F F n )
6 = n (1)
n = 6 (n F )
– F F www.schoolDD.com 20

22. F s2 F F 6 (A6 )
F F s2M F
11.11
2 F F
F F
. F
∫
1 Loop
.
∫
– F F www.schoolDD.com 21

23. - F F
- F
F 14
4.5 F F
F 1 m/s
4.5
F 2.25 = 4.5 m
= 2.0 m Ans
f v=f
f = = = 0.5 Hz Ans
F 15
F F F F 8 cm F F
F F F F 8 F
8.0 cm
F F
8 F F loop F 7 loop ½ loop F 8
loop
8 loop = 8.0 cm
1 loop = 1.0 cm
F 1 loop =
= 2 x 1.0 = 2.0 m Ans
– F F www.schoolDD.com 22

24. 11.12
F F F F
- F
- F
- F F F F (d) F F
( )
d> d<
- F F F F
F F F F
F F F F F FF F F F
F F
F F
F F
F
F
– F F www.schoolDD.com 23

25. - F F
F
- F F d>
- F F d<
N N
N A A
N
A0 A A0 A
11.13 F (Resonance)
F F F F
F F F
F F F F F
F F F F
F
F F F F
f= f=
F F
T= F f= =
f g
k
T= F f= =
k f K
m m
– F F www.schoolDD.com 24

26. F
F F F F
F
= L , f1 = = = F 1
= L , f2 = = = F 2
= L , f3 = = = F 3
L
fn = = F n
fn = F F F
n = loop
- F F F F F F F ( )
F F F F
– F F www.schoolDD.com 25