1. The document discusses simple harmonic motion (SHM) and wave motion. It provides equations and graphs relating to SHM and defines terms like amplitude, wavelength, frequency, and period. 2. Examples are given to demonstrate how to use the wave equation to calculate velocity, frequency, and wavelength given other variable values. 3. Reflection of waves is described and examples show how to use trigonometry to relate angles of incidence and reflection to wavelength and velocity of waves.

1.    SchoolDD.com
11
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2. 11
F
F F F F ˆˉ
F
F F
F
- F F F F F F
- S.H.M. ˈ
y = A sin ߱t
y= y
A=
߱ =
t= F
FF F F y = A sin ߱t F S.H.M
y F
r
θ
y = r sin θ
r=A θ = ߱t
F y = A sin ߱t
– F ˆ 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. ˈ F F
F
2. F ˂ ˈ F F
F ˈ 2
1.
ˈ F
F
2.
ˈ F
– F ˆ F www.schoolDD.com 2

4. 11.2
ˈ F F ˈ
λ
A A’
O
P
B F B’ F
λ
- 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 2π
F F ˈ (m)
ߣ ߣ ߣ ߣ
ߣ
F F λ
F ( ) F 1
– F ˆ 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 ˈ /
(1) ୱ
= v=
୲
t s F λ F
F T
ୱ
‫׵‬
ߣ
= fλ
(2)
୲ ୘
v= =
v=fૃ
v =
f = F F F
F ˈ / F (Hz)
T= F F F F ˈ ˈ
F
λ= F ˈ
- F F
– F ˆ F www.schoolDD.com 4

6. ˈ F F F F F F ˈ
A 0°
గ
B B 90° ଶ
A C 180° ߨ
C E ଷగ
D 270° ଶ
D
E 360° 2ߨ
- F F λ F 360˚ 2ߨ
2 F
1. F 2π, 4π, 6π,
2. F λ , 2λ , 3λ ,
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 π, 3π, 5π,
2. F λ/2, 3λ/2, 5λ/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 ˆ F www.schoolDD.com 5

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

8. ଵ ଵ
T= =
୤ ଷ
‫ ׵‬T = 0.33 s Ans
F 3
A ˈ 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
ୱ ଷ.଴
‫׵‬ = 1.5 m/s Ans
୲ ଶ
v= =
f v = fλ
λ = 4 cm
ଵ.ହ
‫׵‬f=
୴
= 0.375 Hz Ans
ସ
=
஛
F 4
F F 20 cm/s 5 / F
F F 1.0 m F F F
ˁ
1.0
F F v = 20 cm/s , f = 5 Hz
λ v = fλ
– F ˆ F www.schoolDD.com 7

9. ଶ଴
‫׵‬λ=
୴
= 4.0 cm = 0.04 m Ans
ହ
=
୤
F F
ଷ஛
s = 1.0 + ସ
= 1.03 m
ୱ
୲
v=
ୱ ଵ.଴ଷ
‫׵‬ = 5.15 s Ans
୴ ଴.ଶ଴
t= =
F 5
F 100 / F 0.5 F ߨ/4
0.50
0 ߨ/4
F ߨ/4 F F
0.5
F 2ߨ 0.5x2ߨ/( ߨ/4) = 4.0
F F
‫ ׵‬λ = 4.0 m Ans
v v = f λ = 100x4.0
‫ ׵‬v = 400 m/s Ans
11.4
ˈ F F
F F F
– F ˆ F www.schoolDD.com 8

10. - F ˈ F ( - F )
- ˈ F F
11.5 F
ˈ F F F
1 F F
F ˈ ˈ F F
F F
- F F
11.5 F
F F F
F
F
F F F
F F
11.6 F
F ˈ F
F F F F F F F
F
– F ˆ 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
ୱ ଶ.଴
‫׵‬ = 2.0 s Ans
୴ ଵ.଴
t= =
= 1.0 + 1.0 = 2.0 m Ans
– F ˆ F www.schoolDD.com 10

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

13. F F ˈ
F
F
F ˈ F
F F 2 cm
t F s= vt
ୱ ଶ.଴
‫׵‬ = 2.0 s Ans
୴ ଵ.଴
t= =
2. F
F F F F F F F
F F F F F
F
F
F F
F
θ1 θ2
θ1 θ2 F
ી1 = F ી2 F
θ1 , θ2 = F F F
F = F F
- F F F
F 8
F F F
50°
120°
– F ˆ F www.schoolDD.com 12

14. 11.9
F F
F
F
F F F
C λ1 B
θ2
1
θ1 θ1
2
A θ2 λ2
D
୆େ ஛భ
sin θଵ = = ------
୅୆ AB
୅ୈ ஛మ
sin θଶ = = ------
୅୆ AB
ୱ୧୬ ஘భ ஛భ ୚భ /୤భ ୴భ
‫ ܖܑܛ‬ી૚ ૃ૚ ‫ܞ‬૚ / ,
ୱ୧୬ ஘మ
= ஛మ
= ୚మ /୤మ
=
୴మ
‫ ܖܑܛ‬ી૛ ૃ૛ ‫ܞ‬૛
= =
F f1 = f2
θ1 =
= F
θ2 =
- F F F F ˈ
F
v >v
ୱ୧୬ ஘భ ୴
ୱ୧୬ ஘మ ୴
=
‫ ׵‬sin θଵ > sin θଶ
F θ1 > θ2 ( F sin θ θ )
θ1
F F F F F
θ2
- F F
– F ˆ F www.schoolDD.com 13

15. F 9
F 1 m/s F F F
ˈ 0.50 m 1.0 m
θ1
v1 = 1 m/s θ2 v2 = ?
λ1 = 0.5 m λ2 = 1.0 m
୴భ ஛భ
୴మ ஛మ
=
ଵ ଴.ହ
F F ୴మ
=
ଵ.଴
‫ ׵‬v2 = 2 m/s Ans
f v=fλ
୴భ ୴మ ଶ.଴
f=
஛భ
=
஛మ
=
ଵ.଴
= 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°
θ1 = 53°
θ2 = 53° - 16° = 37°
ୱ୧୬ ஘భ ஛భ
ୱ୧୬ ஘మ ஛మ
=
ୱ୧୬ ହଷ ஛భ
ୱ୧୬ ଷ଻ ஛మ
=
ସ/ହ ଶ.଴
F F ଷ/ହ
=
஛మ
– F ˆ F www.schoolDD.com 14

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

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

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

20. F
F ˈ F An
F n F d = nλ ( F F n )
10 = n (2)
n = 5 (n ‫׵‬ F )
F ˈ 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
λ = 2 cm
+ +
s1 d =7 cm s2
F F F s1 s2 ˈ
F n F d = nλ ( F F n )
7 = n (2)
n = 3.5 ( n F ‫׵‬ )
F F F F ˈ
– F ˆ F www.schoolDD.com 19

21. F n d = (n - ଵ) λ
ଶ
7 = (n - ଵ) (2)
ଶ
n=4
F F F s1 s2 ˈ 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
ˈ 12 cm 8 cm F F s2 M
A0
M
12 cm 8 cm
λ = 1 cm
+ +
s1 d =6 cm s2
F F F M s2 ˈ
F M ˈ
F n F | s1M s2M | = n λ ( F F n )
| 12 8 | = n (1)
n = 4 (n ‫׵‬ F )
F M F F 4 (A4 )
F s2 ˈ
F n F d = nλ ( F F n )
6 = n (1)
n = 6 (n ‫׵‬ F )
– F ˆ F www.schoolDD.com 20

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

23. - F F ˈ
- F ˈ
F 14
4.5 F F ˈ
F 1 m/s
4.5
F 2.25 λ = 4.5 m
‫ ׵‬λ = 2.0 m Ans
f v = fλ
‫ ׵‬f = ஛ = ଵ.଴ = 0.5 Hz Ans
୴
ଶ.଴
F 15
F F F F 8 cm F F
F F F F 8 F
8.0 cm
ˈ 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 = λ/2
‫ ׵‬λ = 2 x 1.0 = 2.0 m Ans
– F ˆ F www.schoolDD.com 22

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

25. - F F
ˈ F
- F F ʽ d >λ ˈ
- F F ʽ d< λ ˈ
N N
N A A
N
A0 A A0 A
11.13 F (Resonance)
ˈ F F F ˈ F
F F F
F F F F F
F F F F
F
F F F F
ଵ ௚ ଵ ୩
f= ට f= ට
ଶగ ℓ ଶగ ୫
F F
ℓ
ℓ
T = 2ߨට௚ F f = ୘ = ଶగ ට௚
ଵ ଵ
ℓ
ଵ
f ‫ן‬ g
√ℓ
ଵ ଵ ୏
k
T = 2ߨට୫
୏
F f = ୘ = ଶగ ට୫
ଵ
k f ‫ן‬ K
m √୫
m
– F ˆ F www.schoolDD.com 24

26. F
F F F F
F
஛భ ୴ ୴
ଶ
= L , f1 = ஛ = ଶ୐ = F 1
భ
୴ ୴
λଶ = L , f2 = = = F 2
஛మ ୐
୴ ୴
λଶ
஛ ୐
ଷ஛య ୴ ଷ୴
ଶ
= L , f3 = ஛ = ଶ୐ = F 3
య
L
୬୴
fn =
ଶ୐
= F n
fn = F F F
n = loop
- F F F F F F F ( )
F F F F
– F ˆ F www.schoolDD.com 25