### SOUND

SOUND

1. Natural or free vibrations:-
When a body is set into vibration and then left itself, the vibrations are called natural or free vibrations.

2. Damped vibrations:-
Periodic vibrations of decreasing amplitude are called damped vibrations.

3. Forced vibrations:-
When a body executes vibrations under the action of an external periodic force then the vibrations of the body are called forced vibrations.

4. Resonance:-
Resonance is the phenomenon in which if one of the two bodies of the same natural frequency is set into vibrations, the other body also vibrates with larger amplitude under the influence of the first body.

Example:-1
1. Four simple pendulums A,B,C,D are suspended side by side from a horizontal stretched rubber tube MN as shown in the figure. 2. Let the length of the pendulum ‘A’ and ‘B’ be equal.
3. ‘C’ is shorter and ‘D’ is longer compared to ‘A’ and ‘B’.
4. Set the pendulum ‘A’ into vibration. The remaining pendulums also vibrate.
5. After a short time the pendulum ‘B’ will continue to vibrate with increasing amplitude since the natural frequencies of A and B are equal. Hence, they are in resonance.

6. The pendulum ‘C’ and ‘D’ make forced vibrations with smaller amplitude because their lengths are different from that of A and B.

Example:-2 1. Arrange two hollow sound boxes A and B opened at one end such that their opened ends face each other.

2. Mount two tuning forks A and B of same frequency on them.

3. If one of the tuning forks is excited the other begins to vibrate and a loud sound is heard.

4. The amplitude becomes maximum due to resonance.

5. Write any four applications of resonance phenomenon
Or
Describe a few incidents of resonance phenomenon observed in your day-to-day life

1. When soldiers cross a suspension bridge, they are asked to break their steps. This is because if the frequency of the vibration of their marching becomes equal to the natural frequency of the bridge, the bridge would vibrate with a large amplitude due to resonance and the bridge could collapse.

2. A pronounced rattling sound may occur in a car when it is traveling at a particular speed , but if it travels faster or slower than this speed no rattle occurs. This is due to the resonance between the car engine and the body of the car.

3. When we tune a transistor radio, we are actually adjusting its natural frequency to that of the incoming carrier electro magnetic waves from a radio transmitter. When the two frequencies match maximum energy is absorbed from the incoming wave and the sound is clearly heard with appreciable amplitude.

4. Consider a swing on which a child sits. When the swing is given a series of pushes by the mother of child with a frequency equal to natural frequency of the swing, the swing oscillates with larger amplitude. In this case resonance occurs between the oscillatory force applied by the mother and the swing.

6. Progressive wave:-
A wave originating in a source and travelling forward in a medium is called progressive wave.

7. Types of Progressive waves:-
There are two types of progressive waves. They are
1. Longitudinal Progressive waves.

2. Transverse Progressive waves.

8. Longitudinal waves:-
If the particles in the medium vibrate parallel to the direction of the propagation of the waves, such waves are called longitudinal waves.
Properties:-
1. Particles of the medium vibrate parallel to the direction of the propagation of wave.

2. Compressions and rarefactions occurs in the medium.

3. The distance between two successive compressions or rare factions is equal to wave length(λ).

4. Different particles are in different phases. But, the period of vibration is the same for all the particles.

5. Longitudinal waves can be produced in solids, liquids and gases.

6. Longitudinal waves cannot be polarized.

9. Transverse waves:-
If the particles of the medium vibrate perpendicular to the direction of the propagation of waves, such waves are called transverse waves.
Properties:-
1. Particles of the medium vibrate perpendicular to the direction of propagation of wave .

2. Crests and troughs are formed in the medium.
3. The distance between two successive crests or troughs is equal to the wavelength(λ) .

4. Different particles are in different phases. But the period of vibration for all the particles is the same.

5. Transverse waves can be polarized.
6. Transverse waves can be produced in solids only.

10. Stationary waves:-
Stationary wave is defined as a resultant wave formed when two waves of equal frequency and amplitude travels in opposite directions along the same path.
Properties:-
1. The wave is confined to a limited region and does not advance.
2. Different particles vibrate with different amplitudes.
3. The period of vibration is the same for all the particles.
4. Some particles always vibrate with maximum amplitude. They are called antinodes.

5. Some particles do not vibrate at all . They are called nodes. Positions of Nodes (N) and Anti nodes (AN) in a standing wave

1&3 – Complete P.E
2. Complete K.E
4. Loop
6. The distance between two successive nodes or antinodes is equal to half of the wave length.

7. Energy is not transmitted by a standing wave.

I. Answer the following:-

11. Differences between progressive and stationary waves

 Progressive waves Stationary waves 1.  These waves are produced by vibrating source and continuously travel forward in the medium. 1.  These waves are formed when two waves of equal frequency and equal amplitude travel in opposite directions along the same path. 2.  These waves travel in the form of crests and troughs (or compressions and rare factions) through the medium in all directions 2.  These waves are confined to a fixed region of the medium where they form nodes and antinodes. 3.  All the particles  have same amplitude and frequency every where in the medium.  Every particle undergoes the maximum displacement at one time or the other. 3.  Amplitude of different particles  in the medium are different at  different points.  It varies from a minimum at nodes to a maximum at antinodes. 4.  The phase of vibration changes for different points along the wave.  At any particular instant different particles have different phases. 4.  The vibration of all the points with in a loop (between nodes) are in phase and are out of phase with respect to the points in the adjacent loop. 5.  Distance between successive crests  (compressions) or troughs (rare fractions)  is λ. 5.  Distance between successive nodes or  antinodes is . 6.  Energy is carried continuously by forward moving waves through out the medium. 6.  Energy is trapped in a fixed region of  medium. 7.  Every particle undergoes maximum  displacement at one time or other. 7.  The particles at nodes undergo only minimum displacement, while at antinodes, they undergo only maximum displacement.

12. Why is thunder heard after the lightining is seen though they are produced simultaneously
Velocity of light is more than the velocity of sound. Hence, light reaches the earth earlier than the sound even though they are produced simultaneously.

13. Why do marching men step out (break out) when crossing a suspension bridge
While marching on the suspension bridge if the frequency of the vibrations of their marching becomes equal to that of the natural frequency of the bridge, bridge vibrates with large amplitude due to resonance and the bridge may collapse. Hence, the marching men are asked to step out when they cross the suspension bridge.

14. A pronounced rattling sound may occur in a car when it is traveling at a particular speed. Why
A pronounced rattling sound occur in a car when it is traveling at a particular speed due to the resonance between the car engine and the body of the car.
15. When we tune a transistor radio a particular broad casting of radio transmitter can be heard? Why
When we tune a transistor radio we are actually adjusting its natural frequency to that of the incoming carrier electro magnetic waves from a particular radio transmitting station. When the two frequencies coincide, maximum energy is absorbed from the incoming wave and the sound is clearly heard with appreciable amplitude.

16. Amplitude:-
the maximum displacement of the vibrating particle from its mean position is called the amplitude.

17. What will be the energy carried by a propagating wave
The energy carried by the propagating wave is the sum of potential and kinetic energy of the vibrating particles at every point.

18. Do the vibrating particles of the medium move forward along with the progressive wave
No, the vibrating particles of the medium do not move forward along with the progressive wave but the vibrating particles of the medium transfer energy to other particles.

19. What are nodes and Antinodes? Draw a figure
Nodes:-
In a stationary wave the points where the particle are at rest are called nodes.
Antinodes:-
In a stationary wave, the points where the particles have the maximum displacement are called antinodes. N- Node AN- Anti node

20. Draw a diagram showing resonance in pendulum 21. Draw a diagram showing resonance between two indentical tuning forks. 22. Draw a diagram showing the formation of a standing wave 1. Electrically Vibrating Tuning Fork 2. Pulley 3. Loop

23. Write the formula for velocity of sound in air
Or
Write Newton-Laplace formula to determine velocity of sound in air
Velocity of sound in air is given by γ=ratio of specific heats of a gas.
p=pressure.
ρ=density of the medium.
Note:-
Velocity of sound in air is given by
V=νλ
ν=frequency and
λ=wave length.

24. Air column:-
A glass tube with open ends when immersed in water to certain extent, the air inside the glass tube is said to form air column.

25. Resonating air column:-
When the natural frequency of the air column coincides with the frequency of the vibrating tuning fork, the air column would be in resonance with the tuning fork such an air column is called resonating air column.

26. Describe a method to determine the velocity of sound in air
Description of the apparatus:-

1. Take a long glass jar ‘J’ of a large diameter (about 30 cms) and height (about 50cm) Experimental arrangement to determine the velocity of sound in air
2. Pour water into the jar to about three-forth( th) of the level.
3. Take another glass tube ‘T’ of length 40 cm and diameter about 3 cms. Both the ends should be opened.

4. Fix the tube to a clamp ‘c’ of the retort stand ‘R’.

5. Immerse the tube in the water of the jar as shown in the figure.

Determination of velocity of sound:-

6. Strike the prongs of the tuning fork with the rubber hammer.

7. Hold the vibrating tuning fork just above the air column in the tube.

8. When the first loud sound is heard, the length of the air column is observed to be l1. Here node ‘N’ is formed at the bottom of the air column. Antinode is formed at the top of the air column near the open end. The distance between a node and an 9. When the second loud sound is heard, the length of the air column is observed to be l2. Here, there should be at least one node and one antinode between the two ends of the air column.
Therefore in this case the length of the air column is equal to the 3 λ/4. from equations (1) and (2) Since, l1 and l2 are known from the experiment λ can be calculated.
Velocity of sound is determined by the formula
V=νλ
Or
V=2ν(l2-l1)

Velocity of sound in air is

V=2ν(l2-l1)
Where,
ν=frequency of the tuning fork.

27. Draw figures to indicate first and second modes of resonating air column in a closed tube Resonating Air Columns

28. What is the formula for finding the velocity of sound in air by resonating air column method?
Velocity of sound in air using resonating air column method is
V=2ν (l2-l1)

Where, ν=frequency of the tuning fork.
29. In one of the tuning forks kept on a hollow box is set to vibrate, the other tuning fork kept on another hollow box also vibrates. Why?
The first tuning fork sets vibrations in the air column of its sound box. These vibrations travel to the air column of sound box of the other tuning fork. This air column of the second tuning fork vibrates with the frequency of the first and transmits these vibrations to the second one and excites it. Then the second tuning fork is said to be in resonance with the first.

II. Problems:-

1. In a resonating air column experiment, a tuning fork of frequency of 412 Hz is used. In this experiment first and second resonance occurs when the length of the air column is 20 cm and 60 cm respectively. Find the velocity of sound in air.
Given,
Frequency of tuning fork= ν=412 Hz.
Length of the first resonating air column=l1=20cm=0.2m
Length of second resonating air column=l2=60cm=0.6m
Velocity of sound in air =?
We know that,
V=2 ν (l2-l1)
V=2×412(0.6-0.2)
V=824(0.4)
V=329.60 m/s
Velocity of sound in air=329.60 m/s

2. Find the wavelength of the wave if the distance between two successive nodes is 40cm.
Given, λ=40×2
λ=80cm
The wavelength of the wave = λ=80 cm.

3. The distance between two successive antinode is 15cm. Find the wavelength of the stationary wave.
Given,
Distance between two successive antinodes= =15cm =15cm
λ=15×2
λ=30cm
The wavelength of the stationary wave=λ=30cm

4. Find the wavelength of the wave if the distance between one node and next antinode is 20cm.
Given,
Distance between one node and next antinode= =20cm =20cm
λ=20×4
λ=80cm
The wavelength of the wave=λ=80cm

5. The wavelength of the stationary wave is 100 cm. Find the distance between two successive nodes
Given,
Wavelength of the stationary wave= λ=100cm
We know that,
The distance between two successive nodes is  =100/2
The distance between two successive nodes= =50cm

III. Match the following:-
A B
1. Between two bodies of same (d) a)

natural frequency.
2. Between two bodies of different (g) b)
natural frequency.

3. Distance between two successive (a) c)
nodes.

4. Distance between a node and its (e) d)Resonance.
Adjacent antinode.

5. Newton-Laplace formula to find (b) e)
velocity of sound in air.

f)

g)forced vibrations.

2. A B

1. Decrease in amplitude (e) a)forced vibrations.

2. External periodic force (a) b)stationary wave.

3. Same natural frequencies (d) c)transverse progressive
waves.

4. Nodes, Antinodes (b) d)Resonance.

5. Crests, troughs (c) e)Damped oscillations.

3. A B

1. Velocity of sound (e) a) λ

2. Distance between two successive nodes (c) b)γ

3. (b) c)

4. 2ν(l2-l1) (d) d)V

5. Distance between two successive crests (a) e)nλ

IV Fill in the blanks:-
1. Velocity of sound in air is (b).
a) b)
c) d)

2. In a resonating air column experiment with a close end tube first resonance occur when the length of the air column is 10-cm second resonance occurs at 30cms.
Solutions:-
l2=3l1
l2=3×10
l2=30cms

3. A medium transmits a sound wave through it by the virtue of its (d)
a)elasticity. b)inertia
c)density d)elasticity and inertia

4. The wave length of a wave is the (c)
a)Distance between two vibrating particles with a phase difference of П(1800)
b)Distance between a crest and a consecutive trough.
c)Distance between any two particles vibrating in the same phase.
d)Distance between any two particles in out of phase by .
5. Distance between a node and the adjacent antinode in a stationary wave is 10 cms, then the wave length is 40cms.
Solution:-
=10
λ=4×10
λ=40cms.

6. In a stationary wave the point at which the displacement is maximum is antinode.
7. Sound waves in air are examples of longitudinal waves.
8. If the distance between two successive nodes is 30cms then the wavelength of the wave is 60cm.
Solution:-
=30
λ=2×30
λ=60cms.

9. If the distance between a node and the adjacent antinode is 30cms then the wavelength of the wave is 120cms.
Solution:-
=30
λ=30×4
λ=120 cms

10. Sound cannot travel in vacuum.

11. If a rope fixed at one end is moved up and down holding it by the other end, the waves produced are stationary waves.

12. If the amplitude of a simple pendulum of constant length has been changed by exerting energy its frequency (a)
a)does not change b)changes
c)doubled d)halfed

13. The distance between two successive antinodes in a stationary wave is 15cms. The wavelength is 30cms.
Solution:-
=15
λ=2×15
λ=30cms

14. In a stationary wave the points at which the displacement is minimum are called nodes.

15. The waves that consist of compression and rarefactions are called longitudinal waves.

16. In the formula then γ=(d)
a) b)CpxCv c)Cp-Cv d)

17. The velocity of sound in air at 00c is (in m/sec) (b)
a)258 b)331 c)1400 d)1269

18. If the band plays music outside it makes vessel to rattle. This phenomenon is called resonance.

19. The sound of thunder has been heard 10sec after the lightining is seen the distance at which the thunder took place is (velocity of sound is 330 m/sec) (b)
a)330m b)3300m c)3300 kms d)33m
Solution:-
S=vt
S=10×330
S=3300 m

20. In a stationary wave the distance between a node and its successive antinode is (b)
a) b) c) d) λ

21. The velocity of sound in air is V and its frequency is f then its wavelength λ is (b)
a)Vf b) c)V d)Vf2.
22. The velocity of sound in air is 350 m/sec. Find the wave length of the sound in air if the frequency is 10,000Hz (a)
a)3.5cm b)28.5cm c)2.85cm d)35cm
Solution:-
V=350 m/sec
f=10,000Hz
V=f λ
λ=
λ=
λ=0.035 m
λ=0.035×100 cm
λ=3.5 cm

23. The frequency of a tuning fork depends on its dimensions.

24. The frequency of the simple pendulum depends on length of the pendulum

25. When a body is set into vibrations and then left to itself, the vibration are called Natural (or) free vibrations.

26. Periodic vibrations of decreasing amplitude are called damped vibrations.

27. The vibrations of a table top on which the stem of a vibrating tuning fork is pressed are called forced vibrations.

28. When you tune a transistor radio the phenomenon which enables us to catch a carrier electromagnetic wave of a particular frequency is called resonance.

29. A wave originating from a source and travelling forward in a medium is called progressive wave.

30. When the displacement of the particles of a medium is at right angles the direction of propagation of wave, then the wave is called transverse waves.

31. When the displacement of the particle of a medium is parallel to the direction of propagation of wave, then the wave is called longitudinal wave.

32. A wave that consists of a series of crests and troughs is called transverse wave.

33. In a wave any two successive particles vibrating with the same phase are separated by a distance equal to (c).
a) b) c) λ d) 2λ

34. The vibrating particles in a wave transfer energy.

35. On reflection from a rigid or fixed end a wave undergoes a phase change of (d).
a) radians b) radians
c) radians d) П radians

36. Π radians = 1800.

37. If two waves of equal frequency and amplitude travel in opposite direction along the same path then the wave formed is called stationary wave.

38. A stationary wave actually traps energy between two fixed ends.

39. The points in a stationary wave where the amplitude is maximum are called antinodes

40. The points in a stationary wave where the amplitude is zero are called nodes.

41. In a stationary wave, the distance between two successive nodes is and successive antinodes is .

42. In a stationary wave, two successive nodes are separated by a distance of 50cms, the wave length of the wave is 100cms.
Solution:-
=50
λ=50×2
λ=100 cms.

43. In a stationary wave the vibrations of the particle in a medium in a loop will be having different amplitudes.

44. The wave length and frequency of a stationary wave are the same as that of the incident wave.

45. In a stationary wave, energy is trapped in a fixed region of the medium.

46. In a progressive wave all the particles have same amplitudes.

47. Energy is carried continuously by progressive waves.

48. At the open end the particles are free to vibrate and hence it acts always as an antinode.

49. Every system has its own frequency called natural frequency.

50. The vibrations that take place under the influence of an external periodic vibration are called forced vibrations.

51. When two waves of equal frequency and amplitude travel in opposite direction stationary waves are formed.

52. A wave under goes a phase change of Π (or) 1800 on reflection.

53. The distance between a node and an antinode is λ/4.

54. Particles undergo maximum displacement at antinode in a stationary wave.
55. Particles undergo minimum displacement at node in a stationary wave.
56. The velocity (V) of the sound wave, frequency (ν) and wave length (λ) is given by V=νλ.

57. In order that mechanical wave should travel through a medium, the medium should have elasticity and inertia.

58. A load suspended from a spring when pulled and released starts vibrating with certain frequency.

59. Air around a vibrating object offers a resistance to vibrations.

60. Resonance is the phenomenon in which if one of the two bodies of the same natural frequency is set into vibration the other body also vibrates with larger amplitude under the influence of the first body.

61. When soldiers cross a suspension bridge they are asked to break their steps to prevent resonance.

62. A pronounced rattling sound may occur in a car due to resonance between the car engine and the body of the car.

63. In case of a swing, resonance occurs between the oscillatory force applied by the mother and the swing.

64. When two frequencies of transistor radio and carrier electro magnetic wave match maximum energy is absorbed.

65. The sound waves from an electric bell propagate through the air indefinitely till the energy carried by them becomes zero because of damping.

66. When the displacement of particles of medium is at right angles to the direction of propagation of wave, the wave is said to be a transverse wave.

67. A longitudinal progressive wave travels along its length in the form of compressions and rarefactions.

68. The elevation in a transverse wave is called crest.

69. The distance travelled by the wave in a time period is called λ (wave length).

70. The depressions in a transverse wave are called troughs.

71. The number of complete waves (cycles) produced in one second by vibrating body is called frequency.

72. The wave produced by a stone dropped on the surface of the water in a pond is called transverse-progressive wave.

73. Units of frequency is hertz (or) cycles/second.

74. The relation between frequency (n) and time period ‘T’ is .

75. S.I. unit of wave length is metres.

76. The phase difference between two successive compressions and rarefactions is 2Пradians.

77. The frequency at which an object performs its free vibrations is called natural frequency.

78. The oscillations made by a body when it is subjected to a periodic force are called forced oscillations.

79. Sound is produced by bodies when they are in vibrating state.

80. The waves that oscillate between nodes and antinodes are called stationary wave.

81. The velocity of sound is the product of its frequency and its wave length.

82. The vicinity formed by a increase in the mean molecular distance in a medium is called rarefaction.

83. The vicinity formed by a decrease in the mean molecular distance in a medium is called compression.

84. Velocity of sound in air is 350 m/s the frequency of the tuning fork is 350 Hz, then the wave length of the sound wave produced is 1m.
Solution:-
=1m.

85. Sound do not propagate through vacuum because of the absence of material medium.

86. In the first mode of vibration in a resonating air column, the length of air column and in the second mode is .

87. The bridge on the river seins in Paris had collapsed when an army marching along it. The reason was resonance.

88. Stationary waves are formed in a resonating air column.