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PRASAD’S INSTITUTE OF CHEMICAL SCIENCES (PICS)
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SOUND
Atoms and subatomic particles get disturbance in almost of all branches of physics. This
disturbance is nothing but a 'wave'. We are all familiar with water waves, sound waves, light
waves, radio waves and other electromagnetic waves. In this paragraph we confine our
attention to waves in deformable or elastic media. These waves, among which ordinary
sound waves in air are one example. They originate in the displacement of some portion of
an elastic medium from its normal position, causing it to oscillate about an equilibrium
position. Because of the elastic properties of the medium, the disturbance is transmitted
from one layer to the next. This disturbance (wave) consequently progress through the
medium. Note that medium it does not move as a whole along with the wave motion, the
various parts of the medium oscillate. Only in limited paths. For example, in water waves,
small paper pieces or a cork show that the actual motion of various parts of the water is
slightly up and down and buck and forth. Yet the water waves move steadily along the water.
As they reach floating objects they set them in motion, thus transferring energy to the...
Energy can be transmitted over considerable distances by wave motion. One energy in the
waves is like the kinetic and potential energy of the matter, but the transmission of the
energy comes about by its being passed along from one part of the matter to the next, not
by any long range motion of the matter itself.
Types of waves
1. Transverse wave: we can distinguish different kinds of waves by considering how
motions of the particles of matter are related to the direction of propagation of the waves
themselves. If the motion of matter particles conveying the wave are perpendicular to the
direction of propagation of the wave itself, then it is called a transverse wave
Example:
a. When a vertical string under tension is set oscillating back and forth at one end, a
transverse wave travels down the string; The disturbance moves along the string but the
string particles vibrate at right angles to the direction of propagation of the disturbance.
b. Light waves
2. Longitudinal wave: If the motion of the particles conveying a mechanical wave is back
forth along the direction of propagation, then it is called a longitudinal wave.
Example: The coils vibrate back and forth in the direction in which the disturbance travels
along the spring. Sound waves in a gas are longitudinal waves.
Sound: Those are longitudinal mechanical waves. They can be propagated in solids, liquids
and gases. Frequency of wave means, the number of cycles (vibrations) made per a
second. Sound waves can stimulate the human ear and brain to the sensation of hearing.
This range is from about 20 cycles/sec to about 20,000 cycles/sec and is called audible
range. A longitudinal mechanical wave whose frequency is below the audible range is called
an infrasonic wave and one whose frequency is above the audible range is called an
ultrasonic wave. Infrasonic waves are usually generated by larger sources of earth quake
waves. Ultrasonic waves may be produced by elastic vibrations of Quartz crystal induced by
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resonance with an applied alternating electric field. It is possible to produce ultrasonic
frequencies as high as 6 × 108 cycles/sec.
Audible waves originate in vibrant strings (violin, human vocal cords), vibrating air
columns (organ, clarinet) and vibrating plates and membranes (Xylophone, loudspeaker
drum. All of these vibrating elements alternately compress the surrounding air on a forward
movement and rarely it on a backward movement. The air transmits these disturbances
outward from the source as a wave. Upon entering the ear these waves produce the
sensation of sound.
Natural Vibrations: The natural or free vibrations of a vibrating body are the vibrations
executed by it when it is just displaced from its equilibrium position and then 'let go'. The
frequency of a body executing ''free vibrations'' is known as its natural frequency. For
example as long as the length of the pendulum does not charge, it oscillates with the same
frequency. Similarly, the spring mass system vibrates with the same frequency as long as
the spring and mass suspended remain same.
Damped Vibrations:If a tuning fork strike with a rubber hammer, it vibrate with certain
frequency. After some time we observe that amplitude of vibrating body continuously
decreases with time. The air around it offers resistance to vibration. Those periodic vibration
of decreasing amplitude are called damped vibrations.
Forced Vibrations: Take a tuning fork and strike it with rubber hammer and press its stem..
against the top of a dining table or any other surface with large area. The sound becomes
louder because the table is forced to vibrate with the frequency of the tuning fork. Since the
table top has a much larger vibrating area than the tuning fork, these vibrations produce a
louder or more intense sound. The vibrations of the table top which take place under the
influence of the external periodic force are called forced vibrations. The frequency of the
external periodic force (Tuning fork) need not be equal to the natural frequency of the
vibrating body.
Some more examples for forced vibration:
A bridge vibrates under the influence of marching soldiers, the housing of a motor
vibrates owing to periodic impulses from an irregulation in the shaft, and a tuning fork
vibrates. When exposed to the periodic force of a sound waves. These forces oscillations
have the frequency of the external force and not the natural frequency of the body.
However,the response of the body depends on the relation between the forced and natural
frequency. A child using a swing learns that by pumping at proper time intervals he can make
the swing move with a large amplitude.
Resonance: Forced vibrations are set up in an elastic body when it coupled to a vibrating
body. If a natural frequency of the coupled body is the same as that of the vibrator, there is
resonance. For resonance there is a rapid transfer of energy and a resultant louder sound.
The reinforcement of sound by resonance with its accompanying release of large amount
of energy has many useful and many obnoxious consequences. Resonance of a radio
loudspeaker to certain frequencies produces an objectionable distortion of speech or music.
But the resonance of the air column in an organ pipe amplifies the otherwise almost
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inaudible sound of the vibrating air jet.
We define resonance as, 'If one of the two bodies of the same natural frequency is set
in to vibrations, the other body also vibrates with larger amplitude under the influence of the
first body"
Progressive waves: The sound waves propagate through the air indefinitely fill the energy
carried by them becomes zero because of damping. Such waves are called progressive
waves. They do not return to the source at all. For example
1. If a man standing on a mountain cliff and shout loudly, the sound waves travel in all
directions through the air around the source. If the waves, on their way do not encounter
obstacles, they continue to travel in the medium without interruption.
2. When a stone dropped in to a pond of water, waves travel from the point of disturbance
till they reach shore.
Transverse waves and longitudinal waves are also progressive waves.
Stationary waves: Stationary waves are formed when two waves of equal frequency and
equal amplitude travel in opposite directions along the same path.
Consider a wave pulse travelling down along a stretched rope tied to a rigid pole when
the pulse arrives at the pole, it exerts an upward force on the support.
By Newton's third law, the pole exerts an equal but opposite force on the rope. this
reaction by the pole generates a pulse at the pole which travels back along the rope in a
direction opposite to that of the incident pulse. The reflected pulse returns with its transverse
displacement ''reversed''. Hence a wave reflected from a rigid end undergoes a phase
change equal to π (180°)
As the rope continuously producing pulses, we observe continuous reflections take place
at the pole (fixed end). This means that two waves, one incident and other reflected, travel
through the rope simultaneously. The two waves the superpose on each other. This super
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position gives rise to a resultant wave, that is stationary wave.
The single rope appears as double because of the formation of loops or segments. The
appearance of loops is due to simultaneous travelling of incident and reflected waves and
are seen as such because of the persistence of vision of our eye. In stationary wave there
are particles which undergo minimum displacement. These points are called 'nodes'' (N).
Similarly there are particles which under go maximum displacement and the points are
called antinodes (A.N). We know that distance between as wave length denoted by symbol
λ . The two successive antinodes or nodes are separated by a distance equal to λ /2.
Distance between a node and the successive antinode is equal to λ /4.
The vibration of all points with in a loop (between nodes) are in phase and are out of
phase with respect to the points in the adjacent loop. Energy is trapped in a fixed region of
medium.
Velocity of sound in Air: The speed of wave is the distance it moves per unit time. The
speed depends upon the kind of wave and the properties of the medium. The speed of
sound varies greatly with the material through which it travels. The following table shows
values for the speed of sounds in several common substances.
Speed of Sound at 0° C (32°F) in Various Medium
MEDIUM
m/sec
Air
331.5
Hydrogen
1270
Carbondioxide
258
Water
1450
Iron
5100
Glass
5500
Since sound waves are longitudinal waves, the speed v is given by the equation (1)
...............................(1)
Where E is the bulk modules for fluids Young's modules for solid rods and ρ is the density
of the medium.
In a gas at constant temperature, the bulk modules is the pressure of the gas. When
sound waves travel through a gas, the compressor and rare fractions. Occur so rapidly that
the changes are practically adiabatic. The adiabatic modules of elasticity is γ times the
isothermal modules P, Where γ is the ratio of the specific heat of the gas constant pressure
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to the specific heat at constant volume (C v)
For gases then
v=
γp
p
C
γ
Where
= C
p
v
(γ = 1.40 for air and other diatomic gases)
However, there is a simpler and direct method of finding the value of v. This method
involves the formation of standing waves in air and the phenomenon of resonance. When
sound of certain of frequency (n), travels through air with velocity v, the value of v is velocity
= frequency × wave length
i.e. v = nλ
Very Short Answer Questions
1 Mark
1. What is a damped vibration?
A- Periodic motion of decreasing amplitude are called damped vibrations.
2. Define Natural vibrations of a body?
A- The oscillation or vibrations of a body are called natural or free vibrations if it is vibrating
without the influence of any external periodic force.
3. Define vibration of a body?
A- To and fro motion of a body about its mean position is called vibration.
4. Define a progressive wave?
A- A wave originating by a source and travelling forward in a medium is called a progressive
wave.
5. What are 'nodes' and 'antinodes' in a stationary wave?
A- Nodes are the points in a stationary wave where the particles undergo minimum
displacement and antinodes are points where the displacement is maximum.
6. Define Resonance?
A- 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 vibrate under the influence of the first
body.
7. On what factors does the frequency of a body depends?
A- The frequency of a body depends on its
a) elastic constants b) dimension and c) nodes of vibration.
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Short Answer Questions
2 Marks
1. Explain the terms natural and forced vibrations what is the difference between
them?
1. When a body is set into vibrations and then left to itself, the vibrations are called natural
or free vibrations
2. When a body executes vibrations under the action of a external periodic force then the
vibration of the body are called forced vibration.
3. Natural vibrations repeat at the free or natural frequency of the vibrating body.
4. Whereas forced vibrations execute vibrations under the influence of an external periodic
force.
2. What is a resonating air - column?
1. When the natural frequency of the air column of a tube coincides with the frequency of
the vibrating tuning fork the air column would be in resonance with tuning fork
2. Such an air column is called a resonating air column.
3. Why do marching men step-out, when crossing a bridge?
- While marching on the bridge, if the frequency of vibrations of their marching become
equal to that of bridge, the bridge starts vibrating with large amplitude to resonance and
the bridge may collapse. Hence the marching men are asked to step out when they are
crossing the bridge.
4. A node is created on the surface of water in the glass tube whey?
- On the surface of water in the glass tube which acts as the rigid end, the air particle are
not free enough to vibrate longitudinally. There fore anode is formed at this point.
5. Draw the figure of stationary wave label node and antinode.
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Essay Questions
4 Marks
1. Derive v = 2ν (l2 - l1) or derive an expression to determine the velocity of sound
using resonating air-columns?
A. Let l1 be the length of air-column at the first over tone of resonating air column. The
excited tuning fork is kept horizontally just above the open-end of the glass tube. The
distance between open-end of the glass tube and tuning fork is considered to be the end
correction ''e'' A node is formed at water level in the glass tube and an antinode is formed
near the open-end. The distance between a node and antinode is λ /4.
∴ l1 = λ /4
When the reservoir of water "R" is further lower a second mode of vibrating in resonating
air column is obtained at 3λ / 4
∴ l2 = 3λ / 4 .............. (2)
To eliminate the end correction we subtract (1) from (2)
l2 - l1 = 3λ / 4 - λ / 4 = λ /2
(or) λ = 2 (l2 - l1) ......................(3)
The velocity of sound in air at room temperature is given by v = nλ
Considering ν as the frequency of the tuning fork and l as wavelength.
Substituting (3) in (4) we get
v = ν × 2 (l2 - l1)
∴ v = 2ν (l2 - l1)
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2. Distinguish between transverse and longitudinal waves?
Transverse wave
longitudinal wave
1. Vibrations of particles of medium 1. Vibrations of particles of medium
are at right angles to the direction
are parallel to the direction of wave
of wave propagation.
propagation.
2. A wave consist of a crest and
trough.
2. A wave consist of a compression
and a rare fraction.
3. It exhibits polarisation.
3. It does not exhibit polarisation.
4. The distance between two
successive crests (or troughs) is
equal to λ (wave length)
4. The distance between two successive
compression (or rarefaction) is equal
to λ (wave length)
5. It can be produced in solids
and to little extent in liquid (water)
5. It can be produced in solid, liquids
and gases.
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3. Distinguish 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 are formed when two waves
of equal frequency and equal
frequency and equal amplitude
travel in opposite directions along
the same path.
2. These waves travel in the form of
crests and troughs through the
medium in all directions.
2. These waves are confined to a fixed
region of the medium where they
form node and antinodes.
3. All the particles have same
amplitude
and
frequency
everywhere in the medium, Every
particle undergoes the maximum
displacement at one time or the
other.
3. Amplitudes 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 far
different points along the wave at
any particular instant different
particles have different phases.
4. The vibration of all the points within
a loop are in phase and are out of
phase with respect to he points in
the adjacent loop.
5. Distance
between
crests or troughs is λ
5. Distance
between successive
nodes or antinodes λ /2
successive
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 particle at nodes undergo only
minimum displacement, while at
antinodes they undergo only
maximum displacement.
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Objective Type Questions.
I. Multiple Choice Questions.
1. Velocity of sound in air is
a) v =
ρ
γ p
b) v =
ρ p
γ
c) v =
γ p
ρ
d) v=
p
ρ
()
2. In a resonating air column experiment with a closed-end tube, first resonance occurs
when the length of the air column is 10 cm. Second resonance occurs at
()
a) 5 cm
b) 20 cm
c) 30 cm
d) 40 cm
3. A medium transmits a sound wave by virtue of its?
a) elasticity
b) inertia
c) density
d) elasticity & inertia
()
4. The wavelength of a wave is the
a) distance between two vibrating particles with a phase difference of π
b) distance between a crest and a consecutive trough.
c) distance between any two particles vibrating in same phase
d) distance between any two particles in out of phase by π /2
5. Distance between a node and the next antinode in a stationary wave is 10 cm. Then the
wavelength is
()
a) 5 cm
b) 40 cm
c) 20 cm
d) 10 cm
6. In a stationary wave, the point at which displacement is maximum is called. ( )
a) node
b) antinode
c) crest
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d) trough
7. If a spring is compressed and released, then the wave generated is
a) longitudinal
b) transverse
c) stationary
d) None of these
()
8. Periodic vibrations of decreasing amplitude are called
a) forced vibrations
b) damped vibrations
c) natural vibrations
d) None of these
()
9. On reflection form a rigid or fixed end, a wave undergoes a phase change of ( )
a) π °/2
b) π °
c) 3π °/2
d) 2π °
10.Which of the following relations is wrong?
()
a)
v=
γ p
ρ
b)
c) v = 2ν (l2 - l1)
d) γ = cv / cp
11. Velocity of sound in vacuum is
a) zero
b) 330 m/s
c) 340 m/s
d) None of these
()
12.The reason for the continuous decrease of the amplitude of vibrating bodies ( )
a) Weight of body
b) lapse of time
c) resistance offered by surrounding air
d) None of these
13.On reflection from a rigid end a wave undergoes a phase change of
a) 0°
b) 90°
c) 180°
d) 360°
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14.The verify of sound in air can be determined experimentally using the formulae?
a) v = nλ
b) v =
c) γ =
()
λ p
ρ
cp
cv
d) v = 2υ (l2 - l1)
15.The distance between two successive node is
a) λ /2
b) λ /4
c) λ
d) 2λ
16.The distance between two successive peaks is
a) λ /2
b) λ
c) λ /4
d) 2λ
()
17.Wavelength of sound whose velocity 350 m.s -1 and frequency 1000 Hz is
a) 3.5 cm
b) 35 cm
c) 28.5 cm
d) 26.5 cm
()
()
II. Fill in the blanks
1. Every system has its own frequency called _______
2. The vibrations that take place under the influence of external periodic force are called
_______
3. When two waves of equal frequency and amplitude travel in opposite direction _______
are formed.
5. Distance between two successive node is _______
6. Distance between a node and the next antinode is _______
7. Particles undergo maximum displacement at _______ in a stationary wave.
8. Particles undergo minimum displacement at _______ in a stationary wave.
9. The velocity (v) of sound wave of frequency (n) and wavelength (λ ) is given by _______
10.Periodic vibrations of decreasing amplitude are called _______
11. SI unit of wavelength is _______
12.SI unit of frequency is _______
13.The vibrating particle is a medium carry only _______
14.The frequency of the tuning fork depends on its _______
15.The frequency of the simple pendulum depends only on its _______
III. Match the following
1. On reflection from a rigid wave undergoes
a phase change of
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( ) a. λ /4
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( ) b. λ /2
( ) c. 180°
( ) d. 330 m/s
2. Newton-laplace formulae
3. Energy is trapped in a fixed region
4. Distance between a node and the
successive antinode is
γ p
5. At 0°C the velocity of sound in air
( ) e. v = ρ
f. 350 m/s
g. stationary wave
h. zero
Answers
I. Multiple Choice Questions
1. c
2. c
4. d
5. c
7. b
8. a
10. d
11. a
13. c
14. d
16. b
17. b
3. c
6. d
9. b
12. c
15. a
II. Fill in the blanks
1. Natural frequency
2. Forced vibrations
3. Stationary waves
4. π or 180°
5. λ /2
6. λ /4
7. Antinode
8. node
9. nλ
10. damped vibrations
11. Metre
12. Hz
13. energy
14. dimensions
15. length
III. Match the following
1. c 2. e 3. g 4. a
5. d
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