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Physics > Natural, Damped and Forced Vibrations; Resonance > Flashcards

Natural, Damped and Forced Vibrations; Resonance Flashcards

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1
Q

Define free vibrations

A

Vibrations that occur in the absence of an external resistive force are called free or natural vibrations. Their amplitude never decreases & the period or frequency of free vibrations depends on the shape and size of the body.

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2
Q

Where do natural vibrations of a body occur?

A

Only in vacuum

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3
Q

Why do natural vibrations occur only in vacuum?

A

The presence of a medium around the body offers some resistance due to which the amplitude of vibration does not remain constant, but continuously decreases

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4
Q

Give the formula for natural frequency of the bob of a simple pendulum

A

f = 1/2π * √g/l

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5
Q

What is the natural frequency of a simple pendulum of length 1.0 m on earth’s surface?

A

0.5 Hz

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6
Q

State the two factors on which the natural frequency of a load suspended from a string depends

A
  1. The hardness (or force constant K) of the spring

2. The mass m of the load

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7
Q

What is the force constant K of a spring?

A

The force needed to produce unit extension in it. It is more for a hard spring and less for a soft spring

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8
Q

Give the formula to find the natural frequency of a load when stretched (or compressed) & released

A

f = 1/2π * √K/m

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9
Q

Which waves do vibrations of a tuning fork form?

A

Longitudinal waves

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10
Q

What is a sound of a single frequency called?

A

A pure note

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11
Q

When a tuning fork is struck against a hard rubber pad, what sound does it produce?

A

A pure note of a single frequency

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12
Q

On what does the natural frequency of a flute or an organ pipe depend?

A

It is inversely proportional to the length of the air column (f ∝ 1/l)

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13
Q

How are notes of different frequencies produced in a flute?

A

By changing the effective length of the air column when different holes in it are closed

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14
Q

In which instrument are the modes of vibrations of the frequencies in the ratio 1:2:3:..?

A

An organ pipe of given length open at both ends

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15
Q

In which instrument are the frequencies of different modes in the ratio 1:3:5:..?

A

In an organ pipe with one end closed

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16
Q

Which vibrations are produced in string instruments?

A

Transverse vibrations

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17
Q

Give the factors on which the frequency of vibration in a stretched string depends

A
  1. the length l (f ∝ 1/l)
  2. the radius r (f ∝ 1/r)
  3. the tension T (f ∝ √T)
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18
Q

Give the formula to find the frequency of note produced by a string stretched between its ends

A

f = 1/2l * √T/πr2d
d is the density of the material of the string
πr2d = m is the mass of unit length of the string

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19
Q

How can the frequency of a note produced by a string instrument be increased?

A
  1. By decreasing the length of the string
  2. By decreasing the radius of the string
  3. By increasing the tension in the string
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20
Q

Why do various strings in a piano have their own natural frequency?

A

Because they are of different thickness and under different tensions

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21
Q

If a string stretched between its ends is plucked in the middle, in how many loops does the string vibrate?

A

In one loop. This vibration is called principal note of frequency f

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22
Q

If a string stretched between its ends is plucked at one-fourth length of string from one end, in how many loops does the string vibrate?

A

It vibrates in two loops. This vibration is called the first subsidiary vibration of frequency 2f

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23
Q

If a string stretched between its ends is plucked at one-sixth length of string from one end, in how many loops does the string vibrate?

A

It vibrates in three loops. This vibration is called the second subsidiary vibration of frequency 3f

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24
Q

In which ratio are the frequencies of different modes of vibration in a stretched string?

A

1 : 2 : 3

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25
Q

What is the wavelength of the principal note, if l is the length of the string?

A 
Frequency = f 
Wavelength = 2l
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26
Q

What is the wavelength of the first subsidiary, if l is the length of the string?

A 
Frequency = 2f
Wavelength = 2l/2
27
Q

What is the wavelength of the third subsidiary, if l is the length of the string?

A 
Frequency = 3f
Wavelength = 2l/3
28
Q

What is the nature of natural vibrations?

A

They are simple harmonic vibrations under the restoring force, the amplitude and frequency of which remain constant

29
Q

Which vibrations is it difficult to realise in practice?

A

Natural vibrations, because in practice it is very difficult to have vacuum, and the vibrations of a constant amplitude can occur only in vacuum.

30
Q

Define damped vibrations

A

The periodic vibrations of a body of decreasing amplitude in presence of a resistive force are called damped vibrations

31
Q

Give examples of natural vibrations

A
  1. A bob of a simple pendulum
  2. A load suspended from a spring, when released
  3. When a tuning fork is struck against a hard rubber pad
  4. When an air column in a flute or organ pipe is made to vibrate
  5. When strings in instruments are plucked
  6. When we strike the keys of a piano
  7. A string stretched between its ends plucked at different points
32
Q

Name the two forces which act on the body on damped vibrations

A
  1. the restoring force

2. the friction (or resistive) force due to the surrounding medium

33
Q

Why does the amplitude of motion decrease in damped vibrations?

A

The energy of the vibration body continuously dissipates in doing work against the force of friction and so its amplitude gradually decreases

34
Q

What is the frictional force at any instance proportional to?

A

To the velocity of the body

35
Q

What does frictional force have a tendency to resist?

A

Motion

36
Q

What does the energy lost by the vibrating body change into in damped vibrations?

A

It changes continuously into heat energy and it gets dissipated into the surrounding medium

37
Q

What does the rate at which the energy is lost to the surrounding (or the rate of decrease of amplitude) depend on in damped vibrations?

A

It depends on the nature (viscosity, density, etc.) of the surrounding medium and also on the shape and size of the vibrating body

38
Q

Give examples of damped vibrations

A
  1. A tree branch being pulled and released
  2. A tuning fork when stroked on a rubber pad
  3. A simple pendulum oscillating in air
  4. The vibrations of a spring having mass at its end
39
Q

Give one difference between free and damped vibrations with respect to external force

A

In natural vibrations, no external force acts on the vibrating body. The vibrations are only under the restoring force. Whereas in damped vibrations, the damping force also acts on the body to oppose its motion

40
Q

In damped vibrations, what is the frequency of vibrations less than?

A

The natural frequency

41
Q

Define forced vibrations

A

The vibrations of a body which take place under the influence of an external periodic force acting on it, are called forced vibrations

42
Q

By which forces is the body executing forced vibrations acted upon?

A
  1. The restoring force
  2. The frictional/ resistive/ damping force
  3. The external periodic force
43
Q

Give another name for the external applied force?

A

Driving force

44
Q

What happens to the natural frequency of the vibrating body in forced vibrations?

A

When an external applied force is applied on a vibrating body, it no longer vibrates with its natural frequency, but gradually acquires the frequency of the driving force

45
Q

What does the amplitude of the forced vibrations depend on?

A

It depends on the frequency of the external force

46
Q

What happens to the amplitude of oscillations if the frequency of the driving force is different from the natural frequency?

A

The amplitude of oscillations is very small which die out soon due to the presence of damping forces

47
Q

How is it possible to keep the amplitude of vibrations constant in forced vibrations?

A

By applying an external force such that the external periodic force compensates for the loss of energy in each vibration due to the damping forces

48
Q

Define sympathetic vibrations

A

It is possible to keep the amplitude of forced vibrations constant by applying an external periodic force such that the external periodic force compensates for the loss of energy in each vibration due to the damping forces. The vibrations of the body are then called sympathetic vibrations

49
Q

Give examples of forced vibrations

A
  1. The stem of a vibrating tuning fork being pressed against the top of a table
  2. The vibrations produced in the diaphragm of a microphone sound box with frequencies corresponding to the speech of the speaker
  3. In a guitar, when an artist plays on its strings by his fingers, the vibrations in them cause forced vibrations in the air enclosed in its hollow box
  4. In stringed instruments, strings are made to vibrate which can produced forced vibrations in the air of the hollow sound box. The surface area of the air in the sound box is large, so the forced vibrations send forth a greater energy and cause a loud sound
50
Q

What does the amplitude at resonance depend on?

A

Depends on the frictional forces

51
Q

Define resonance

A

Resonance is a special case of forced vibrations where the frequency of the externally applied periodic force on a body is equal to its natural frequency. This is when the body readily begins to vibrate with an increased amplitude. This phenomenon is known as resonance.

52
Q

What are the vibrations of large amplitude called?

A

Resonant vibrations

53
Q

What is the condition for resonance?

A

Resonance occurs only when the applied force causes forced vibration in the body and the frequency of the applied force is exactly equal to the natural frequency of the vibrating body

54
Q

Why is a loud sound heard at resonance?

A

The body vibrating with a very large amplitude sends forth a large amount of energy in the medium

55
Q

What does it mean when we say vibrations A are in phase with vibrations B?

A

They reach their extreme positions on either side simultaneously

56
Q

Give examples of resonance

A
  1. Resonant vibrations of pendulums
  2. Resonance in machine parts
  3. Resonance in stretched string and sound box of musical instruments and sonometer
  4. Resonance in air column and tuning fork
  5. Resonance in a bridge
  6. Resonance in radio and TV receivers
57
Q

What is the effect of making one pendulum vibrate on another pendulum of the same length?

A

The other pendulum starts vibrating with a large amplitude and in same phase because of resonance

58
Q

Can resonance only occur in certain machines?

A

No, resonance can occur in all kinds of machines while operating in a particular condition

59
Q

Which part of the vehicle makes to and fro motion that causes resonance?

A

The piston of the engine makes to and fro motion at a frequency depending upon the speed of the vehicle

60
Q

When is a rattling sound heard in a vehicle?

A

At a certain speed of the vehicle, some parts of the vehicle may have a natural frequency of vibration that is equal to the frequency of the to and fro movement of the piston. At this speed, that particular part or frame starts vibrating vigorously due to resonance and causes a rattling sound

61
Q

How is a hollow sound box constructed so as to promote a loud sound?

A

The box is so constructed that the column of air inside it, has a natural frequency which is same as that of the string stretched on it, so that when the string is made to vibrate, the air column inside the box is set into forced vibrations, with the same frequency as that of the string.

62
Q

Why are soldiers asked to break their steps when a troop crosses a suspension bridge?

A

When soldiers march in steps, each soldier exerts a periodic force in the same phase and therefore the bridge executes the forced vibrations of frequency equal to the frequency of their steps.

If the frequency of the steps become equal to the natural frequency of the bridge, the bridge may vibrate with a large amplitude due to resonance and collapse

63
Q

How does resonance work in radio and TV receivers?

A
  1. The radio and TV receivers have electronic circuits which produce electromagnetic vibrations, the frequency of which can be changed by varying the values of the electronic components.
  2. When we want to tune a radio receiver, we merely adjust the values of electronic components to produce vibrations of frequency equal to that of the radio waves which we want to receive.
  3. When both the frequencies match, resonance occurs and only the energy of the signal of that particular frequency is received from the waves present in space.
  4. The signal received is them amplified in the receiver set.
64
Q

Name the electronic components in radio and TV receivers whose values can be varied to change the frequency of electromagnetic vibrations

A
  1. The capacity of the condenser (usually)

2. The inductance of the coil

Physics (19 decks)

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