General Waves Properties - Questions And Answers
General Waves Properties - Questions And Answers
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Physics For Class X
Unit 10: General Waves Properties
Questions And Answers
Q.1: Define wavesAns: WAVES:
A method transport energy from one point to another point without transfer of matter is called wave. Waves are means of energy transfer without transfer of matter. The wave is a disturbance in a medium that transfers energy from one place to another.
For example:
Q.2: Describe wave motion as illustrated by vibrations in rope, slinky spring, experiments with water waves. OR Describe the formation of waves?
Ans: FORMATIONS OF WAVES OR WAVES MOTION:
Disturbance of medium cause of formation of wave. like, we can produce waves by using a rope, slinky spring, and water waves in ripple tanks.
Wave Motion by using a Rope:
We can produce waves on a rope by attaching one end to a wall and continuously moving the other end up and down. These up-and-down movements produce oscillations or vibrations.
We can observe that the generated rope waves travel towards the wall, whereas the rope itself moves only up and down. The rope is the medium through which the waves travel or propagate.
Conclusion: Up end down movements produce a transverse wave.
Waves in a Slinky Spring:
"A slinky spring is a pre-compressed helical or coiled spring."
We can perform several experiments with a slinky in the laboratory to understand the phenomenon of different types of wave motion.
Experiment 1: Attach one end of the spring with a wall. Now moving the free end of the slinky horizontally left and right continuously on the table will be able to see the coils of the spring moving left and right, whereas humps travel to the other end.
Conclusion:
Experiment 2: Now moving the free end of the attached wall slinky spring continuously back and forth as horizontally. We can observe the individual coils moving forwards and backwards. Where the coils are compressed, are seen traveling from the fixed end to the other end.
Conclusion:
Water wave in (Ripple Tank:
"A ripple tank is a shallow glass tank of water used to demonstrate the basic properties of waves."
It is a particular type of wave tank. The ripple tank is usually illuminated from above so that the light shines through the water to visualize the wave being produced.
In the laboratory, we can produce water waves with the ripple tank. In the ripple tank, a small vibrator moves up and down the water surface, resulting in the water particles at the surface that are in contact with the dipper being made to move up and down. This up and down motion soon spread to other parts of the water surface in the tank in the form of ripples. Here the water is the medium through which the ripples travel or propagate.
Conclusion:
Up end down movements of water surface produces a transverse wave.
Q.3: What is slinky spring? Explain the types of wave motion using a slinky? OR Identify transverse and longitudinal waves in mechanical media, slinky springs
Ans: SLINKY SPRING:
The direction in which the displacement takes place within a wave motion affects the properties of the wave. These wave types can be illustrated using a slinky.
A slinky is a long flexible steel coil or spring, which rests on a smooth table during use. Wave energy can be transmitted, for example, by a slinky, and for illustrations, each of the coil turns can represent a particle of the medium through which a wave is traveling.
TYPES OF WAVE MOTION:
There are two types of wave motions.
Q.4: Define the following terms: amplitude, crest, trough, compression and rarefaction.
Ans: AMPLITUDE:
Amplitude is the maximum displacement moved by a point on a vibrating body from the rest or mean position.
It is the height of a crest or depth of a trough measured from the rest position.
Unit: Its SI unit is meter (m).
CREST:
Crest is a point on a surface wave where the displacement of the medium is at a maximum. OR
The positive/upper part of wave is called crest.
TROUGH:
Trough is a point on a surface wave where the displacement of the medium is at a minimum.
COMPRESSION:
Compression, in the longitudinal waves this is a region where turns of the coil or particles are closer together than average.
RAREFACTION:
Rarefaction, in the longitudinal waves this is a region where turns of the coil or particles are further apart than average.
Q.5: Describe that waves are means of energy transfer without transfer of matter? OR Wave motion transfers energy without moving matter. Justify this statement with an example.
Ans: Waves are means of energy transfer without transfer of matter:
The wave is a disturbance in a medium that transfer energy from one place to another, but waves can not move matter the entire distance.
Example No.1:
When the calm water surface is disturbed by a stone dropping into it, circular water ripples spread out from the point where the stone hits the water. Similarly the continuous disturbance of the water surface by the blasts of the wind caused by a helicopter hovering above creates water waves that move outwards. If we place a cork on the surface of water. We observed that when the waves reaches the cork, it will move up an down along the motion of water particles by getting energy from waves but remain at its position. Thus the disturbance on the water surface moves outwards, carrying energy, and no water, because after the waves pass, the cork on water remains where it was before the wave was produced.
Example No.2:
A tide can travel many kilometres. The water moves up and down - a disturbance that travels in a wave, transferring energy, not matter. Let's consider the example of a buoy bobbing in the ocean. The buoy is moved up and down by the waves that pass by it but doesn't move directionally across the water. Waves transfer energy but not mass. When particles in water become part of a wave, they start to move up or down. This means that kinetic energy (energy of movement) has been transferred to them. As the particles move further away from their normal position (up towards the wave crest or down towards the trough), they slow down. This means that some of their kinetic energy has been converted into potential energy - the energy of particles in a wave oscillates between kinetic and potential energy.
This activity shows that water waves like other waves transfer energy from one place to another without transferring matter, i.e., water.
Q.6: Describe the two main categories of waves?
Ans: Categories Of Waves:
There are two main categories of waves:
Waves which require a medium for their propagation are called mechanical waves. These waves are produced by vibratory motion in the respective medium. Mechanical waves consists of transverese as well as longitudinal waves.
Examples:
Sound waves, water waves and seismic waves are some examples of mechanical waves.
ELECTROMAGNETIC WAVES:
Waves which do not require a medium for their propagation are called electromagnetic waves. These waves are produced by a changing of electric and magnetic fields. Electromagnetic waves only comprised of a transverse wave in nature.
Examples:
Radio waves, microwaves, light waves, U.V waves and infrared waves are some examples of electromagnetic waves.
Q.7: Distinguish between:
(i) Transverse and Longitudinal waves
(ii) Mechanical and Electromagnetic waves.
Ans: Difference Between Transverse Waves And Longitudinal Waves:
Q.8: Describe properties of waves such as reflection, refraction, and diffraction with the help of ripple tank?
Ans: PROPERTIES OF WAVES:
Let us consider some wave properties such as reflection, refraction, and diffraction concerning the ripple tank.
Reflection of the waves:
Definition:
Refraction of waves:
Definition:
Diffraction of waves:
Definition:
Diffraction is only significant if the size of the gap is about the same as the wavelength of the incident wave, narrow the gap whose width is equal to the wavelength of the incoming ripples, the ripples that pass through the gap are almost circular and seem to originate from a point source situated in the gap. Wider gaps produce less diffraction.
Q.9: What are wave characteristics? OR Define the terms speed (v), frequency (f), wavelength (λ), time-period (T), cycle, wavefront?
Ans: WAVES CHARACTERISTICS:
The following are some terms used to describe wave motion.
1. Time-Period (T):
It is the time taken for any one point on the wave to complete one oscillation. It is denoted by "T".
Unit: The SI unit of the period is second (s).
2. Frequency (f):
It is the number of complete waves produced by a source per unit of time.
In general, Frequency is also defined as the reciprocal of the period. It is denoted by "f".
Thus,
Frequency = Number of complete waves produced / time taken
If the number of waves produced = is 1
And time is taken = T
Then f = 1/T
Unit: The SI unit of frequency is the hertz (Hz).
3. Wavelength (λ):
It is the linear distance between two successive crests or troughs in a transverse wave and two successive compressions and rarefactions in a longitudinal wave. It is denoted by (λ)
Unit: Its SI unit is meter (m).
4. Wave speed (v):
It is the speed at which a wave travels.
It is defined as the distance traveled by a given point on the wave, such as a crest in a given interval of time. It is denoted by (v)
Unit: In the SI system, the wave speed is measured in meter per second (m / s).
5. The Wavefront:
It is an imaginary line on a wave that joins all points that are in the same phase.
A wavefront is usually drawn by joining all wave crests.
There are two types of the wavefront, depending on how the waves are produced, which are:
(b) In a ripple tank, a plane dipper can produce plane waves. These waves have a plane wavefront.
Q.10: What is the relation between velocity frequency and wavelength? OR Derive the relation between wave speed and frequency?
Ans: Relation Between Velocity (Wave speed), Frequency And Wavelength:
The wave is a disturbance in a medium that transfer energy from one place to another. It travels from one place to another and hence has a specific velocity. This called the velocity (Speed) of the wave and is denoted by Velocity = Distance traveled / time taken or
If the time taken by the wave to move from one point to another is equal to its time period 'T', then the distance travelled by the wave will be equal to one wavelength = λ
then
The speed of wave can also be written as V = fλ
Q.11: Define periodic motion?
Ans: PERIODIC MOTION:
A motion repeating itself in an equal time interval is referred to as periodic or oscillatory motion or harmonic motion.
Q.12: Define and explain simple harmonic motion (SHM)?
Ans: SIMPLE HARMONIC MOTION:
Definition:
When an object oscillates about a fixed position (mean position) its acceleration is directly proportional to its displacement from the mean position and is always directed towards the mean position. Its motion is called SHM.
Explanation:
An object in such a periodic motion oscillates about an equilibrium position due to a restoring force or a restoring torque. Such force or torque will return the system to its equilibrium position. This type of motion is called Simple Harmonic Motion.
Mathematically:
SMH is defined as:
Q.13: Define restoring force?
Ans: RESTORING FORCE:
The restoring force is a force which acts to bring a body to its equilibrium position.
Q.14: What is a simple pendulum?
Ans: SIMPLE PENDULUM:
A simple pendulum consists of a small metallic bob of mass 'm' suspended from a light inextensible string of length ‘l’ fixed at its upper end.
Examples: Old-fashioned clocks, a child's swing, and a fishing sinker are pendulum examples.
Q.15: Draw forces acting on a displaced pendulum? OR Which force acts on simple pendulum to displaced it?
Ans: Forces Acting On A Displaced Pendulum:
When the bob of the pendulum is displaced at a small angle '𝞱' to an extreme position.
The forces that act upon are:
Q.16: With the help of diagram explain SHM in simple pendulum? OR Prove that a simple pendulum executes simple harmonic motion? OR Explain SHM with simple pendulum?
Ans: MOTION OF A SIMPLE PENDULUM AND SIMPLE HARMONIC MOTION (SHM):
Let us think of an experiment to prove that a simple oscillating pendulum executes Simple Harmonic Motion.
Forces Acts:
When the bob of the pendulum is displaced at a small angle '𝞱' to an extreme position at point ‘A’ or ‘B’. The forces that act upon are:
Observation:
Conclusion:
Simple pendulum executes simple harmonic motion.
Time Period:
For the simple pendulum executing SHM, we have the following formula for its period:
- Water Wave: A little wave can travel across the water in a glass, and a very large tide can travel over the sea many kilometers. The water moves up and down- a disturbance that travels in a wave, transferring energy, not matter.
- Sound waves: Every sound we listen to depends on sound waves.
- Light wave: Every sight we see depends on light waves.
Q.2: Describe wave motion as illustrated by vibrations in rope, slinky spring, experiments with water waves. OR Describe the formation of waves?
Ans: FORMATIONS OF WAVES OR WAVES MOTION:
Disturbance of medium cause of formation of wave. like, we can produce waves by using a rope, slinky spring, and water waves in ripple tanks.
Wave Motion by using a Rope:
We can produce waves on a rope by attaching one end to a wall and continuously moving the other end up and down. These up-and-down movements produce oscillations or vibrations.
We can observe that the generated rope waves travel towards the wall, whereas the rope itself moves only up and down. The rope is the medium through which the waves travel or propagate.
Conclusion: Up end down movements produce a transverse wave.
Waves in a Slinky Spring:
"A slinky spring is a pre-compressed helical or coiled spring."
We can perform several experiments with a slinky in the laboratory to understand the phenomenon of different types of wave motion.
Experiment 1: Attach one end of the spring with a wall. Now moving the free end of the slinky horizontally left and right continuously on the table will be able to see the coils of the spring moving left and right, whereas humps travel to the other end.
Conclusion:
- An upward pulse moves to the right, followed by
- A downward pulse.
- When the end of the Slinky is moved up and down continuously, a transverse wave is produced.
Experiment 2: Now moving the free end of the attached wall slinky spring continuously back and forth as horizontally. We can observe the individual coils moving forwards and backwards. Where the coils are compressed, are seen traveling from the fixed end to the other end.
Conclusion:
- A compressed region moves to the right, followed by
- A stretched region.
- When the end of the Slinky is moved back and forth continuously, a longitudinal wave is produced.
Water wave in (Ripple Tank:
"A ripple tank is a shallow glass tank of water used to demonstrate the basic properties of waves."
It is a particular type of wave tank. The ripple tank is usually illuminated from above so that the light shines through the water to visualize the wave being produced.
In the laboratory, we can produce water waves with the ripple tank. In the ripple tank, a small vibrator moves up and down the water surface, resulting in the water particles at the surface that are in contact with the dipper being made to move up and down. This up and down motion soon spread to other parts of the water surface in the tank in the form of ripples. Here the water is the medium through which the ripples travel or propagate.
Conclusion:
Up end down movements of water surface produces a transverse wave.
Q.3: What is slinky spring? Explain the types of wave motion using a slinky? OR Identify transverse and longitudinal waves in mechanical media, slinky springs
Ans: SLINKY SPRING:
The direction in which the displacement takes place within a wave motion affects the properties of the wave. These wave types can be illustrated using a slinky.
A slinky is a long flexible steel coil or spring, which rests on a smooth table during use. Wave energy can be transmitted, for example, by a slinky, and for illustrations, each of the coil turns can represent a particle of the medium through which a wave is traveling.
TYPES OF WAVE MOTION:
There are two types of wave motions.
- Transverse wave
- Longitudinal wave
- TRANSVERSE WAVE:
Definition:“Transverse waves are waves that travel in a direction perpendicular to the direction of wave motion".Transverse Wave In Slinky:
The slinky is used to produced the transverse wave. Move the free end of the slinky up and down repeatedly. These up and down movements of the coils produce oscillations. We Have noticed that when coils move up and down, the direction of the wave motion is perpendicular to the direction of oscillation. We call this type of wave is a transverse wave.
Transverse Wave In Ripple Tank:
Transverse wave motion can also be observed on the surface of the water in a pond or a ripple tank. We can produce plane waves by using a straight dipper in a ripple tank. These waves can be seen as bright and dark lines on a screen below the tank. These bright and dark lines represent the crests and troughs of the plane waves respectively.
Transverse Wave In Guitar:
Vibrations in a guitar string also produce transverse wave.
Example:
Other essential type of transverse wave is electromagnetic wave e.g., light waves, microwaves, radio waves. - LONGITUDINAL WAVE:
Definition:"Longitudinal waves are waves that travel in a direction parallel to the direction of wave motion".Longitudinal Wave In Slinky:
The slinky is used to produce the longitudinal wave. Move the free end of the slinky forward and backward (i.e. push and pull) to expand and compress the slinky repeatedly. These forwards and backwards propagation of wave movements of the coils produce oscillations. We Have noticed that when coils move forwards and backwards, direction of the wave motion is parallel to the direction of oscillation. We call this type of wave is a longitudinal wave.
Example: Common example of a longitudinal wave is sound waves.
Q.4: Define the following terms: amplitude, crest, trough, compression and rarefaction.
Ans: AMPLITUDE:
Amplitude is the maximum displacement moved by a point on a vibrating body from the rest or mean position.
It is the height of a crest or depth of a trough measured from the rest position.
Unit: Its SI unit is meter (m).
CREST:
Crest is a point on a surface wave where the displacement of the medium is at a maximum. OR
The positive/upper part of wave is called crest.
TROUGH:
Trough is a point on a surface wave where the displacement of the medium is at a minimum.
COMPRESSION:
Compression, in the longitudinal waves this is a region where turns of the coil or particles are closer together than average.
RAREFACTION:
Rarefaction, in the longitudinal waves this is a region where turns of the coil or particles are further apart than average.
Q.5: Describe that waves are means of energy transfer without transfer of matter? OR Wave motion transfers energy without moving matter. Justify this statement with an example.
Ans: Waves are means of energy transfer without transfer of matter:
The wave is a disturbance in a medium that transfer energy from one place to another, but waves can not move matter the entire distance.
Example No.1:
When the calm water surface is disturbed by a stone dropping into it, circular water ripples spread out from the point where the stone hits the water. Similarly the continuous disturbance of the water surface by the blasts of the wind caused by a helicopter hovering above creates water waves that move outwards. If we place a cork on the surface of water. We observed that when the waves reaches the cork, it will move up an down along the motion of water particles by getting energy from waves but remain at its position. Thus the disturbance on the water surface moves outwards, carrying energy, and no water, because after the waves pass, the cork on water remains where it was before the wave was produced.
Example No.2:
A tide can travel many kilometres. The water moves up and down - a disturbance that travels in a wave, transferring energy, not matter. Let's consider the example of a buoy bobbing in the ocean. The buoy is moved up and down by the waves that pass by it but doesn't move directionally across the water. Waves transfer energy but not mass. When particles in water become part of a wave, they start to move up or down. This means that kinetic energy (energy of movement) has been transferred to them. As the particles move further away from their normal position (up towards the wave crest or down towards the trough), they slow down. This means that some of their kinetic energy has been converted into potential energy - the energy of particles in a wave oscillates between kinetic and potential energy.
This activity shows that water waves like other waves transfer energy from one place to another without transferring matter, i.e., water.
Q.6: Describe the two main categories of waves?
Ans: Categories Of Waves:
There are two main categories of waves:
- Mechanical waves
- Electromagnetic wave
Waves which require a medium for their propagation are called mechanical waves. These waves are produced by vibratory motion in the respective medium. Mechanical waves consists of transverese as well as longitudinal waves.
Examples:
Sound waves, water waves and seismic waves are some examples of mechanical waves.
ELECTROMAGNETIC WAVES:
Waves which do not require a medium for their propagation are called electromagnetic waves. These waves are produced by a changing of electric and magnetic fields. Electromagnetic waves only comprised of a transverse wave in nature.
Examples:
Radio waves, microwaves, light waves, U.V waves and infrared waves are some examples of electromagnetic waves.
Q.7: Distinguish between:
(i) Transverse and Longitudinal waves
(ii) Mechanical and Electromagnetic waves.
Ans: Difference Between Transverse Waves And Longitudinal Waves:
| S.NO. | Transverse Waves | Longitudinal Waves |
|---|---|---|
| 1. | In transverse wave, particles of the medium vibrates perpendicular to the direction of propagation of waves. | In longitudinal wave, particles of the medium vibrates parallel to the direction of propagation of waves. |
| 2. | This wave is made up of crests and troughs. | This wave is made up of compressions and rarefactions. |
| 3. | The production of this wave can take place in liquid and gas mediums only. | The production of this wave can take place in any medium - solid, gas, or liquid. |
| 4. | The polarization or alignment of this wave is certainly possible. | The polarization or alignment of this wave does not happen. |
| 5. | This wave acts in two dimensions. | This wave acts in one dimension. |
| 6. | An example of a transverse wave is the light wave. | An example of a longitudinal wave is the sound wave. |
Difference Between Mechanical Waves And Electromagnetic Waves On The Basis Of Medium:
| S.NO. | Mechanical Waves | Electromagnetic Waves |
|---|---|---|
| 1. | Mechanical waves are such waves that need a medium for propagation. | Electromagnetic waves are such waves that do not need a medium for propagation. |
| 2. | Mechanical waves are produced by vibratory motion in the respective medium. | Electromagnetic waves are produced by a changing of electric and magnetic fields. |
| 3. | Mechanical waves consist of transverse as well longitudinal waves. | Electromagnetic only comprised of a transverse wave in nature. |
| 4. | Mechanical waves cannot travel through the vacuum. | Electromagnetic waves travel through the vacuum at the speed of 3×108 m/s. |
| 5. | All mechanical waves travel through their media at different speeds depending upon the physical properties of the respective medium. | All electromagnetic waves can travel through transparent media at different speeds depending upon the refractive index of the respective medium. |
| 6. | Sound waves, water waves and seismic waves are some examples of mechanical waves. | Radio waves, microwaves, light waves, U.V waves and infrared waves are some examples of electromagnetic waves. |
Q.8: Describe properties of waves such as reflection, refraction, and diffraction with the help of ripple tank?
Ans: PROPERTIES OF WAVES:
Let us consider some wave properties such as reflection, refraction, and diffraction concerning the ripple tank.
Reflection of the waves:
Definition:
“Bouncing back of waves into same medium by striking other medium surface is called reflection.”
When a vertical straight surface is placed in the path of the incoming waves. The incident waves are reflected from the surface at the same angle. It can be seen that the reflected waves obey the law of reflection, Example: the angle of the incident wave along the normal will be equal to the angle of the reflected wave. This effect is called reflection.
Refraction of waves:
Definition:
“When a wave enters from a region of deep water to a region of shallow water at an angle, the wave will change its direction.”
When a flat piece of a block is immersed in the ripple tank, water depth becomes shallow. We will find that the wavelength of the plane waves shortens and changes direction, as they move from the boundary between two media, deep to shallow water. However, the frequency of water waves stays the same in both waves because it is the same as the frequency of the vibrator. This result shows that the speed of a wave in water depends on water depth. Waves travel faster in deep water than in shallow water. This effect is called refraction.Diffraction of waves:
Definition:
“The spreading of the waves near an obstacle is called diffraction.”
When an obstruction or a straight surface with a gap in the ripple tank is placed in the path of the incoming water waves, they strike it, the waves will bend around the sides of an obstruction or spread out as they pass through a gap. This phenomenon is called diffraction.Diffraction is only significant if the size of the gap is about the same as the wavelength of the incident wave, narrow the gap whose width is equal to the wavelength of the incoming ripples, the ripples that pass through the gap are almost circular and seem to originate from a point source situated in the gap. Wider gaps produce less diffraction.
Q.9: What are wave characteristics? OR Define the terms speed (v), frequency (f), wavelength (λ), time-period (T), cycle, wavefront?
Ans: WAVES CHARACTERISTICS:
The following are some terms used to describe wave motion.
1. Time-Period (T):
It is the time taken for any one point on the wave to complete one oscillation. It is denoted by "T".
Unit: The SI unit of the period is second (s).
2. Frequency (f):
It is the number of complete waves produced by a source per unit of time.
In general, Frequency is also defined as the reciprocal of the period. It is denoted by "f".
Thus,
Frequency = Number of complete waves produced / time taken
If the number of waves produced = is 1
And time is taken = T
Then f = 1/T
Unit: The SI unit of frequency is the hertz (Hz).
3. Wavelength (λ):
It is the linear distance between two successive crests or troughs in a transverse wave and two successive compressions and rarefactions in a longitudinal wave. It is denoted by (λ)
Unit: Its SI unit is meter (m).
4. Wave speed (v):
It is the speed at which a wave travels.
It is defined as the distance traveled by a given point on the wave, such as a crest in a given interval of time. It is denoted by (v)
Unit: In the SI system, the wave speed is measured in meter per second (m / s).
5. The Wavefront:
It is an imaginary line on a wave that joins all points that are in the same phase.
A wavefront is usually drawn by joining all wave crests.
There are two types of the wavefront, depending on how the waves are produced, which are:
- (a) concentric circles and
- (b) plane straight lines
(b) In a ripple tank, a plane dipper can produce plane waves. These waves have a plane wavefront.
Q.10: What is the relation between velocity frequency and wavelength? OR Derive the relation between wave speed and frequency?
Ans: Relation Between Velocity (Wave speed), Frequency And Wavelength:
The wave is a disturbance in a medium that transfer energy from one place to another. It travels from one place to another and hence has a specific velocity. This called the velocity (Speed) of the wave and is denoted by Velocity = Distance traveled / time taken or
v = S / t
Let us consider for a wave,If the time taken by the wave to move from one point to another is equal to its time period 'T', then the distance travelled by the wave will be equal to one wavelength = λ
then
Q.11: Define periodic motion?
Ans: PERIODIC MOTION:
A motion repeating itself in an equal time interval is referred to as periodic or oscillatory motion or harmonic motion.
Q.12: Define and explain simple harmonic motion (SHM)?
Ans: SIMPLE HARMONIC MOTION:
Definition:
When an object oscillates about a fixed position (mean position) its acceleration is directly proportional to its displacement from the mean position and is always directed towards the mean position. Its motion is called SHM.
Explanation:
An object in such a periodic motion oscillates about an equilibrium position due to a restoring force or a restoring torque. Such force or torque will return the system to its equilibrium position. This type of motion is called Simple Harmonic Motion.
Mathematically:
SMH is defined as:
a ∝ - x
a = - kx
- Where k is spring constant
- x is displacement and
- a is the acceleration of a body
Q.13: Define restoring force?
Ans: RESTORING FORCE:
The restoring force is a force which acts to bring a body to its equilibrium position.
Q.14: What is a simple pendulum?
Ans: SIMPLE PENDULUM:
A simple pendulum consists of a small metallic bob of mass 'm' suspended from a light inextensible string of length ‘l’ fixed at its upper end.
Examples: Old-fashioned clocks, a child's swing, and a fishing sinker are pendulum examples.
Q.15: Draw forces acting on a displaced pendulum? OR Which force acts on simple pendulum to displaced it?
Ans: Forces Acting On A Displaced Pendulum:
When the bob of the pendulum is displaced at a small angle '𝞱' to an extreme position.
The forces that act upon are:
- Tension ’T’ along the direction of the string, and
- Weight W = mg, acting vertically downwards.
Q.16: With the help of diagram explain SHM in simple pendulum? OR Prove that a simple pendulum executes simple harmonic motion? OR Explain SHM with simple pendulum?
Ans: MOTION OF A SIMPLE PENDULUM AND SIMPLE HARMONIC MOTION (SHM):
Let us think of an experiment to prove that a simple oscillating pendulum executes Simple Harmonic Motion.
- A simple pendulum consists of a small metallic bob of mass 'm' suspended from a light inextensible string of length ‘l’ fixed at its upper end.
- A pendulum's restoring force is proportional to its displacement for minor displacements under 15 degrees. Simple pendulum has simple harmonic motion.
- At the mean position ‘O’, a pendulum is in its equilibrium position. If no external force were applied, the bob of a pendulum would naturally settle here.
- The curve path ’s’ is the distance the bob of a pendulum travels.
Forces Acts:
When the bob of the pendulum is displaced at a small angle '𝞱' to an extreme position at point ‘A’ or ‘B’. The forces that act upon are:
- Tension ’T’ along the direction of the string, and
- Weight W = mg, acting vertically downwards.
Observation:
- The bob will not stop at ‘O’ and continue to move to extreme positions due to inertia.
- When bob moves to mean position under the action of gravity its velocity is maximum at ‘O’.
- When bob moves from mean position 'O' to extreme positions against the force of gravity its velocity decreases and becomes zero at extreme position.
- The process is repeated again and again and the bob is vibrate between two extreme positions.
Conclusion:
Simple pendulum executes simple harmonic motion.
Time Period:
For the simple pendulum executing SHM, we have the following formula for its period:
T = 2 √ l / g
This formula shows that the period 'T' of a simple pendulum depends upon its length ‘l’ and acceleration due to gravity 'g' over that place. The period of the pendulum is independent of its mass and its amplitude.
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