## Motion

Chapter -1

Motion

Some Real Life Examples of Motion

Motion
If a body does not change its position with respect to time and the surrounding, it is said to be at Rest and else it is said to be in Motion.
Motion and Rest are always relative but never absolute. It means an object in one situation can be at rest but in another situation the same object can be in motion.

Controlled and Uncontrolled Motions

• Uncontrolled Motions
• Controlled Motions

Uncontrolled Motions

• Flooded River
• Hurricane
• Tsunami

Controlled Motions

• Hydro-electric Power

Reference Point

Position

Scalar and Vector Quantities

• Physical quantities with which we can associate only magnitude i.e., number are called Scalar Quantities.
• Physical quantities with which we can associate magnitude i.e., number as well is direction is called Vector Quantities.

Distance
The distance travelled by a body is the actual length of the path covered by a moving body irrespective of the direction. It is a scalar quantity in meter.

Displacement
When a body moves from one position co. another, the shortest distances i.e., straight line between the initial position and final position of the body, along with direction. It is a vector quantity in meter.

Uniform Motion

Uniform Motion

Non-Uniform Motion

Non-Uniform Motion

Uniform and Non-Uniform Motion

• Uniform Motion

•  Non-Uniform Motion

Speed

Speed of an object is defined as the distance travelled by it per unit rime.

km/h to m/s and vice versa
1 km = 1000m
1 h = 60 min = 3600 s

Uniform Speed
If a moving body covers equal distance in equal intervals of time, then the speed of the body is said to be uniform speed or constant speed.

Non-Uniform Speed
If a moving body covers unequal distances in equal intervals of time, then the speed of the body is said to in non-uniform speed or variable speed.

Average Speed
It is defined as the ratio of the total distance travelled by an object to the total time taken.

Average Speed= Total Distance Travelled Total Time Taken

## Velocity and Acceleration

Velocity (Speed with Direction)

Velocity of an object can be changed by changing the object’s speed, direction of motion or both.

Types of Velocity

• Uniform Velocity
• Average Velocity
• Non-Uniform Velocity

Uniform Velocity

If an object covers equal displacements in equal intervals of time without changing direction.

Non-uniform Velocity

If an object covers unequal displacements in equal intervals of time without changing direction.

Average Velocity
It is defined as the average rate of change of position of an object with respect to time.

Acceleration

(Rate of Change of Velocity)

Acceleration

(Rate of Change of Velocity)
Acceleration is defined as the rate of change of its velocity with respect to time.

Graphical Representation of Motion

Distance-Time Graph for Stationary Body
The distance of a stationary body from a fixed point does not change with the passage of rime. It is straight line parallel to time axis.

Distance-Time Graph for Uniform Motion
If a body travels equal distances in equal interval of time, then it moves with uniform speed. For uniform speed, a graph of distance travelled against time is a straight line

## Time Graph and circular motion

Distance-Time Graph for Non-Uniform Motion

If a body travels unequal distances in equal interval of time. then the motion of the body is known as non-uniform motion.

Velocity-Time Graph
Velocity-time graph shows how the velocity of a body changes with passage of times.

Velocity-Time Graph for Body Moving with Constant Velocity
When a body moves with constant velocity i.e., its motion in uniform, its velocity does not change with time.

Velocity-Time Graph for Uniform Accelerated Motion
Velocity-Time Graph Non-Uniform Accelerated Motion and Retardation

Equations of Motion by Graphical Method
Equation for Velocity-Time Relation (First Equation)

Rate change in velocity

On putting the value

Circular Motion
Distance cover in circular motion in time t.

## Force

Chapter -2

Force and Laws of Motion

Force

Any action which causes pull hit or push on a body is called force.
Force SI unit is Newton.
1 newton = 1 kg-ms–2

Balanced Force
When the net effect produced by a number of forces on a body is zero, the forces are said to be Balanced Forces.

Unbalanced Force
When the net effect produced by a number of forces on a body is non-zero, the forces are said to be Unbalanced Forces.

Newton’s Laws of Motion
Newton’s First Law of Motion.

Application of Newton’s First Laws of Motion

• If an object is kept on the ground at a certain place that will remain on the ground unless an external force is applied to move it.
• A person standing in a moving bus falls forward if driver applies brakes suddenly.
• When the pile of coin on the carom-board hit by a striker, coin only at the bottom moves away leaving rest of the pile of coin at same place.

Inertia and Mass
The first law of motion is also known as the law of inertia.

Inertia of Rest
The tendency of a body to oppose any change in its state of rest is known as inertia of rest.

Inertia of rest
The tendency of a body to oppose any change in its state of rest is known as inertia of rest.

Inertia of Motion
The tendency of a body to oppose any change in its state of uniform motion is known as inertia of motion.

## Momentum

Momentum

• Momentum measures the quantity of motion possessed by a body.
•  It is defined as the product of mass and velocity of the body

Newton’s Second Law of Motion
The rate of change of momentum is directly proportional to the force applied in the direction of force.

Application of Newton’s Second Laws of Motion
(i) During athletics meet, a high jumping athlete is provided either a cushion or a heap of sand on the ground to fall upon.

(ii)  Now-a-days all the cars are provided with seat belts for passengers to prevent injuries in case of an accident.

Mathematical Formulation
If a body of mass (m), moving at velocity (u) accelerates uniformly at a for time (t), so that it its velocity changes to v, then
Initial momentum, P1 = muSolution
Initial momentum, P2 = mv
Change in momentum = P2 – P1
= mv – mu
= m(v – u)
According to second law of motion, force

F = kma

Here,                          k = 1
Thus,                         F = ma
This also proves that the SI unit of force is newton and it is equivalent to kg-m/s2.
One Newton force is exerted on an object of mass 1 kg to produce an acceleration of 1m/s2 in it.
Step II:- Write formulae used.

Step III:- Substitute the values in step II and solve.

Thus, the acceleration produced in the body is 5m/s2 and velocity attained it is 10 m/s.

Recoil of Gun
When bullet is fired from a gun, the bullet also pushes the gun in opposite direction, with equal magnitude of force.

Law of Conservation of Momentum
Total initial momentum of the system
= mAuA + mBuB

Total final momentum of the system
= mAvA + mBvB

To Prove
mAuA + mBuB = mAvA + mBvB

Proof
From Newton’s third law,
Force exerted by mA on mB = - (force exerted by mB on mA)
Force F = ma

MAuA + mBuB = mAvA + mBvB Hence Proved.

## Gravitation

Chapter:- 3

Gravitation

Gravitation

Gravitation is defined as the non-contact force of attraction between any two

bodies in the universe, no matter how far the bodies.

Characteristics of Gravitation Force

(i):- Gravitational force is action at a distance force, i.e., it does not need any  contact between the two bodies.

(ii):- Gravitational force is an inverse square force because it is inversely proportional to the square of the distance between the two bodies.

(iii):- Gravitational force between two bodies form action-reaction pair.

(iv):- Gravitational force between two small bodies is very small.

(v):- On the other hand. gravitational force between two large bodies (say the sun and the earth) is large.

Universal Law of Gravitation

The attractive force  between any two objects in the universe is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

Combining eqs. (i) and  (ii) we get

Importance of Universal Law of Gravitation

Universal law of gravitation successfully explained several phenomena like.

(i):- The force that binds us to the earth.

(ii):- The motion of the moon around the earth.

(iii):-The motion of planets around the sun.

(iv):-The tides due to the moon and the sun.

(v):- The flow of water in rivers is also due to gravitational force the earth on water

(vi):-The gravitational force of the earth is responsible for holding the atmosphere

around the earth..

(vii):-The predictions about solar and lunar eclipses made on the basis of this law always come out to the true.

## Free fall and weight

Free Fall

Whenever objects fall towards the earth under the earth’s gravitational force alone, are called freely falling objects and such fall is called Free Fall.

Let mass of earth be M and r an object falling freely towards it be m. Distance between centers of earth and the object is R.

From Newton’s law of gravitation,

Also, from second law of motion, force exerted on object,

F = ma

Since, a = g (i.e., acceleration due to gravity)

F = mg        …(ii)

Equation RHS of Eqs. (i) and (ii), we get

From the formula, it is clear that acceleration due to gravity does not depend on the mass of a falling object. It depends only on the mass of the body towards which it falls freely.

To Calculate the Value of g

The value of g at the surface of earth may be calculated as follows

Mass of earth = 6 x 1024kg

Radius of earth = 6.4 x 106m

Universal gravitational constant = 6.67 x 10-11Nm2/kg2

ge = 9.8 m/s2

Motion of objects under the Influence of Gravitational force of the Earth

The three equation of free fall near the surface of earth for all uniformly acceleration objects are

v = u + gt, h = ut + 1/2gt2,         v2 = u2 + 2gh

where h is the height from which the object falls, t is the time of fall. u is the initial velocity and v is the final velocity when the body accelerates at g.

(i):- If an object falls vertically downward then acceleration due to gravity is taken as positive (âˆµ its velocity increases while falling.)

(ii):- If an object is thrown vertically upward then acceleration due to gravity is taken as negative (âˆµ its velocity decreases as it moves upward.)

(iii):- If an object is dropped freely from a height, its initial velocity u is zero.

(iv):- If an object is thrown vertically upwards, its final velocity v becomes zero.

(v):- Time taken by an object to fall from a height is same as that taken by it to rise the same height.

Mass

Mass is a quantity which measure's the inertia of a body. Mass always remains constant everywhere. The mass of the body cannot be zero.

Weight

The weight of an object is the force, with which it is attracted towards the earth.

Weight of an object, w = mg

where m = mass, g = acceleration due to gravity

Here, M = mass of the earth and

R =  radius of the earth.

(i):- Weight of an object on the moon is 1/6th weight on the earth.

(ii )Weight is a vector quantity, it acts in vertically downward direction and its SI unit is newton

N Weight of I kg mass is 9.8 newton.

(iii):- Weight of an object is not constant, it change place to place.

(iv):- In the place where g = 0, weight of an object is zero.

(v):- At the centre of earth, weight becomes zero. due to the fact that g in all directions become equal and all forces cancel each other.

Weight of an Object on the Moon

Let the mass of an object be m and its weight on the moon be Wm. Suppose the mass of the moon is M and its radius be R. According to universal of law gravitation, the weight of an object on the moon will be

Let the weight of the same object on the earth be Wm. But the mass of the earth is 100 times that of the moon and the radius of the earth is 4 times that of the moon.

Now dividing Eq. (i) by Eq.(ii), we have

Thus, the weight of the object on motion is one-sixth of the weight on the earth.

## Thrust and Pressure

Chapter:- 4

Floatation

Thrust and Pressure

Thrust is the force or push acting on an object perpendicular to its surface.  Effect of thrust depends on the area on which it acts. The unit of thrust is the same as that of force, i.e., the SI unit of thrust is newton (N). It is a vector quantity.

Pressure

Pressure is the force acting perpendicularly on a unit area of the object.

The SI of pressure is N/m2, which is also called pascal (Pa) named after the scientist Blaise Pascal. It is a scalar quantity.

1 Pa = 1N/m2

Some Daily Life Applications of Pressure

• The handles of bags, suitcase, etc . are made broad, so that the small pressure is exerted on the hand.
• Buildings are Provided with broad foundations. so that the pressure exerted on the ground becomes less.
• Railway tracks are laid on cement or iron sleepers, so that the pressure exerted by train is spread over the larger area and thus, pressure becomes less.
• Cutting tools have sharp edges to reduce the area so that with lesser force more pressure is exerted.
• The tractors have broad tyres so that there is less pressure on the ground and the tyres do not sink into comparatively soft ground in the field.

Pressure in Fluids

Those substances which can flow easily are called fluids. All the liquids and gases are fluids. Water and air are two most common fluids. Solids exert pressure on a surface due to their weight.

Fluids also exert pressure on the base and walls of the container in which they are enclosed. Fluid (liquid or gas) exerts pressure in all directions, upwards also.

Buoyancy

The tendency of liquid to exert an upward force on an object immersed in it, is called buoyancy.

Buoyancy Force is an upward force which acts on an object when it is immersed in a liquid: It is also called upthrust. It is the buoyant force due to which heavy object seems to be lighter in water. As we lower the position of object into a liquid, the greater upward pressure of liquid underneath it, provides an upward force.

For Example, a piece of cork is held below the surface of water.

When we apply a force by our thumb, the cork immediately rises

to the surface. This is due to  the fact that every liquid

exerts an upward force on the objects immersed in it.

## Factors Affecting Buoyant Force

Factors Affecting Buoyant Force

(i) Density of the Fluid

The liquid having higher density exerts more upward buoyant force on an object than another liquid of lower density. This is the reason, why it easier to swim in sea water in comparison to normal water, because sea water has higher density and hence, exerts a greater buoyant force on the swimmer than the fresh water having lower density.

(ii)Volume of Object Immersed in the Liquid

As the volume of solid object immersed inside the liquid increases, the upward buoyant force also increases.  The magnitude of buoyant force acting on a solid object does not depend on the nature of the solid object. It depends only on its volume.

For Example, when two balls made of different metals having different weights but equal volume when fully immersed in a liquid they will experience an equal upward buoyant force as both the balls displace equal weight of the liquid due to their equal volume.

Floating or Sinking of Objects in Liquid

When an object is put in a liquid, then following two forces act on it.

• Weight of object which acts in downward direction. i.e., it tends to pull down the bject.
• Buoyant Force (upthrust) which acts in upward direction.i.e., it tends to push up the object.

There are three conditions of floating and sinking of objects

(i):- If the buoyant force or upthrust exerted by the liquid is less than the weight of the object, the object will sink in the liquid.

(ii):- If the buoyant force is equal to the weight of the object, the object will float in the liquid.

(iii):- If the buoyant force is more than the weight of the object, the object will rise in the liquid.

Note:- So far an object floating in a liquid the weight of object should be equal to buoyant force acting on it.

Law of Floatation

According to this law, an object will float in a liquid if the weight of object is equal to the weight of liquid displaced by it. Mathematically, it is expressed as

Weight of object = weight of liquid displaced by it

Density

The density of a substance is defined as mass per unit volume.

The SI unit of density is kilogram per metre cube (kg/m3). It is a scalar quantity.

## Archimedesâ€™ Principle

Archimedes’ Principle

When an object is fully or partially immersed in a liquid, it experiences a buoyant force or upthrust, which is equal to the weight of liquid displaced by the objects.

Buoyant force or upthrust acting on an object = Weight of liquid displaced by the object

Even gases like air, exert an upward force or buoyant force on the objects placed in them. It is buoyant force or upthrust due to displaced air which makes a ballon rise in air.

Application of Archimedes’ Principle

• Designing ships and submarines
• Lactometer (used to determine the purity of milk)
• Hydrometer (used for determining the density of liquid)
• Determining the relative density of a substance

How does a Boat Float in Water?

A boat floats in water due to upward force called buoyant force (or upthrust) which is caused by the pressure of water pushing up the bottom of the boat. When this buoyant force becomes just enough

to support the weight of boat, the boat stops sinking down in water.

Relative Density

The relative density of a substance is the ratio of its density to that of water.

Since,  the relative density is a ratio of similar quantities it has no unit. The relative density of a substance expresses the heaviness of the substance in comparison to water. By saying that relative density of iron is 8.7, we mean that iron is 8.7 times as heavy as an equal volume of water.

Note:- Density of water is 1000kg/m3  or 1g/cm3.

## Work and Energy

Chapter:- 5

Work and Energy

Introduction

All living beings need food for getting energy and to perform severl basic activities to survive. Actiities like playing, singing, reading, writing, jumping, cycling and running require more energy and hence more work is done.

Work

Work is said to be the physical activity involving a force and movement in the direction of the force and an equal amount of energy is used up when work is being done.

Work Done by a Constant Force

Let a constant force F acts on an object and let object be displaced through a distance s in the direction of the force. Let work done W be equal to the product of the force and displacement.

Work done = Force x Displacement in the direction of force

or                  W = Fxs               ….(i)

Thus, work done by a force on an object is equal to the

magnitude of the force multiplied by the

distance moved in the direction of force.

In Eq. (i), if F = 1N and s =1 m, then the work done by the

force will be 1 N-m.

The SI unit of work is newton-metre (N-m) or joule ( J).

1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m

along the line of action of the force.

Work is a scalar quantity, it has only magnitude and no direction.

Work Done by a Force Acting at an Angle with the Direction of Displacement

When force F on an object acts in such a direction that it makes an angle θ with the direction of displacement s, then the work done by the force is

Positive Work

When the force F and displacement s are in the same direction (angle between direction of force and displacement is 0°), work done will be positive, i.e. work is done by the force.

For Example, a boy pulls an object towards himself.

W = +F x s

Negative Work

When the force F and displacement s are in opposite

direction (angle between direction of force and

displacement is 180°), work done will be negative,

i.e. work is done against the force.

For Example, (frictional force acts in the direction opposite to the direction of displacement, so work done by friction will be negative.

W = –F x s

Zero  Work

When the force and displacement are in perpendicular direction (angle between direction of force and displacement is 90°), work done is zero.

For Example, a man carrying load on his head. In this case, force is acting vertically downward (weight of load) and displacement is along horizontal direction, i.e., force and displacement are

perpendicular to each other.

W = 0

Energy

It is the ability to do work. It is always essential for performing any mechanical work. An object having  capacity to do work is said to possess energy. The object which does work, losses energy and the object on which work is done, gains energy.

An object having energy can exert a force on another object. When it happens, energy is transferred from former object to latter object. The energy of an object is measured in terms of its capacity of doing work.

The SI unit of energy is same as that of work, i.e., joule (J). 1 joule of energy is required to do 1 J of work. A larger unit of energy is kJ.

1 kilo joule (kJ) =103 J

For Example,

• When a fast moving cricket ball hits a stationary wicket, the wicket is thrown away.
• When a raised hammer falls on a nail placed on a piece of wood, it drives the nail into the wood.

Kinetic Energy

It is that energy which is possessed by an object due to its motion.  In other words, energy due to the motion of a body is called kinetic energy. Its SI unit is joule (J). Kinetic energy of a body moving with a certain velocity is equal to the work done on it make it acquire that velocity. Kinetic energy of an object increases with its speed.

• Due to kinetic energy, a bullet fired from a gun can pierce a target.

The kinetic energy possessed by an object of mass m, moving with a uniform velocity v is

Calculation of Kinetic Energy

The kinetic energy of an object is measured by the amount of work, it can do before coming to rest. Consider an object of mass m moving with a uniform velocity u. A force F is applied on it which displaces it through a distance s and it attains a velocity v.

Then, work is done to increase its velocity from u to v.

W = Fs                                      ...(i)

According to the equation of motion,

v 2  – u2 = 2as

where, a is uniform acceleration

Also from, F = ma

Substituting the values of F and s in Eq. (i), we have

If initial velocity,              u = 0

Total work is equal to change in kinetic energy.

This work done is equal to the kinetic energy of the object.

Some Important Results can be Derived from the Formula KE =1/2mv2

These are given below

(i):- If the mass of an object is doubled, its kinetic energy also gets doubled.

(ii):- If the mass of an object is halved, its kinetic energy also gets halved.

(iii):- If the speed of an object is doubled, its kinetic energy becomes four times.

(iv):- If the speed of an object is halved, its kinetic energy becomes one-fourth.

(v):- Heavy objects moving with high speed have more kinetic energy than small objects moving with less speed.

## Potential Energy

Potential Energy

The energy possessed by a body due to its change in position or shape, is called potential energy. Its SI unit is joule (J). We can say that the potential energy possessed by a body, is the energy present in it by virtue of its position or configuration. e.g., a stretched rubber band, spring, string on the bow, etc.

Now, we can say that a body possesses energy even when it is not in motion.

Examples of Potential Energy are:-

• Water stored in dam has potential-energy due to its position at the height.
• A stone lying on the roof of the building has potential energy due to its height.
• A wound spring of a watch has potential energy due to its shape.

Expression for Potential Energy

Consider a body of mass m, lying at a point A on the earth's surface. Here, its potential energy is zero and its weight mg acts vertically downwards. To lift the object to another position B at a height h, we have to apply a minimum force which is equal to mg in the upward direction. So, work is done on the body against the force of gravity. Therefore,

Work Done = Force x Displacement

or              W = F x s

As,             F = mg (weight of the body)

s = h

Therefore,   W = mg x h = mgh

i.e.                                 PE = mgh

This work done is equal to the gain in energy of the body. This is the potential energy (PE) of the body.

Law of Conservation of Energy

According to law of conservation of energy, energy can only be transformed from one form to another; it can neither be created nor be destroyed. The total energy before and after transformation, always remains constant.

Conservation of Energy During the Free Fall of a Body

Consider a body of mass m, lying at position A. It is made to fall freely from a height h above the

ground as shown in figure.

At Point A

At the start, the potential energy is mgh and Kinetic energy is

zero (as its velocity is zero).

i.e.                   PE = mgh

KE = 0

At Point B

As it falls, its potential energy will change into kinetic energy.

If v is the velocity of the object at a given instant,

its kinetic energy would be 1/2mv2.

PE = mg(h – x)

Total energy = mg(h – x) + mgx = mgh

Total Energy = mgh

At Point C

As the fall of the object continues, the potential energy would decrease while the kinetic energy would increase. When the object is about to reach the ground, h = 0 and v will be the highest.

PE = 0

Thus, the sum of the potential energy and kinetic energy of the object would be the same at all points, i.e.

PE + KE = constant

Transformation of Energy (Are various energy forms interconvertible?)

One form of energy can be converted into other forms of energy, this phenomenon is called transformation of energy. When an object is dropped from some height potential energy continuously converts into kinetic energy. When an object is thrown upwards, its kinetic energy continuously converts into potential energy.

For Example,

(i):- When we throw a ball, the muscular energy which is stored in our body, gets converted into kinetic energy of the ball.

(ii):- The wound spring in the toy car possesses potential energy. As the spring is released, its potential energy changes into kinetic energy due to which, toy car moves.

(iii):- Green plants prepare their own food (stored in the form of chemical energy) using solar energy through the process of photosynthesis.

## Rate of Doing Work: Power

Rate of Doing Work: Power

The rate of doing work or the rate at which energy is transferred or used or transformed is called power. If work W is done in time t, then

The SI unit of power is watt in honour of James Watt having the symbol W. We express larger rate of energy transfer in kilowatt (kW)

1 W =1 J/s or lkW =1000 W =1000 Js-1

1 MW =106 W

1 (horse power) HP = 746 W

Average Power

Average power is defined as the ratio of total work done by the total time taken. An agent may perform work at different rates at different intervals of time. In such situation, average power is considered by dividing the total energy consumed by the total time taken.

Commercial Unit of Energy

The unit joule is too small to express large quantities of energy conveniently. Therefore, a bigger unit of energy is used. The bigger unit is the commercial unit of electric energy, known as kilowatt-hour (kWh).

It is the amount of electric energy consumed by an appliance of power 1000 W in one hour.

1 kWh = l kW x lh

=1000W x 3600s =1000 Js-1 x 3600s

kWh = 3.6 x 106 J

The energy used in households, industries and commercial establishments is expressed in kilowatt hour is expressed in terms of units.

1 unit = 1 kilowatt hour

## Sound

Chapter:- 6

Sound

Production of Sound

Sound is produced by vibrating objects. Vibration means a kind of rapid to and fro motion of an object. The sound of human voice is produced due to vibrations in the vocal cords. We can produce sound by striking the tuning fork, by plucking, scratching, rubbing, blowing or shaking different objects. They all produce sound due to vibrations.

Propagation of Sound

When an object vibrates, it sets the particles of the medium around it in vibration. The particles of the medium do not move forward but the disturbance is carried forward. Sound waves require a medium to travel so, they are called mechanical waves. Compression is the part of a longitudinal wave in which they particles of medium are closer to one another than they normally are and it is the region of high pressure. It is denoted by C. Rarefaction is the part of a longitudinal wave in which the particles of the medium are farther apart than they normally are and it is the region of low pressure. It is denoted by R.  As the object moves back and forth rapidly, a series of compressions and rarefactions is created in air. These make the sound wave that propagates through the medium. Propagation of sound can be visualized as propagation of density variations or pressure variations in the medium in a given  volume. More density of the particles in the medium gives more pressure and vice-versa.

Sound Needs a Medium to Travel

The substance through which sound travels is called a medium. It can be solid, liquid or a gas. Sound wave is a mechanical wave and requires a material medium like air, water, steel, etc., for its propagation. Sound wave cannot travel in vacuum.

Types of waves

Mainly there are two types of waves

(i) Longitudinal waves

(ii) Transverse waves

Logitudinal Waves

In longitudinal waves, the individual particles of the medium move in a direction parallel to the direction of propagation of the disturbance. The particles do not  move from one place to another but they simply oscillate back and forth about their positions of rest. This is exactly how a sound wave propagates, hence sound waves are longitudinal waves. Longitudinal waves can be produced in al the three media such as solid, liquids and gases.

The waves which travel along a spring when it is pushed and pulled at one end, are the longitudinal waves.

When coils are closer together than normal, compressions (C) and observed in spring. When coils are farther apart than normal, rarefactions (R) are observed. A long flexible spring which can be compressed or extended easily is called slinky.

Transverse Waves

In transverse waves, the individual particles of the medium move about its mean position in a direction perpendicular to the direction of wave propagation.

For Example:- The water waves (or ripples) formed on the surface of water in a pond (when a stone is dropped in the pond of water) are transverse waves.

Terms to Describe Sound Waves

Sound waves can be described by its

(i):- Wavelength              (ii):- Frequency                 (iii):- Time period

(iv):- Amplitude               (v):- Speed

## Wavelength

Wavelength

The distance between the two consecutive compressions (C) or two consecutive rarefactions (R), is called the wavelength. Wavelength is the minimum distance in which a sound wave repeats it self.

In other words, it is the combined length of a compression and an adjacent rarefaction. It is represented by a lambda λ. Its SI unit is metre (m).

Frequency

The number of complete waves produced in one second is called frequency of the wave. It is the number of vibrations that occur per second. If we can count the number of the compressions or rarefactions that cross us per unit time, we will get the frequency or sound wave. The frequency of a wave is fixed and does not change even when it passes through different substances. It is denoted by v (Greek letter, nu).

• Its SI unit is hertz (symbol, Hz)
• 1 hertz is equal to 1 vibration per second
• 1 kHz = 1000 Hz

Time Period

The time taken by two consecutive compressions or rarefactions to cross a fixed point is called the time period of the wave. In other words, the time required to produce one complete wave (or oscillations) is called time period of the wave. It is denoted by symbol T. Its SI unit is second (s). The time period of a wave is the reciprocal of its frequency, i.e.,

T = 1/v

or Time period = 1/Frequency or Frequency = 1/ Time period

Amplitude

The maximum displacement of the particles of the medium from their original mean positions on passing a wave through the medium, is called amplitude of the wave. It is usually denoted by the letter A. Its SI unit is metre (m).

The amplitude of wave is the same as the amplitude of the vibrating body producing the wave.

Speed

The distance travelled by a wave in one second is called speed of the wave or velocity of the wave. Under the same physical conditions, the speed of sound remains same for all frequencies. It is represented by letter v. Its SI unit is metre per second (m/s or ms–1). Relationship between speed, frequency and wavelength of a wave:

Suppose distance travelled by a wave is λ (wavelength), in time T, then the speed is given by v = λ/ T

We know that frequency, v = 1/T

Therefore,   v = λ × v    or     v =

or    Speed (velocity) = Frequency × Wavelength

Loudness

It is the measure of the sound energy reaching the ear per second. Greater the sound energy reaching our ear per second, louder the sound will appear to be. If the sound waves have a small amplitude, then sound will be faint or soft but if waves have a large amplitude, then the sound will be loud.

Since the amplitude of a sound wave is equal to the amplitude of vibrations of the source producing the sound waves. Loud sound can travel a larger distance as it is associated with higher energy. A sound wave spreads out from its source, as it moves away from the source, its amplitude as well as its loudness decreases. The loudness of sound is measured in decibel (dB).

Intensity

The amount of sound energy passing each second through unit area is known as the intensity of sound. Loudness and intensity are not same terms. Loudness is a measure of the response of the ear to the sound. Even when two sounds are of equal intensity, we may hear one as louder than the other, simply becomes our ear detects it in better way.

• The SI unit of intensity is watt per square metre (W/m2) .

Pitch or Shrillness

It is that characteristic of sound by which we can distinguish between different sounds of the same loudness.

• Pitch of a sound depends on the frequency of vibration.

The faster the vibration of the source, the higher is the frequency and hence, higher is the pitch, as shown in figure.

Quality or Timbre

The quality or timbre of sound is that characteristic of sound which enables us to distinguish one sound from another having the same pitch and loudness. The pleasant sound is said to be of a rich quality. Noise is unpleasant to ear, music is pleasant to ear and is of rich quality. The sound produced by different musical instruments like flute, violin, sitar, tanpura.

## Speed of Sound in Different Media

Sonic Boom

When the speed of any object exceeds the speed of sound, it is said to have supersonic speed.  Many objects such as some aircrafts, bullets and rockets, etc travel at supersonic speeds. When a sound producing source moves with a speed higher than that of sound, it produces shock waves in air, which carry a large amount of energy. The tremendous air pressure variations caused by the hock waves produce a loud burst of sound, known as sonic Boom.

Echo

When a person shouts in a big empty hall, we first hear his original sound, after that we hear the reflected sound of that shout. This reflected sound is echo. the repetition of sound caused by reflection of sound waves is called an echo.

The sensation of sound persists in our brain for about 0.1 s. To hear a distinct echo, the time interval between the original sound and the reflected one must be atleast 0.1 s.

The speed of sound in air is 344 m/s. The distance travelled by the sound in

0.1 s = speed × time = 344 × 0.1= 34.4 m

So, echo will be heard if the minimum distance between the source of sound and the obstacle is

To hear an echo, our distance from the reflecting surface should be atleast 17.2 m.

Reverberation

The persistence of a sound in a big hall due to repeated reflections from the walls, ceiling and floor of the wall is known as reverberation.

A short reverberation is desirable in a concert hall, where music is being played, as it boots the sound level. Excessive reverberation is highly undesirable, because sound becomes blurred, distorted and confusing due to overlapping of different sounds.

Uses of Multiple Reflection of Sound

The reflection of sound is used in the working of devices such as megaphone, horns, stethoscope and sound board.

Range of Hearing

The average frequency range over which the human ear is sensitive is called audible range.

The audible range of sound for human beings is from 20 Hz to 20000 Hz. Children under the age of 5 and some animals such as dogs can hear upto 25000Hz. As people grow older, their ears becomes less sensitive to higher frequencies.

Infrasonic Sound

The sound of frequencies lower than 20 Hz are known as infrasonic sounds or infrasound, whales, elephants and rhinoceroses produce infrasonic sound of frequency 5 Hz.

Ultrasonic Sound

The sounds of frequencies higher than 20000 Hz are called ultrasonic sounds Dogs can hear ultrasonic sounds of frequency upto 50000 Hz. Monkeys, bats, cats, dolphins, leopard and porpoises can also hear ultrasonic sounds.

Hearing Aid

This is a device used by people who are hard of hearing. It receives sound through a microphone which converts the sound waves to electrical signals.

These electrical signals are amplified by an amplifier. The amplified electrical signals are given to a speaker of the hearing aid. Which converts the amplified electrical signals to sound.

Ultrasound and its Applications

Ultrasounds are high frequency waves.  They travel in straight line without bending around the corners. They can penetrate into matter to a large extent. Due to these properties, ultrasound is used in industry and in hospitals for medical purposes.

Some of the important applications of ultrasound are given below

(i):-Ultrasound is used to clean parts located in hard-to-reach-places, such as spiral tubes, odd-shaped machines and electronic components, etc.

(ii):-Ultrasound is used in industry f

(iii):- Ultrasound is used to investigate the internal organs of human body such as liver, gall bladder, pancreas, kidneys, uterus and heart, etc.

Ultrasound helps us to see inside the human body and to give pictures of the inner organs by converting into electrical signals. This technique is called ultrasonography.

Ultrasound is also used for diagnosing heart diseases by scanning the heart from inside. This technique is echocardiography.

Ultrasound may be employed to break small stones formed in the kidneys into fine grains which later get flushed out with urine) This way, the patient gets relief from pain.

## Sonar and Human Ear

Sonar

The word SONAR stands for Sound Navigation and Ranging. Sonar is an apparatus used to find the depth of a sea or to locate the underwater things like shoals of fish, shipwrecks and enemy submarines. It use ultrasonic waves to measure the distance and speed of underwater objects.

SONAR consists of two parts:-

(i):- A transmitter (for emitting ultrasonic waves)

(ii):- A receiver (for detecting ultrasonic waves),

The transmitter produces and transmits ultrasonic waves.

These waves travel down the sea-water towards the bottom of the sea. When the ultrasonic sound pulse strikes the bottom of the sea, it is reflected hack in the form of echo and are sensed by the detector.

This will give us the depth of the sea. Let the time interval between transmission and reception of ultrasound signal be t and the speed of sound through sea-water be v. The total distance, 2d travelled by the ultrasound is, then 2d = v × t. This method is called echo-ranging.

Ultrasonic sound waves are used in SONAR, because

• These waves have a very high frequency and very short wavelength, due to which they can penetrate into sea-water to a large extent to locate the underwater objects or to determine the depth of the sea.
• These waves cannot be confused with engine noises or other sounds made by the ship as they cannot be heard by human beings.

Use of Ultrasonic Waves by Bats

Bats search out prey and fly in dark night by emitting and detecting reflections of ultrasonic waves. The method used by some animals like bats, tortoises and dolphins to locate the objects by hearing the echoes of their ultrasonic squeaks is known as echolocation.

Bats emit high frequency or high pitched ultrasonic squeaks while flying and listen to the echoes produced by reflection of their squeaks from the obstacles or prey in their path. From the time taken by the echo to be heard, bats can determine the distance of the obstacle or prey and can avoid the obstacle by changing the direction or catch the prey.

Human Ear

The ears are the sense organs which helps us in hearing sound. It allows us to convert pressure variations in air with audible frequencies into electric signals which travel to the brain via auditory nerve.

(i):- Outer Ear It consists of a broad part pinna and about 3 cm long passage ear canal. At the end of ear canal, a thin, elastic and circular membrane, eardrum is present, which is also called tympanum or tympanic membrane.

(ii):- Middle Ear contains three small bones – hammer, anvil and stirr up, which are connected with each other. One end of hammer is touching the eardrum and the free end of stir up is touched to oval-window of inner ear. The lower part of middle ear has a narrow tube, Eustachian tube going to the throat. It ensures that the air pressure inside the middle ear is the same as that on the outside.

(iii):- Inner Ear has a coiled tube, cochlea.  One side of cochlea is connected to middle ear through elastic membrane over the oval window. A liquid is filled in cochlea, which contains nerve cells that are sensitive to sound. The other side of cohlea is connecred to auditory nerve going into the brain.

Hearing Aid

This is a device used by people who are hard of hearing. It receives sound through a microphone which converts the sound waves to electrical signals.

These electrical signals are amplified by an amplifier. The amplified electrical signals are given to a speaker of the hearing aid. Which converts the amplified electrical signals to sound.

Working of Human Ear

Pinna collects the sound waves from the surroundings. These collected sound waves pass through the car canal (auditory canal) and fall on the eardrum (tympanum) or tympanic membrane. Since, sound waves are longitudinal waves, these waves consists of compressions (high pressure regions) and rarefactions (low pressure regions). When a compression of the medium reaches the eardrum the pressure on the outside of the membrane (eardrum) increases and forces increases and forces the eardrum inward. Similarly, when the rarefaction of sound wave falls on the eardrum, the pressure on the outside of the membrane (eardrum) decreases and it moves outward. In this way, when sound waves fall on the eardrum, it starts vibrating back and forth rapidly.

These vibrations are amplifies several times by the three bones (hammer, anvil and strip) in the middle ear and then passes to the liquid in the cochlea. Due to this, the liquid in the cochlea begins to vibrate and the cochlea. These electrical signals are carried by auditory nerve to the brain. The brain interprets them as sound and we get the sensation of hearing.