Modern Graded Science - 9

Here,

First weight (L1) = 20 N
Second weight (E1) = 40 N
Third weight (E2) = 10 N
Distance between L1 and fulcrum (Ld1) = 30 cm
Distance between E1 and fulcrum (Ed1) = 5 cm
Distance between E2 and fulcrum (Ed2) = 20 cm
Now,

i. Anti-clockwise moment = L1 × Ld1
= 20 × 30 = 600 N

ii. Clock-wise moment = (E1 × Ed1)+ (E2 × Ed2)
= (40 × 5) + (10 × 20)

= 200 + 200 = 400 N

iii. The lever will not be balanced as the clockwise moment and anti-clockwise moment
are not equal.

iv. To balance the lever by changing the location of 10 N weight, there should be-

Clockwise moment = Anti-clockwise moment

or, (E1 × Ed1) + (E2 × Ed2) = L1 × Ld2
or, (40 × 5) + (10 × Ed2) = 20 × 30
or, 200 + 10 Ed2 = 600

Thus, the lever can be balanced by keeping the 10 N weight at a distance of 40 cm from the
centre of lever.

S me Reasonable Facts

1. The value of VR in a single movable pulley is two, although in a single fixed pulley
its value is one. This is because in single movable pulley, load is supported with two
segments of string. It makes the effort distance double of the load distance. Due to it, VR
in single movable pulley is two. But in the case of single fixed pulley, effort distance and
load distance are equal.

2. A machine is never 100% efficient, because no machine is friction free and due to
friction, some of the input energy is wasted in the form of heat energy.

3. The value of VR is always greater than MA because MA is reduced by friction but VR is
not affected by friction.

Machine 47

4. Usually, tall trees collapse in storms. This is because perpendicular distance of the line of
action of the force from the fulcrum is found more in tall trees. It causes more turning
effect of the force applied by wind on the tall trees and they may collapse.

5. Winding roads are made on hills to make the surface slanted. It increases the effort
distance by remaining the load distance constant. In this condition, less effort is required
to roll vehicles on the hill.

6. Probability of breaking a branch increases when a person moves towards the end of the
branch of a tree. This is because, the distance of the line of action of the force from the
fulcrum increases in it. In this condition, the turning effect of the force applied by the
person on the branch increases.

7. Magnitude of input work is greater than the magnitude of output work because some of
the input work is wasted due to friction.

8. Long spanners are used to open a rusted nut. This is because the nut can be opened only
when more turning effect of the force is produced on it. It is possible by long spanners
only due to the longer distance between the fulcrum and the line of action of the force.

9. Lubricants (oil and grease) are used in machines to reduce friction. This helps to increase
mechanical advantage and efficiency of the machines.

10. Wheel and axle is considerd a continuous lever. It is because it has load, effort and
fulcrum and the location of effort and load changes continuously on the rim of wheel
and axle when the machine is in use.

Things To Know

1. The simple instruments which make our work easy and convenient to do are called
simple machines.

2. Simple machines help us by magnifying force, accelerating work and by changing the
direction of force.

3. The principle of simple machines states that in an ideal machine, effort × effort distance
= load × load distance.

4. MA is affected by friction but VR is not affected by friction hence the value of VR is
always greater than M. A.

5. Mechanical advantage of a machine is the ratio of load overcome to the effort applied in
that machine.

Or MA = L/E
6. Velocity ratio is defined as the ratio of distance covered by the effort to the distance of a

machine covered by load in that machine.
Or V.R = Ed/Ld

48 Modern Graded Science Class 9

7. Efficiency of a machine is the ratio of the output work to the input work in that machine.

Or η= output work × 100%
input work
8. Friction is reduced in machines by lubricating, making the sliding surfaces smooth and
by using ball bearings.

9. In pulleys, the velocity ratio is calculated by the number of pulleys used or by the number
of rope segments that supports the load.

VR of pulley = No. of segment of string/chain & supporting the load.

10. In an inclined plane, length of slope (l) is effort distance and height of slope (h) is load
distance, hence velocity ratio is calculated by the ratio of l to h.

Or VR of inclined plane = /h

11. In a wheel and axle, velocity ratio is calculated by the ratio of circumference of the big
cylinder (2πr) to the circumference of the small cylinder (2πr).

Or VR of wheel and axle = 2πR/2πr = R/r
12. Moment of force is the turning effect produced by that force.
13. Moment is affected by two factors, they are:

i. The amount of force applied.
ii. The perpendicular distance between the fulcrum and the line of action of force

applied.
14. Law of moment states that “in the condition of equilibrium of a lever, the clockwise

moment is equal to the anti-clockwise moment.”
Or clockwise moment = anti-clockwise moment.

Things To Do

1. Take a 1 foot long scale and adjust a cylindrical pencil at the middle of it by the help of a
rubber band.

2. Adjust the scale in a balanced condition over
two identical bottles.

3. Take eight 1 Re coins. Place 6 coins about 2cm
far from the pencil (Fulcrum) and try to balance
by using two coins at the other side. Calculate
E×Ed and L×Ld.

4. Repeat the activity 3 about four times by
changing the number and place of coins.

Machine 49

Test Yourself

1. Multiple choice questions (MCQs)

a. Which formulae of following can give the value of velocity ratio of the wheel and

axle?

A. effort arm/Load arm B. l/h C. R/r D. L × Ld

b. Which of the following is an example of wheel and axle?

A. staircase B. screwdriver C. scissors D. nut-cracker

c. Mechanical advantage is the ratio of

A. two force B. two works C. two distances D. two loads

d. Which of the following is velocity ratio?

A. L/E B. Ld/Ed C. Ed/Ld D. E/L

e. Which of the following is not affected by friction?

A. VR B. efficiency C. MA D. B and C both

f. Which of the following is law of moment in balanced condition of a lever?

A. E × Ld = L × Ed B. E × Ed = L × Ld C. E/Ed = L/Ld D. E/Ld = Ed/L

g. Which work of following is done by effort?

A. input work B. output work C. resultant work D. useful work

h. Which of following has 100% efficiency?

A. hydraulic machine B. perfect machine

C. simple machine D. compound machine

i. Turning effect of force is called

A. efficiency B. mechanical advantage

C. velocity ratio D. moment

j. l/h gives velocity ratio of

A. lever B. inclined plane C. pulley D. wheel and axle

2. Answer the following questions.

a. Define mechanical advantage and efficiency of a machine. What factor affects the
mechanical advantage of a machine?

b. Define an ideal machine. What are output work and input work?

c. What is velocity ratio of a lever is 3 and efficiency of a pulley is 60%?

d. What should be done to make a simple machine more efficient?

e. What is moment? What are the two factors which affect moment?

f. How is moment calculated in the following conditions? Write formulae only.

50 Modern Graded Science Class 9

i. When force is perpendicular with the distance between fulcrum and the line of
action of force.

ii. When force is parallel to the distance between the fulcrum and the line of
action of force.

iii. When force is forming an angle smaller than 90° with the distance between the
fulcrum and the line of action of the force.

g. State the law of moment of force.

h. There is no gain in mechanical advantage in a single fixed pulley. Explain why the
pulley is then used.

i. In the case of block and tackle arrangement, mechanical advantage increases
with the number of pulleys. Why?

ii. Write two uses of the inclined plane, pulley and wheel and axle each.

iii. What should be done to lift the same load by applying less effort on an inclined
plane?

3. Differentiate between: b. input work and output work
a. MA and VR d. VR and efficiency
c. moment and displacement

4. Give reasons.
a. The value of velocity ratio is greater than the value of mechanical advantage.

b. The value of efficiency is never 100% or more in practice.

c. Input work is always greater than output work.

d. It is easier to climb up a slanted slope than a vertical slope.

e. Usually, tall trees collapse in storms.

f. Usually, long spanners are preferred more than short spanners to unscrew a very
tight and rusted nut.

g. The possibility of breaking the branch increases when a person goes to the tip of the
branch.

h. Metal cutters have long handles.

i. It is easier to lift the same load by using three-pulley system than by using two-
pulley system.

ii. Wheel and axle is called a continuous lever.

Machine 51

5. Diagrammatic questions:

a. The diagram shows a lever of uniform mass supported
at the middle point. Six coins of equal mass are placed
at mark 4 on the left hand side.

i. Can you balance the lever with 12 more coins of

equal mass? If yes, where would you place them? If not,

why?

ii. With six coins still on the left, three coins are
put on the right at mark 4. Where on the right
should you pile an addition of six coins to get a
balance?

b. A crowbar used for turning a stone is shown in the diagram. In which direction (A
or B) is the pivot to be shifted to increase the mechanical advantage? Write with a
reason.

6. Numerical Problems
a. A load of 680 N is lifted from A to C by 500 N force
on an inclined plane as shown in the diagram.
Study the diagram and calculate:

i. Output work ii. Input work

iii. Mechanical advantage

iv. Velocity ratio v. Efficiency

(Ans: i. 5.44×103 J, ii. 6×103 J, iii. 1.36, iv.1.5, v. 90.6%)

b. A load of 800 N is lifted using a block and tackle having 5 pulleys. Show in a diagram
how the string is adjusted in this pulley system. If the applied effort is 200 N, calculate:

i. Mechanical advantage ii. Velocity ratio iii. Efficiency

iv. Output work if load is lifted 5m high v. Input work.

(Ans: i. 4, ii.5, iii.80%, iv.4×103 J, v. 5×103 J)

c. The radius of the wheel is 40 cm and the radius of the axle is 0.1 metre in a wheel
and axle. If a load of 1200 N is overcome up to 4m by applying an effort of 400 N,
calculate:

i. mechanical advantage ii. velocity ratio iii. efficiency

iv. output work v. input work

(Ans: i. 3, ii. 4, iii. 75%, iv.4.8×103 J, v. 6.4×103 J)

52 Modern Graded Science Class 9

d. Efficiency of a lever is 60%. If its MA is 3, calculate:

i. effort applied to lift a load of 1200 N by using the lever.

ii. velocity ratio of the lever

iii. output work if load is turned 10 cm high

iv. input work (Ans: i. 4×102N, ii. 5, iii. 1.2×102 J, iv. 2×102J)

e. In the inclined plane shown in the diagram, the distance
between A and C is 16m and between B and C is 5 m. If
its mechanical advantage is 2.5, calculate the distance:

i. effort applied to lift the load.

ii. velocity ratio iii. efficiency

iv. output work v. input work

(Ans: i. 3.4×102 N, ii. 3.2, iii. 78.12%, iv. 4.25×103 J, v. 5.44×103 J)
f. Four pulley system is shown in the diagram. If its efficiency is 80%, calculate by using

the formula:

i. the effort applied to lift the load
ii. output work when the load is lifted up to 6 metres
iii. input work
iv. mechanical advantage

(Ans: i.5.63×102 N ii. 1.08×104 J iii. 1.35×104 J iv. 3.2)

g. What force is required to balance the wheelbarrow shown in the given figure?
Calculate by using the formula.
(Ans: 31.25cm)

h. The figure shows a simple machine.
i. Identify the machine.
ii. If R = 25 cm and r = 5 cm, find the velocity ratio of
the machine.

(Ans: i. Wheel and axle ii. 5)

i. A lever is shown in the given figure. Three weights 60 N, 30
N and 10 N are suspended on it. Now, calculate:

i. Clockwise moment

ii. Anti-clockwise moment

iii. Can the lever be in the condition of
balance in this situation?

iv. What will be the location of 10 N weight

by keeping other loads unchanged to

balance the lever?

(Ans : i. 103N cm, i. 2.4×103 N cm, iii. No, iv. 1.5×102cm)

Machine 53

j. A man is riding a bicycle, whose paddle is at a distance of 20 cm from the fulcrum.

The man can exert the force of 40 N. What is the moment produced on the crank of

the bicycle when the paddle makes the angle of (i) 90°, (ii) 45°, (iii) 30° with the line

of action of force?

(Ans: i. 8×102N cm, ii. 5.66×102 cm, iii. 4×102N cm)

k. Study the diagram and find the moments when
the force of 500 N is applied at different points
‘a’, ‘b’ and ‘c’. Is the moment clockwise or anti-
clockwise?

(Ans: 5×103 cm 104N cm, 1.25×104N cm)

Friction : the process of opposing motion of a body

Coaxial : able to move at the same axis

Hinge : a metallic device used to join the door with the frame

Ball bearing : a device made by keeping metal balls between two rings which is
used for reducing friction

Pitch : distance between two consecutive threads

∆∆∆

54 Modern Graded Science Class 9

Chapter Work, Energy and Power

4

Total estimated Pds: 7 (5T/2P

Competencies
On completion of this chapter, the students will be competent to:

identify different forms of energy (potential energy, kinetic energy etc.).
interpret the inter-relation among work, energy and power with their unit and differentiate them.
describe human power.
solve simple problems on work, energy and power.

A. Work

The term work as understood in everyday life, has a different meaning in scientific sense. The
term work is considered to be a synonym of labour, effort, etc. For example, when a student
sits at his/her chair studying a book, he/she is not doing any work in the scientific sense. In
scientific sense, work is said to be done when a force acting on a body displaces it.

Thus, work done by a force acting on a body is defined as the product of force and displacement
of the body in the direction of the force. It is a scalar quantity.

Mathematically,

Work = Force × Displacement (in the direction of the force)

AB

Fig. 4.1 a body in motion

If ‘F’ is the applied force on a body and ‘d’ is its displacement in the direction of the force, the
work done ‘W’ by the force will be given by

W = F.d …………………......... (i)

The SI unit of force is newton (N) and that of displacement is metre (m). From the equation

Work, Energy and Power 55

(i), the unit of work is newton-metre (Nm), which is called joule (J).

or, 1 J = 1 N.1 m

or, = (1 kg × 1 m/s2).1 m (1 N = 1 kg × 1 m/s2)

∴ 1 J = 1 kgm2s-2

Thus, one joule of work is said to be done when one Newton force displaces a body through
one metre in its own direction.

Kilo joule (kJ) and mega joule (MJ) are the bigger units of work. The relation between them is
as follows-

1 kJ = 103 joules

1 MJ = 106 joules or 103 KJ.

In C.G.S. system, We know that
work is measured
in erg. 1 erg work 1 J = 1 Nm = 1 kg m/s2.m
is that in which 1
dyne force covers = 1000g × 100 cm/s2.100 cm
a distance of 1 cm.
1 dyne force is that = 107 g cm2 s-2 = 107 dyne cm [ 1 dyne = 1 gcms-2]
which can produce
an acceleration of 1 = 107 erg [ 1 erg = 1 dyne cm]
cms-2 on 1 g mass. Thus, 1 J = 107 erg

1 Erg = 1 dyne cm
1 J = 107erg
Equation (i) indicates that W = 0 when either F or d = 0. That is, force acting on a body must
produce a displacement for the work is to be done by the force. Thus, for work to be done, the
following two conditions must be fulfilled:

1. A force must be applied, and
2. The applied force must produce a displacement in any direction except perpendicular to

the direction of the force.
In general, work is done against friction and gravity.

a. Work against friction

Force is to be applied to move, roll or drag a body over a surface of another body. While in
motion, frictional force comes into action, which opposes or tends to oppose the motion of
the body. The body sets in motion only if the applied force overcomes the frictional force.
Some examples of this type of work are to slide a box and to roll a drum.

56 Modern Graded Science Class 9

Activity 4.1
To demonstrate work against friction

1. Let a spring balance be attached to a wooden box. The box is kept on a table.
2. Now the box is pulled as shown in the figure.

It moves by a displacement 'd'. Here, we have to apply force against the frictional force between
the surface of the box and the table to set the box in motion. Thus, work is done against the
friction.

b. Work against gravity

To lift a body to a height 'h', we have to apply force against the force of gravity. This is because
the force of gravity always acts vertically downwards. The acts of lifting or throwing things
upwards are examples of this work.

Activity 4.2
To demonstrate work against gravity

1. Hang a wooden block in a spring balance.
2. Raise the block up to the height 'h' as shown in the diagram.
The pointer of the spring balance gives the force applied 'F'
against the gravity. The product of the force (F) and height (h)
raised gives the work done against gravity in this case.

Measurement of work

On the basis of the direction of motion of a body and the
direction of force applied, the way of calculation of work
done is determined. Study the following situations for better
concept.

1. When a body moves in the direction of force applied:
In the above conditions (work against friction and work against gravity) the direction of
motion of body and the direction of force applied are the same. In both the cases, we can use-
Work done (W) = Force (F) × Displacement (d).

Work, Energy and Power 57

2. When a body moves oblique to the direction of force applied:
Consider a body is pulled on an inclined plane AC. The direction of force applied on it is
in AC direction but the motion direction is AB.
In this condition,





 Fig. 4.4 a body sliding on a slanted surface
It shows that in this condition less work is done, as the value of Cosθ is always less than 1.
If the body as shown above is pulled, here both types of work (work against gravity and work
against friction) are done. It is because the body is not moving only horizontally but vertically too.
Here, work against friction (Wƒ) = F×s = F×d Cos θ (Along horizontal direction)
and work against gravity (Wg) = F×s = F×d Sin θ (Along vertical direction)
Therefore
The total work done (Wt) = Wƒ+ Wg or, Wt = F.d cos θ + F.d Sin θ

∴ Wt = F.d (Cos θ + Sin θ)

Example 1: How much work is done by a force of 20 N while moving an object through a
distance of 1m in the direction of the force?
Solution
Here, Force (F) = 20 N
Displacement (d) = 1 m
Work done (W) = ?
We have,
W = F.d
= 20 ×1 = 20 J
Therefore, work done by the force is 20 J.

58 Modern Graded Science Class 9

Example 2: Calculate the amount of work done by a person while taking a bag, whose mass is
100 kg, to the top of a building of height 10 m. (Use g = 10 m/s2). The mass of the person is 50 kg.

Solution
Here, Mass of the bag (m1) = 100 kg
Mass of the person (m2) = 50 kg
Height (h) = 10 m
Acceleration due to gravity (g) = 10 m/s2
We have,
W = F.d
= m.g.h. [ F = m.g and d = h]
= 150 × 10 × 10 = 1.5 × 104J [ m = m1+m2 = 100 + 50 = 150 kg]

Thus, work done against the gravity is 1.5 × 104 J.
Example 3: A trolley is pulled on a slanted surface by applying an effort of 150 N. If the length
of the slope is 10 m and the angle between the horizontal surface and inclined slope is 15O,
calculate the total work done.

Solution
Given

d = 10 m

F = 150 N

θ = 15O

We have,

W = F.d (Cosθ + Sin θ)

= 150.10 (Cos 15O + Sin 15O)

= 150×10 (0.9659+0.2588)

= 150×10×1.2247 = 1837.05 J

Thus, work done on the slope is 1837.05 J

B. Energy

We get energy from food which we take. The energy thus got is spent while doing daily
activities. Fuels such as petroleum, coals etc. provide necessary energy to different vehicles
and other machines to run them. No work can be done without energy. Energy is the capacity
or ability of a body to do work. Work is done on the expense of energy. It is a scalar quantity.
Its SI unit is the same as that of work i.e. joule (J). In CGS system, energy is measured in
calorie (4.2 joule = 1 calorie).

Work, Energy and Power 59

There are various forms of energy. Some of them are as follows:

1. Mechanical energy 2. Electrical energy

3. Heat energy 4. Light energy

5. Sound energy 6. Magnetic energy

7. Chemical energy 8. Nuclear energy

1. Mechanical energy

Energy possessed by a body by the virtue of its motion or its position or its configuration is
called mechanical energy. It is of two types: kinetic energy and potential energy.

a. Kinetic energy

The energy possessed by a body by the virtue of its motion is called kinetic energy of the body.
A flying bird, a moving car, running water, wind, a bullet fired from a gun, an arrow left from
a bow, rolling stone, etc. are some examples of kinetic energy.

The kinetic energy of a moving body is determined by the formula:

KE = 21 mv2 Here,
m = mass of the body

v = velocity of the body Fig. 4.5 a rolling body

To prove that KE = 1 mv2
2

Consider, a body of mass 'm' is lying at rest (initial velocity = 0) on a smooth surface as shown
in the figure. Let a constant force F displaces this body in its own direction by a displacement
'd'. Let 'v' be its final velocity. The work done 'W' by the force is given by

60 Modern Graded Science Class 9

b. Potential energy

Energy possessed by a body by the virtue of its position or configuration is called potential
energy of the body. An arrow on a stretched bow, a stretched catapult, compressed gas, a
compressed spring, a stretched rubber, a body at height, water in a reservoir etc. are some
examples of potential energy.
The potential energy of a body at a height is determined by the formula:

P.E .= mgh Here, m = Mass
g = Acceleration due to gravity

h = Height

To prove that PE = mgh

Suppose a body of mass 'm' is lying on the ground. The weight 'mg' of
the body acts vertically downwards, where 'g' is the acceleration due
to gravity. Let 'h' be the height through which the body is lifted as
shown in the figure. In order to lift the body, a force 'mg' is required in
the upward direction. Now, the work done is given by

W = F.d

i.e. W = mgh ( F = mg and d = h)

This work done is stored in the body as potential energy which is Fig. 4.6, lifting body
called gravitational potential energy.

∴ Gravitational potential energy (P.E.) = mgh. Proved.

The potential energy possessed by a stretched rubber, a compressed spring etc. is called elastic
potential energy.

Example 1: Calculate the kinetic energy of a body of mass 5 kg moving with a velocity of 0.4
metre per second.

Solution
Here, Mass (m) = 5 kg
Velocity (v) = 0.4 m/s
Kinetic energy (KE) = ?
We have,

Thus, the kinetic energy of the body is 0.4 J.

Work, Energy and Power 61

Example 2 : A bag of rice weighs 100 kg. To what height should it be raised so that its potential
energy may be 9800 joule? (g = 9.8 m/s2)

Solution

Here, Mass (m) = 100 kg

Potential energy (PE) = 9800 J

Height (h) = ?

Acceleration due to gravity (g) = 9.8 m/s2

We have, PE = mgh

or, 9800 = 100 × 9.8 × h

or, 100 × 9.8 × h = 9800

or, = 10 m

Thus, required height is 10 m.

2. Electrical energy

Electrical energy is the energy possessed by the continuous flow of electrons or by the change
in number of electrons in bodies.
Electrical energy is the most essential energy for us in the modern days. Electronic devices
like computers, telephones, televisions, mobiles, calculators etc. use electrical energy. As
electrical energy can be cheaply and easily converted into other forms of energy. Electrical
energy is produced by a cell, battery or generator. In our country, we get electrical energy
mainly from hydro-power stations. It also can be obtained from diesel-power stations and
solar-power stations.

3. Heat energy

A substance is made of tiny particles called molecules. The molecules are vibrating about their
mean position. Due to this motion, each molecule possesses kinetic energy. The sum of total
of kinetic energy of all constituent molecules of the body is heat energy of that body. Heat
can flow from hotter bodies to colder bodies and it gives sensation of warmth. If the body is
heated, the molecular vibration increases and consequently it possesses more heat energy.

4. Light energy

Light is a form of energy which produces the sensation of sight. If a body is heated up to red/
white hot, it emits light. In the process of photosynthesis, plants absorb solar energy (light
energy) and convert it into chemical energy which is stored in the form of food they have
prepared. The main source of heat and light on the earth is the sun. Solar batteries are also in
use, which store light energy of the sun in the form of electrical energy.

62 Modern Graded Science Class 9

5. Sound energy

Sound is a form of energy which is produced by the vibration of sounding bodies. It is
transmitted in the form of longitudinal waves. Sound requires a material medium for its
propagation. We communicate by verbal method and enjoy by listening music because of
this energy.

6. Magnetic energy

The energy possessed by a magnet or a current carrying conductor that effect on magnetic
bodies is called magnetic energy. Magnetic energy is used in many electronic devices such as

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Šnƒu˜c‹leof‰aur rsigiof—iinn…sŽsii‡ssiƒocc”naa ‘llllo”eer‹dd‰n‹nnuuu cc‹c•llleee …aaaƒrrrŽeŽef‡nnu†eesr rgigoy—y.n.…TŽi‡shƒuc”sa ,‡ltlhe‡ed”‰en›nuǤe cr glŠeyƒap–r o‹e•sǡsn eteshsreegdyeǤfn r eormgya pnuocslseearssfiesdsiofrnoomr nauclear
„ ” ‡‘ƒ—Ž””‡…‹ ƒŽ‹—‡–•N(e ƒŠK‡n”u › er ȋc‘†ˆ)r l‹gˆe”•aƒ ya‘•n‡Ȍ.r‹‰dǡF‘ f‡‡iots”h”r s› ‹‰rie•o’e›x —enƒ–Ǥa ‘… nmi ’Žs‡e‘”p auƒȋ‘”l” tp e…r r‡,”ˆ‡oo—wȌš•n c•ƒ•ƒhse‡ e‘sa –sn†rˆ’‘ eo •Ža –f‡‰p’Šusǡ‹rŽ” ˜p‹or‡™–‡ald–‡in t‹ŠuŠ ti‡ic‡u‰n‡eŽm g‹—d— —–uƒ’wa” pt ‘i‘—o toˆmh”f •—ƒƒat …ƒi hŠshŽ‹”e‡—‡eb‡‹raƒo e™’v˜ml y”e›‹ƒ‘–abn Š–†sau‘e —r—–cdŠo……leeŽf‡‡ ‡du †‹e”—•snb ‡ •™ieyŽ„n ƒr‹‹t‘ng–›oŠye–•‘l.u i–‘„g tŠŽrˆƒh‹ ‡o‰”‡t nŠ†”ns‡–‡‡u, Ž†”cb‡‰ l—ƒae„›r…•iǤ›i‡Žw u‡ m‘i‹t ˆ™h‡ (‡—tB‹h––aŠ”‡e)‘ ”,r–‰eŠk›l•‡reǡǤy apsetoonf

ͻʹ ʹ͵ͷ Ϊ Ͳͳ ͷ͸ ƒͳͶͳ Ϊ ͵͸ ”ͻʹ Ϊ ͵Ͳͳ Ϊ

Heavy nucleus Light nuclei

Š ›——†……Ž”Ž‡‡‘—tfNƒ‰uh•”‡useǤ ec ˆcl— teao• as—–‹erŠg‘…fi‡oŽuv‡ f e…‹s‹t iƒˆ•hho—• een‡•–lŠ‡s ii‘uus‡ –ˆmn t‘ h’–, Š‰e”nn‹‡‘puu˜ …‡rcc•‡ol—l Šee•cai•‡eǡr wŽ s‹‹sf—iu—ti hns…™iŽ owt‡hŠnƒ—he‹”……io crŠŽˆc‡eh— cl‹•Že ul‹™i‹a‰gr‘ssŠ‹he––aŠt ‡oe‘n ”r–f…dŠ ne…‡wn—u —”e”ce…‡•rletŽg Ž‡hƒ‡iy‹uƒf. u•s†ˆs‡— ge™ •‘e‡ttˆ‡o s‡ g––o‘eŠlt‡‰a—h”‡r•e‰– erŠ‰›nt‡‡Ǥ eo–”r fg•o–‘y‘r.Ž mƒFˆ”‘o a”‡rhite‡ ah”ƒv‰y id›eŠǤrr ‡o nƒg‘˜ue”‹cn ‡l‹”e–n uusc. lIeni

ʹͳ ͳ Ϊ ʹͳ ͳ ʹ ‡Ͷ Ϊ ʹͳ‡ι Ϊ

Hydrogen nucleus (Hydrogen nucleus) (Helium nucleus) (Positron) (Energy)

TranWRseofrlokaartnimdoenantebirogeyntLaiwgrhoetefninuecetlenenri -ewrerlaogtreydk. Heavy nucleus is energy. When a person does

and energy to do work

Actually, capacity
”‘w –oŠr‡k oƒn„‘a˜b‡o d‡yš,ƒthe’eŽn‡•eǡr g™y ‡o fˆt‹he†b –oŠdƒy– in‘cr‡e as–›es’.‡A c‘cˆo r‡di‡n”g‰t›o t…hƒep „ri‡n c…ipŠlƒeo‰f‡c†o n‹se–r‘v ation
ƒ‘–Šo‡f”eǤ n eŠrg‡y ’, t”h‘e…‡sa•m• ‹e•a …mƒŽoŽu‡†nt –o”fƒm•uˆ‘sc”ulaƒr–‹e‘ne r‘gˆy ‡sh‡o”u‰ld›ǤbTehlousst,bcyotnhevepresrsioonn. oFof reenxearmgpyle, if a
from one form to another is called transformation of eWneorrkg, yE.ne r–g—y†a›n d–ŠP‡o wˆ‘eŽrŽ‘™‹‰6 3
‡šƒ’Ž‡•Ǥ

ͳǤ Š‡ …Š‡‹…ƒŽ ‡‡”‰› ™‹–Š‹ ƒ ’‡”•‘ ‹• ‘„–ƒ‹‡† ˆ”‘ –Š‡ ˆ‘‘† Š‡Ȁ•Š‡ ‡ƒ–•Ǥ Š‹•
…Š‡‹…ƒŽ ‡‡”‰› ‹• …Šƒ‰‡† ‹–‘ —•…—Žƒ” ‡‡”‰› „› ”‡•’‹”ƒ–‹‘Ǥ Š‡ Š‡Ȁ•Š‡

person pushes a book lying on a table and it moves, the person does work and he/she loses his/
her some muscular energy. Consequently, the book gains kinetic energy while it is in motion.
Similarly, if a spring is compressed, it stores potential energy and a person loses equivalent

amount of muscular energy. Thus, work done on a system is equal to the increase in its energy.
We eat food to get energy, which contains chemical energy. The chemical energy is changed
into muscular energy in our body during respiration. Due to this energy we are able to do
various types of work in our daily life. We feel weak, if we do not take food for a long time. For
example, if a person sleeps for about six hours after meal, he/she feels hungry after he/she
wakes up. In this case, he/she is not doing any visible work. This is because there is no visible
motion. But, motion takes place inside
his/her body, e.g. the heart pumps
blood, muscles stretch and relax,
several chemical reactions take place Only 10% of electrical energy in a filament lamp is
inside the body. There is a loss of used to create light. 90% of the electrical energy is
energy corresponding to these internal changed into heat energy by the lamp. CFLs (compact
fluorescent lamps) on the other hand, use 80% less

works. The energy which the food electricity relative to filament lamp and last up to 12
provides us is spent in these internal times as long.
processes of our body even though we
do not perform any external works.

Activity 4.3
To demonstrate the relation between work and energy

Procedure:

Consider a brick is on the ground. It
has zero potential energy in it. When
the brick is lifted and kept on the
table, it contains potential energy due
to its height. In this action the brick is
displaced from A to B i.e., work is also
done. By doing the work we store our
muscular energy in the form of potential
energy in the brick. The demonstration
shows a very closed relationship in between work and energy that’s why both of them are
measured in the same unit.

C. Power

A man may take five hours to carry a load from one place to another place. A motorbike may
do the same job in one hour. Both do the same amount of work. Both are doing the same job
and hence both supply the same amount of energy. But, the rate at which they do the work is

64 Modern Graded Science Class 9

different. In this case, the engine of the motorbike supplies energy at a higher rate than that
by the man. The rate of doing work is called power. It is a scalar quantity. It may be defined as
the rate of conversion of energy.

Mathematically, Power (P) = Work done (w)
Time taken(t)

or, P = F.d [ W = F × d]
or, P = t
F×v

The SI unit of power is joule (J) and that of time is second. Therefore, the SI unit of power is
joule per second (Js-1) which is called watt (W).

Thus, a body is said to have one watt of power if it can do one joule of work in one second.
Kilowatt (kW), mega watt (MW) and horse power (HP) are the bigger units of power. The
relation of them with watt is given below-
i.e., 1kW = 103 W
i.e., 1MW = 106 W or 103 kW
1 HP = 746 W (approx. 750 W)

Comparison of work, energy and power

S.N. Work Energy Power

1. It is the product of force and It is the capacity of It is the rate of doing work or
displacement. doing work. rate of conversion of energy.

2. Its SI unit is joule. Its SI unit is joule. Its SI unit is watt.

3. Its value does not depend on Its value does not It value depends on time.
time. depend on time.

4. In general, work is done against It has different It does not have any form.
friction or against gravity. forms.

Human Power

Different persons have diffrent rates of doing work. Same amount of work may be done in
different periods by different persons. Some can do the same work in less time but other may
need longer time to complete the same work. The time consumed for doing work determines
the rate of doing the work by a person. The rate of doing work by a person or human body
is called human power. The person who finishes the same work in less time has more power.

Work, Energy and Power 65

Activity 4.4
To calculate your own power

Select a staircase of few steps, say 15 steps. Measure the height of each step. Suppose the height
of each step is 12 cm. Measure your weight. Suppose it is 45 kg. Now take help of your friend
to keep the recored of time taken to cross the topmost step by running from the first step.
soppose the time is 20 second. Now calculate your power by using the formula

P = W = F×s = m×g×h = 45×10×1.8 15
t t t 20 14

13

= 40.5 W. 12
11

Thus, your power is 40.5 watt. 10

8 [ ]9
7 [∴ g = 10m/s
6 h = 12×15

4 5 = 180 cm = 1.8 m

3
2

1

0 Fig. 4.8 a person on staircase

Example: A 50 kg man runs up a staircase 3m high in 25 seconds. How much power does he
develop?

Solution
Here, Mass (m) = 50 kg
Height (h) = 3 m
Time (t) = 25 s
Power (p) = ?
Here, the work is done against the gravity. Thus, work done (W) is given by, mgh

i.e., P = W = mgh [ w = F × d = m.g.h]
t t

or, P= 50×10×3 = 60 watt
25

Hence, power of the man is 60 W.

66 Modern Graded Science Class 9

S me Reasonable Facts

1. In a tug of war, one team is winning and the other team is being defeated. Here, the winning
team is doing work. This work done is equal to the product of the resultant force and the
displacement that the losing team suffers.

2. Kinetic energy of a body will be increased four times if its speed is doubled. It is because,
kinetic energy is directly proportional to V2. It means that by the time the kinetic energy
of a body increases, the kinetic energy of the body also increases by the square times of
the change in the kinetic energy.

Things To Know

1. The product of force and displacement of a body is called work.

2. In general, work is done against friction or against gravity. or, W = F.d

3. Ability of a body to do work is called energy of that body.

4. Some forms of energy are:

i. mechanical energy ii. electrical energy

iii. heat energy iv. light energy

v. sound energy vi. magnetic energy

vii. chemical energy viii. nuclear energy

5. Kinetic energy of a body of mass 'm' moving with velocity 'v' is 1/2 mv2

6. Gravitational potential energy of a body of mass 'm' kept at height 'h' from a reference
level is mgh.

7. Energy and work are closely related, that’s why both of them are measured by using
same unit.

8. The rate of doing work is called power or p = w/t.
9. The rate of doing work by a human body is called human power.

Things To Do

Do the following activities and find your power:

1. Measure your weight on a weighing machine and note it.

2. Count the number of stairs and height of each stair of the staircase of your school/

house. Calculate the total height of the staircase.

3. Measure the time taken by you to run over all the stairs.

4. Now, use your weight, total height of the staircase and time taken to cover the stairs to find:

(i) Work you have done (ii) Your power

5. Repeat the above activities for four times and find your own average power.

Work, Energy and Power 67

Test Yourself

1. Multiple choice questions (MCQs)

a. Rate of doing work is called:

A. power B. work C. energy D. moment

b. The energy processed by the flow of charged particles is called:

A. magnetic energy B. potential energy

C. atomic energy D. electrical energy

c. Potential energy is calculated by using formula:

A. m d h B. 1/2 m a2 C. m g h 1/2 m v2

d. Which of following is an example of work against friction?

A. rolling a drum B. lifting a chair against friction

C. throwing a stone up D. falling a stone down

e. F.d gives the magnitude of

A. kinetic energy B. power C. work D. force

f. Which of the following is SI unit of power:

A. Hp B. W C. N D. J

g. Which is a suitable formula for the calculation of work against friction if applied
effort is oblique from the direction of motion?

A. w/t B. F×s C. F×S×Cos θ D. F×S×Sinθ

h. Which energy is found in water stored in a dam?

A. kinetic energy B. potential energy

C. chemical energy D. electrical energy

i. If mass of a body remains constant but its velocity is increased by 3 times, by how
many times its kinetic energy increases.

A. 3 times B. 6 times C. 9 times D. 12 times

j. In which unit energy is measured?

A. joule B. watt C. newton D. HP

68 Modern Graded Science Class 9

2. Answer the following questions.

a. Define the following terms:

i. work ii. power iii. energy iv. joule
v. kinetic energy vi. potential energy vii. 1 watt viii. 1 erg

b. Write the formulae relating to work, force and displacement.

c. A body is thrown vertically upwards. Its velocity keeps on decreasing. What happens
to its kinetic energy when its reaches the maximum height? Why?

d. If the speed of a body is increased four times, how will its kinetic energy be affected?
Show by calculation.

e. By how many times will the kinetic energy of a body increase if its speed is tripled?
Show by calculation.

f. What change should be expected in the velocity of a body to maintain the same
kinetic energy, if its mass is increased sixteen times? How?

g. Define human power. If A finishes a work in less time than B, who has more power ?
Explain, why?

h. What do you mean by that 100 W is written on an electric bulb?

i. Name the different forms of energy.

j. Ram travels 50 m on a straight road in 30 s. Hari covers the same distance
on the same road in 45 s. Who has done more work? Who has more power?
Explain in short.

k. Write the type (s) of energy found in the following examples:

i. kerosene ii. stretched rubber

iii. water stored in a reservoir iv. bread

v. rolling stone vi. red hot iron

vii. pendulum clock viii. falling apple

ix. leg lifted to kick a football x. dry cell

l. What kind of energy does a car possess when it is raised on a lift ?

3. Differentiate between:

a. potential energy and kinetic energy
b. work and power
c. energy and power
d. nuclear fission and nuclear fusion

Work, Energy and Power 69

4. Give reasons.
a. A saw becomes warm when it is used to cut a log of wood.
b. A person standing for a long time gets tired when he does not appear to do any work.
c. A nail becomes warm when it is hammered into a plank.
d. Rolling a drum is work against friction.

5. Diagrammatic question.
In the diagram Roshan and Rohan both are carrying
same load for same distance but in different times. Now
answer the following questions.
i. Who of them does more work? Why?
ii. Who of them has more power? Why?

6. Numerical Problems

a. Calculate the work done while lifting 300 kg of water (Ans: 1.8×104 J)
through a vertical height of 6 m. (Assume g = 10 m/s2)

b. If acceleration due to gravity is 10 m/s2, what will be the potential energy of a body
of mass 2 kg kept at a height of 5 m?
(Ans: 102 J)

c. How much energy has 4 × 1010 m3 of water collected in a reservoir at a height of 100
m from the power house? What kind of energy is that? (Given, mass of 1 m3 of water
= 1000 kg)
(Ans: 4 × 1016 J)

d. A body whose mass is 200 kg is lifted up by 2 m. Find the amount of work done and
potential energy of the body at that height. (g = 10 m/s2) (Ans: 4×103 J, 4×103 J)

e. How fast should a girl of 35 kg run so that her kinetic energy becomes 700 J?
(Ans: 6.32 m/s)
f. An engine has a power of 2 kW. Find the energy supplied by the engine working for
two hours.
(Ans: 1.44×107 J)

g. An engine supplies 40,000 J of heat energy per minute. What is the power of the
engine in kilowatts?
(Ans: 6.67×10-1 kW)

h. Radha can throw a stone of 8 N with the average velocity of 12 m/s. Calculate her
power.
(Ans: 96 W)

i. A girl weighing 350 N runs up a hill raising her vertically 5 m in 20 s. Calculate the
power.
(Ans: 87.5×101 W)

j. Calculate the power developed by a man of 80 kg if he climbs up a ladder of 3m
height in 10 s. (Take g = 10 m/s2)
(Ans: 2.4×102 W)

70 Modern Graded Science Class 9

k. If the power of an engine is 600 W, how much time will it take to lift a box of mass 20
kg upto 10 m ? (g = 10 m/s2)
(Ans: 3.33 s)

l. What is the amount of energy converted by a bulb of 60 W in 30 s ? (Ans: 1.8×103 J)

m. What is the horse power of an electric motor which can do 1250J of work in
5 seconds?
(Ans: 3.34×10-1 H.P.)

n. A man whose mass is 60 kg, walks up 15 steps, each 30cm high, in 15s. Find the
power he develops.
(Ans: 1.8×102 W)

o. A sliding box is on a slanted surface as shown in the diagram.

Calculate:

i. Work against gravity

ii. Work against friction

iii. Total work done by the box

(Ans: i. 1000J ii. 1732J iii. 2732 J)

Vacuum : the place/space where is no matter

Fission : the process of splitting

Fusion : the process of combining

Electronic devices : devices those operate on electric power

Fuel : substance consumed to provide energy through combustion
or chemical or nuclear reaction



∆∆∆

Work, Energy and Power 71

Chapter Sound

5

Total estimated Pds: 8 (7T/1P

Competencies

On completion of this chapter, the students will be competent to:

explain the nature of a sound wave.
identify infra-sound waves, audible sound waves and ultra-sound waves, and their sources.
define reflection of sound with examples.
demonstrate intensity and pitch of sound.
determine the speed of sound and give an account of the effect of sound in the environment.
explain the causes and effects of sound pollution.
suggest the methods of reducing sound pollution.

Sound is a form of energy. It is produced by a vibrating body. When a hammer strikes the gong
of an electric bell, the gong vibrates and it produces sound. The sound so produced reaches
our ears through air and we hear this sound. Sound travels in the form of a wave. Like light, it
also undergoes reflection, refraction, etc.

Wave

The path of energy through which the energy travels is called a wave. Waves can be classified
into two types: mechanical wave and electromagnetic wave. A mechanical wave can be
propagated only in a material medium. The wave is also called elastic wave. Sound wave is its
example. On the other hand, electromagnetic wave does not require any material medium for
its propagation.

Wave on water surface

When a stone is dropped into a quiet pool of water, circular projections spread out in all the
directions on the surface of water from the centre of disturbance. They are waves. Water waves
on the surface of water are the examples of wave motion. If a small leaf is placed on the surface
of water, the leaf does not move away along with the wave but moves up and down at the same
place. Thus, the particles of water do not move with the waves but vibrate up and down at the
same place.

72 Modern Graded Science Class 9

Waves in a rope Fig. 5.1 transverse wave

Activity 5.1
To demonstrate transverse wave

If a rope held horizontally is fixed at one
end and the free end is moved up and down
at right angle to the rope, a disturbance
consisting of a series of crests and troughs
travels along the rope. In this case, only the
shape or form of the wave moves forwards
but the individual particles of the rope
merely oscillate up and down.

Sound wave

Fig. 5.2 longitudinal wave

In figure (a) the position of different layers of air are shown when the tuning fork is not
vibrating. When a tuning fork is set into vibration, its prong may move to one extreme
position and the layer of air in front of the prongs gets compressed as in fig. (b). As the prong
moves to the other extreme position, the compression is handed over to the next layer of air
and a rarefaction is formed in the previous position of compression as in fig. (c). As the prong
vibrates, the disturbances travel in the medium with alternate compressions and rarefactions,
fig. (d). In a compression, the distance between any two consecutive particles of a medium is
less than the normal distance. Hence, the density of the medium in compression is more than
normal density. In a rarefaction, the distance between any two consecutive particles of the
medium is more than the normal distance. Hence, the density of the medium in a rarefaction
is less than the normal density.
From the above examples, we are now in a position to define a wave as: "Disturbance set up in
a medium is called a wave and the propagation of disturbance, without involving transfer of
any material within it is called wave motion." It transfers energy, not matter, from one part of
the medium to another part.

Classification of Elements 73

Types of wave motion

On the basis of the nature of medium required for the propagation of waves, we have already
classified the waves into mechanical and electromagnetic waves. Mechanical wave needs
material medium to travel from one place to other. Electromagnetic wave is that, which does
not need material medium to travel.

Waves also can be classified into transverse wave and longitudinal wave on the basis of the
nature of the vibration in the particles of the medium. Transverse waves are those in which
the particles of a medium vibrate at right angles to the direction of propagation of the wave
through the medium. For example, waves produced in a still pond when a stone is dropped in
it, waves produced in a rope when its one end is fixed and other end is jerked, etc. Longitudinal
waves are those in which the particles of a medium vibrate to and fro in the direction of
propagation of the wave through the medium. Sound wave is an example of longitudinal wave.

Comparison of transverse and longitudinal waves

Transverse waves Longitudinal waves

1. Vibrations of particles of a medium are 1. Vibrations of particles of a medium are
perpendicular to the direction of the along the direction of the propagation
propagation of the wave. of the wave.

2. These waves can be produced in solids 2. These waves produce in solids, liquids
and liquids. and gases.

3. A complete wave consists of a crest and a 3. A complete wave consists of a compres-
trough. sion and a rarefaction.

4. Speed of this wave is more. 4. Speed of this wave is less.

5. It can travel in electromagnetic field. i.e. 5. It cannot travel in electromagnetic field
no material medium is required for its but only in material medium.
transmission.

Some terms related to waves

Some important terms which are used frequently while discussing waves are described below
in short.

74 Modern Graded Science Class 9

a. Crest and trough

Both transverse and longitudinal waves are represented Fig. 5.3 crest and trough
graphically by a 'sine curve' as shown in the diagram.
Transverse waves travel in the form of trough and crest.
When the displacement of a particle is maximum above
from its mean position, the particle is said to be at the
crest of the wave. When the displacement of a particle is
maximum below, the particle is said to be at the trough.

b. Compressions and rarefactions

A longitudinal wave travels in the form of compressions Fig. 5.4 compressions and rarefaction
and rarefactions. In compression, particles of a medium
get compressed and hence the density is more than
normal density. In a rarefaction, density is less than
normal density.

c. A complete wave

A complete wave is a complete cycle of different types of disturbances formed in a wave.
One crest and one trough constitute one complete wave in a transverse wave. Similarly, one
compression and one rarefaction constitute one complete wave in a longitudinal wave.

compression crest

rarefaction though

Fig. 5.5 (a) complete wave in a longitudinal wave (b) complete wave in a transverse wave

d. Amplitude (a)

The maximum displacement of a particle from its mean Fig. 5.6 amplitude (a)
position in a wave is called amplitude of that wave. It occurs
at crest and trough in a transverse wave and at compression
and rarefaction in a longitudinal wave. Its SI unit is 'm'.

e. Time period (T)

The time taken by a wave to travel complete one cycle or a complete wave is called time period.
Its unit is second. For example, if a sound wave takes two seconds to complete one cycle, its
time period is two seconds.

Classification of Elements 75

f. Frequency (f)

The number of complete waves, set up in a medium
in one second is called frequency of the wave. The
SI unit of frequency is hertz (Hz). For example, if
a sound wave completes 15 compressions and 15
rarefactions in one second, its frequency is 15 Hz.

Kilohertz (kHz) and megahertz (MHz) are the Fig. 5.7 frequency
higher units of frequency. The relation among
them is given below:

103 Hz = 1 kHz and 103 kHz or 106 Hz = 1 MHz

g. Wavelength ( λ)

The distance between two consecutive troughs or Fig. 5.8 wave length
crests in a transverse wave or the distance between
two consecutive compressions or rarefactions in
a longitudinal wave is called wavelength. It is the
distance travelled by a wave in a time equal to its time
period. Its SI unit is metre (m).

h. Wave velocity (v)

The velocity with which a wave propagates in a medium is called wave velocity of the wave.
Its SI unit is m/s.

i. Wave equation

The equation that shows relationship among wave velocity (v), wave frequency (f) and wave
length (λ) is called wave equation. According to it, the product of frequency and wavelength
is numerically equal to the wave velocity.

 Wave velocity (v) = frequency (f) × wavelength (λ)
The equation indicates that if the speed of wave is constant but wave frequency increases, the
wave length decreases and vice-versa.

Relation between frequency (f) and time period (T)

By the definition of frequency,
f vibrations are completed in one second.

76 Modern Graded Science Class 9

or, 1 vibration is completed in 1 second.
f

But, time to complete one vibration is its The sound of thunder is produced by
time period (T) rapidly heated air surrounding lightning
which expands faster than the speed of
 sound.

Sound and its properties

Sound is a sensation produced in the ear, when energy of vibrations of a vibrating body is
transmitted to the ear through a material medium. Sound travels through a medium by means
of waves set up in the medium. The following are the characteristics of sound:

1. It is produced by a vibrating body.
2. It requires a material medium for its propagation. It cannot travel through vacuum.
3. Its speed is different in different media. Its velocity is the highest in solids and the lowest

in gases.
4. It transmits from one place to another in the form of a longitudinal wave.
5. It may be reflected or refracted like light.

Speed of sound in different media (At 0°C)

S.N. Medium Speed (m/s) S.N. Medium Speed (m/s)

1. In liquids 7 In liquids
2. 8 1400
3. Granite 6000 Water 1210
4. 9 Alcohol
5. Steel 5000-7000 10
6. 11
Aluminium 5100 In gases

Glass 5000 Hydrogen 1260

Wood 4000-5000 Air 330

Brick 3600 Carbon dioxide 258

Factors affecting speed of sound in gas medium

The following factors affect the speed of sound in gases.
1. Density: The speed of sound in gas is inversely proportional to the square root of the

density of the gas.
 ‡Ž‘…‹–› ‘ˆ •‘—†  †‡ͳ•‹–›

Classification of Elements 77

It means, sound travels faster in gases of lower density and vice versa. If the density of the
medium increases by four times, the speed of sound decreases by two times in that medium.

2. Temperature: The velocity of sound varies directly as the square root of the absolute
temperature of the gas.

 ‡Ž‘…‹–› ‘ˆ •‘—†  –‡’‡”ƒ–—”‡

It means if temperature of the medium increases by four times, the speed of sound
increases by two times in that medium. Thus, higher the temperature, lower the density and
higher the speed of sound. That's why, speed of sound is more in hot air than in cold air.

3. Humidity: The term humidity refers to the water vapour (moisture) contained by air
in the atmosphere. As the density of water vapour is less than that of dry air, density of
moist air is lesser than that of dry air. We know speed of sound in gas varies inversely to
the square root of the density of the gas. Therefore, sound travels faster in moist air than
in dry air.

4. Direction of wind: The speed of sound is higher in the direction of wind and lesser in the
opposite direction of wind.

Audibility

A man cannot hear sounds of all frequencies. The range of frequencies which a listener can
distinguish is known as the range of audibility. The range of audibility for human ears is 20Hz
to 20,000 Hz. The sound which has frequency lower than 20 Hz is called infrasonic sound or
subsonic sound or infrasound and the sound which has frequency above 20,000 Hz is known
as ultrasonic sound or ultrasound. Ultrasonic sound may cause acute pain to the ear.

The vibrations of infrasonic sound can be felt, if the source of the infrasonic sound producing
device is touched but the sound cannot be heard. Animals like dogs and cats can hear ultrasonic
sound but they are unable to produce it. Bats can produce and hear ultrasonic sound. Thus,
they detect obstacles in their path in dark night also by producing and hearing ultrasonic
sound which reaches them again after reflection from the obstacles.

Properties of ultrasonic sound or ultrasound

1. They are high frequency sound waves (above 20,000 Hz).

2. Because of short wavelengths, they can travel long distances without loss of sound energy.

3. They produce heating effect in any substance through which they propagate.

78 Modern Graded Science Class 9

4. A beam of ultrasonic waves can bore a hole through hard materials like steel, diamond,
etc.

5. They produce coagulation in liquids.

Applications of ultrasonic sound or ultrasound

Ultrasonics are cheap to produce and easy to use. They have a large number of uses; a few are
given below:
1. They are used in the diagnosis and cure of some diseases. They have been used for

relieving rheumatic and neuralgic pains. They can be used to take photographs of brain.
2. Strong beams of ultrasonics kill bacteria. They are used for sterilization purposes.
3. They are used in bloodless surgery. They can destroy brain tumors and kidney stones.
4. They can be used for welding, local heating and drilling small holes in very hard materials.
5. They can be used to detect cracks and flows in metal moldings.
6. They are used in dry cleaning of clothes as they can remove grease and dirt.
7. They can be used in manufacturing of alloys of uniform composition, mixing of

immiscible liquids, and manufacture of emulsion for photographic films.
8. They are used to locate icebergs and to measure depth of oceans by echo sounding

method. In this method, fathometer (transmitter) sends out ultrasonic which is
reflected back from the sea bed and
received by a hydrophone (detector).
Noting the time interval between the
emission of signal and its arrival back to
the ship, the depth of the sea and location
of an iceberg can be determined. We know
that for echo:

Fig. 5.9 measuring the depth of ocean

Characteristics of notes

Single sound of a certain pitch and duration made by a musical instrument or a voice is called
a note. Notes may be similar to or different from each other in three aspects: (i) pitch, (ii)
loudness (intensity) (iii) quality (tone or timbre). These three quantities define or characterize
a note.

Classification of Elements 79

i) Pitch

Pitch is defined as the sharpness of a sound. Pitch in sound corresponds to colour in light
which depends on the wavelength or frequency of a light wave. Pitch of a note depends only
on the frequency of the sound vibrations. The higher the frequency the shriller the sound and
higher is the pitch. Pitch enables us to distinguish between a high, acute or shrill note from a
low, or grave or flat note.

It must be clearly understood
that pitch is not the same
thing as frequency. Frequency Fig. 5.10 (a) high pitched sound
(b) low pitched sound

is a measurable quantity but pitch is a subjective sensation that cannot be measured. It depends
on frequency. Generally, girls have sharp voices and hence they have a higher-pitched note
than boys. The following are the factors on which pitch depends:

1. Frequency of the sounding body: Greater the frequency higher the pitch.

2. Relative motion between the source of sound and the listener: Pitch depends on relative
motion between the source of sound and the listener. If they are approaching, the
pitch seems to be increasing, and if they are receding, the pitch seems to be decreasing.

3. Thickness : Thin wires have higher pitch than thick wires of the same length. Similarly
the drums with thin layer have higher pitch than the drums with thick layer.

4. Length of wire: Short wires have higher pitch than long wires of the same thickness.

ii) Intensity and loudness

Intensity of sound is a physical quantity having objective existence.
Intensity of sound is the quantity of sound energy per unit time flowing
across a unit area held normally to the direction of propagation of
sound waves.

 –‡•‹–› ‘ˆ •‘—† α •‘–—‹†‡ έ‡ƒ”‡‡”ƒ‰› ‘”ǡ α – έ Fig. 5.11 area around a source of sound

To find the intensity at a distance r from a small source of sound O, we consider a sphere of
radius r. If E is the sound energy which passes through the surface area 4πr2 in the given time
t, then

 



80 Modern Graded Science Class 9



If 'a' is the amplitude of the sound wave emitted from the source O, then calculation shows
that

ƒʹ ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ ȋʹȌ

i.e. intensity of sound is directly proportional to the square of amplitude.

”‘ ȋͳȌ ƒ† ȋʹȌǡ ™‡ ‰‡–
ƒʹ ”ͳʹ ǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤǤ ȋ͵Ȍ

 ƒ ͳ”
Decibel (dB) is the unit of intensity of sound. The word decibel is made of two words. They are
deci (d) and bel (B), means one tenth of bel. 1 decibel intensity is that, in which a sound wave
carries 10–12 watt/m2 sound energy. Increase of intensity by 10 decibels means that the intensity
of a sound is 10 times as great. For example, the sound of 20 decibels is 10 times greater than
that with 10 decibels. 40 decibels sound is 100 times greater than that with 20 decibels and so
on.
Intensity levels (in dB) of some important signals

S. No. Sound Level in dB

1. Threshold of hearing 0 The standard intensity of sound is consid-
ered 0 decibel, which is equal to 10-12 W/
2. Whispering 10 m2.
1 decibel = 1/10 bel or 1 bel = 10 decibel
3. Rustle of leaves 20 The sound, that is 10 times intense of
the standard intensity is called 1 bel or
4. Sea sore 40 10 decibel. A sound, with 2 bel intensity
is ten times intense than the sound having
5. Normal conversation 50 intensity 1 bel. Similarly, the sound of 3 bel
is 100 times intense than the sound of 1 bel
6. Shouted conversation 70 and the sound of 4 bel is 1000 time intense
than the sound of 1 bel and so on.
7. Ringing telephone 80
vacuum cleaner

8. Running motor cycle 90
(at 10 m distance)

9. Rock music 100

10. Jet engine 110

11. Flying jet plane (during take off) 140

A sound above the 80 dB is harmful to our ears.
Continuous exposure to sound above 80 dB can
damage our ears.

Factors on which intensity or loudness depends

1. Amplitude of vibration: Intensity and hence loudness is directly proportional to the square
of the amplitude (I ∝ a2). A louder sound has greater amplitude and a higher intensity
than the amplitude and intensity of a fainter sound.

Classification of Elements 81

2. Distance from the source: Intensity at a point varies inversely as the square of its distance
from the source.

3. Size of sounding body: Larger the size of a sounding body, greater is the intensity and
louder the sound produced.

4. Density of the medium: Intensity is directly proportional to the density of the medium.
That's why, when air in a bell jar is gradually exhausted, the sound produced by the ringing
bell placed in the bell jar becomes fainter and fainter.

5. Presence of other bodies: Reflector of sound amplifies the loudness, while absorbing
material reduces the loudness.

6. Wind: Loudness is greater in the direction of wind than in the opposite direction.

Difference between intensity and pitch

Intensity Pitch
1. It is related to the loudness of sound. 1. It is related to the sharpness of sound.

2. It depends on energy and amplitude of sound. 2. It depends on frequency.

3. Its unit is decibel (dB). 3. It has no unit.
4. It is a measurable quantity. 4. It is a non-measurable quantity.

Activity 5.2
To demonstrate the relation to pitch and intensity with their factors

1. Take a sonometer fitted with a wire as shown in the diagram.

2. Place a weight and adjust equal distance between the wooden prisms and jerk the wire
gently.

3. Now repeat the activity by using thick wire. Feel the difference in the sharpness of sound.

4. Repeat the activity by adding more load. Is there any change in the sharpness of sound?

5. Now, repeat the activity by changing the distance between the prisms P and Q. What
difference in sharpness do you find?

6. Now, jerk the wires one by one by applying less and more forces. Do you feel any change
in the loudness of the sound produced by the wires?

We find that thin wire, tight wire and short wire load
produce sharper sound or high pitched sound than
a thick, loose and long wire. It also demonstrates
that intensity as well as loudness of sound increases
if more force is applied to jerk the wires.

Fig. 5.12 sonometer

82 Modern Graded Science Class 9

iii) Quality or timbre or tone

This characteristic distinguishes notes of the same

pitch and loudness produced by different musical

instruments. As a matter of fact, a note is not a single

"sine curve" but it is combination of different sine Fig. 5.13 number of sine curve
curves. This distinguishes two notes of the same pitch

and loudness produced by two different sources. Hence, a person can be recognized by his/her

quality of voice. If a harmonium and a violin are played to the same pitch and loudness, even

an untrained person can distinguish the two musical notes by their quality.

Reflection of sound

The process in which sound is sent back by a surface
into the previous medium is called reflection of sound.
During reflection of sound it follows the law of reflection
of light. Echo and reverberation are the products of
reflection of sound.

Reflection of sound is useful to identify presence of Fig. 5.14 laws of reflection of sound
iceberg on the way of ship and to know the depth of

ocean. It also can be used to make musical program melodious by creating reverberation.
To predict the presence of minerals and to know the direction any distance of enemy also
reflection can be used.

a. Echo

Sound also follows the laws of reflection just like light. When sound is produced, its reflected
wave returns after striking a wall or any object to the listener. We say an echo is heard. To
hear an echo, the distance between the person and the reflecting surface should be at least
17 m. This condition is easily available in large halls and open fields. Hence, when sounds are
created or speech is delivered, the formation of echoes creates confusion. To avoid this, walls
and ceilings of an auditorium are covered with sound absorbing materials so that echoes can
be minimized. The repetition of sound, which is reflected from walls of a large room or distant
surface is called an echo.

Conditions required for echo

The following conditions are required for an echo to occcur:
1. The distance between the source of sound and reflector should be more than 17m.
2. The loudness of sound should be so sufficient that it can be heard after reflection.
3. The reflector should be hard and cover a large area.
4. There should not be more sound absorbing materials on the way of the sound wave.

Classification of Elements 83

We have noticed that the loudness of the reflected sound (echo) is less than that of the original
source. This is due to the fact that the sound is absorbed during reflection and by the medium
through which it passes.

b. Reverberation

If the distance between the source of sound and the reflector is less than 17m, original sound
and reflected sound mix and the sound is prolonged. This phenomenon is called reverberation.
It is heard in an empty room or newly built room. In a furnished room, furniture and
other materials absorb sound a lot, hence reverberation is not heard. In a musical concert,
reverberation of sound is more beneficial as it makes music melodious providing continuity.
To reduce over reverberation, the windows of a hall should be opened. This is because the
sound passes out through the window instead of being reflected. Good sound absorbents also
reduce reverberation.
If there are a number of reflecting surfaces close to one another, a series of reflection occurs.
Because of this, the original sound and the reflected sound mix to cause the sound prolonged.
This is called reverberation.

Refraction of sound

Sound also follows the laws of refraction as light does. Its speed changes in magnitude
and direction as it passes from one medium to another medium. We know that sound is
clearly heard at night than during day-time. It is because at day-time, the temperature of air
is maximum near the ground and it diminishes upwards. Therefore, layers of air gradually

behave as a denser medium as we go up. Hence, the ray of sound diverges upwards from the
source and less sound waves reach the listener.
At nights or at dusk, the situation is just opposite. The layer of air near the ground behaves as
a denser medium and it gradually becomes rarer and rarer as we go up. Hence, a ray diverging
upwards from a source on or near the surface of the earth is refracted continuously away from
the normal. Finally, the ray undergoes total internal reflection and then it begins to travel
downwards to reach the listener. It makes the sound more distinct at night.

84 Modern Graded Science Class 9

Noise and music

The sound-received impressions are divided into two categories. They are noise and musical
sound. The sound which produces an unpleasant effect on the ears is called noise and a sound
which produces a pleasing sensation on the ears is called a musical sound. However, there is
no sharp demarcation between the two categories because this distinction is quite subjective.
What may be 'music' for one may be a noise for another. A noise, if reflected at regular intervals,
may produce a pleasant sensation; for example, pattering of rain drops on a tin shed, the hum
of a distant market place, etc.
Theoretically, a musical sound is characterized by a regular, continuous vibration with no
sudden discontinuity in it. Further, it must be periodic. All musical sounds have regularity
and rhythm in them, while a noise does not have any of these characteristics. A noise is an
unpleasant, discontinuous, non-periodic, irregular sound. The difference may be apparent
from fig (a) and (b).

Fig. 5.16 (a) music (b) noise

S me Reasonable Facts

1. When a person speaks in a room, the energy produced causes vibrations in air particles
of the room. As the volume of air in the room is less than the volume of air in open areas,
the amplitude of vibrations of air particles in the room is more than the amplitude of
vibrations of air particles in open areas. Hence, it is possible to hear a person speaking
more easily and clearly in a room than in the open air.

2. Sound produced in a big hall is prolonged. This is because of multiple reflections of
sound waves from the walls of the hall, which is called as reverberation of sound.

3. For the propagation of sound, a material medium is needed. Since there is no air on the
moon, two astronauts cannot talk on the surface of the moon as they do on the earth.
Thus, astronauts use electronic devices for communication on the moon's surface.

4. Velocity of sound in air is about 332 m/s but velocity of light is 3 × 108 m/s. Both the
sound and light waves travel the same distance while reaching a place on the ground,
hence light reaches the ground at first and then the sound. That is why, the thunder of
lightning is heard some moments after the flash of light is seen.

Classification of Elements 85

5. Bats emit ultrasonic waves. These waves are reflected by obstacles on their path. The
reflected waves are received back by the bat. Such waves carry information about
distance, size, direction and nature of obstacles. Hence, bats can detect distance, size,
direction and nature of obstacles without seeing at night.

6. The repetition of a sound caused by reflection from a rigid obstacle like cliff, hill or walls
of a building is called echo. For the echo to be heard clearly, the distance between the
source of the sound and the reflecting body should be at least 17m. In a small room, this
distance is less than 17 m. Hence, we cannot hear echo in a small room.

7. The speed of a sound wave is minimum in a gas medium and maximum in a solid
medium. In solids, molecules are very close to each other due to which energy of a
sound wave quickly passes from one molecule to another molecule. Hence, the speed of
a sound wave becomes more. In gases, molecules are not close together and hence the
energy of a sound wave takes more time to pass from molecule to molecule. Hence, the
speed of a sound is less in a gas medium.

Things To Know

1. The path of energy is called a wave.
2. The propagation of disturbance (wave), without involving transfer of any material within

it is called wave motion.
3. In a transverse wave, the vibration of particles of a medium is perpendicular to the

direction of the propagation of wave.
4. In a longitudinal wave, the vibration of particles of a medium is along the direction of

the propagation of waves.
5. A material medium is required for mechanical waves and a material medium is not

required for electro-magnetic waves to propagate them from place to place.
6. One compression and one rarefaction of a longitudinal wave and one crest and one

trough of a transverse wave form a complete wave.
7. The maximum displacement of a particle from its mean position in a wave is called its

amplitude (a).
8. The number of complete waves, set up in a medium in one second is called its frequency (f).

9. The distance between two consecutive crests and troughs or between two consecutive
compressions and rarefactions in a wave is its wave length (λ).

10. The velocity with which a wave propagates in a medium is called wave velocity (v).

11. Speed of sound in solids is the maximum and that in gas is the minimum.

12. The influencing factors on the speed of sound in a gas medium are temperature, density,
humidity and direction of wind.

86 Modern Graded Science Class 9

13. The range of frequency of audible sound is from 20 Hz to 20000 Hz.
14. The sound whose frequency is above 20,000 Hz is ultrasound and that below 20 Hz is

infrasound.
15. Pitch is a non-measurable quantity, responsible for the sharpness of sound. It depends

on the frequency of the sound wave.
16. Intensity is a measurable quantity, responsible for the loudness of sound. It depends on

the amplitude of sound wave i.e. I ∝ a2.
17. Reflection of sound causes echo and reverberation.
18. An echo is that phenomenon in which the reflected sound does not mix with the original

sound and the sound is repeated.
19. Reverberation is that phenomenon in which the reflected sound mixes with the original

sound and the sound is prolonged.
20. Bending of sound, when it passes from one medium to other, is called refraction of

sound.

Things To Do

Make a model to study pitch and intensity of sound:
1. Take a thick wooden plank of about 20 cm wide

and about 30 cm long.
2. Pass screw nails 'a', 'b', 'c', 'd', 'e' and 'f ' as shown

in the diagram. Remember, the distance between
a-b and c-d must be equal.
3. Tie thin wires between a-b and e-f, and a thick
wire between c-d.
4. Plunk the wire gently one by one and feel the sharpness of sound produced by them.
5. Repeat the activity 4 by tightening the wires more.
6. Repeat the activity 4 by plunking the wire forcibly. Now feel the loudness.

Test Yourself

1. Multiple choice questions (MCQs)

a. Cause of sound is:

A. madal B. vibration of bodies C. guitar D. sitar

b. What is frequency of sound?

A. number of complete waves formed in a longitudinal wave

B. number of complete waves formed in a transverse wave

C. number of complete waves formed in one second

D. Time taken to form a complete wave

Classification of Elements 87

c. Which of the following is the frequency of the audible sound?

A. 20Hz to 200Hz B. 20Hz to 2000Hz

C. 20Hz to 20kHz D. 20Hz to 200000Hz

d. Which of the following affects on the pitch of sound?

A. wavelength B. frequency C. amplitude D. time period

e. Which of the following is a cause of intensity of sound?

A. wavelength B. frequency C. amplitude D. time period

f. Which of the following is required to make music melodious?

A. reverberation B. echo C. refraction D. defraction

g. What distance is required between a source of sound and the listener to occur an echo?

A. 14 m B. 15 m C. 16 m D. 17 m

h. Which one of the following formulae can be used to calculate the depth of

2. Answer the following questions
a. How is a sound wave produced?
b. Derive a relation between time period and frequency of a wave.
c. Write the relation between wavelength, frequency and velocity for a sound wave.
d. Write four factors that affect the speed of sound in a gas medium.
e. Give the relation of speed of sound with the density and temperature of air.
f. Distinguish between infrasound and ultrasound.
g. Give any two uses of ultrasonic sound.

h. What will be the effect on the wavelength of a sound wave if the pitch of the sound
is increased?

i. On what condition does an echo take place?

j. State the laws of reflection of sound.

k. Enlist any four effects of sound pollution.

l. Write down any two ways to reduce sound pollution.

3. Differentiate between:

a. longitudinal wave and transverse wave b. mechanical wave and electromagnetic wave

c. sound wave and light wave d. compression and rarefaction

e. hertz and decibel f. pitch and intensity

g. infrasound and ultrasound h. echo and reverberation

88 Modern Graded Science Class 9

4. Give reasons.
a. The back of a large auditorium is curved.
b. Roaring of a lion is different from the sound of a mosquito.

c. The size of temple bells is made large.

d. Walls and ceilings of a cinema hall are covered with sound absorbing materials.

e. Echo is experienced more in a newly constructed room than in a furnished room.

f. Two notes, one produced by a violin and the other by a sitar, may have the same
frequency, yet we can distinguish between them.

g. Reflected sound (echo) is fainter than the original sound.

h. Sounds produced by a thin string as well as thick string on a guitar have equal
velocity in air.

i. Ultrasound can pass even through solids.

j. A sound wave is called a mechanical wave.

k. Radio waves travel faster than sound waves.
l. Astronauts use an electronic medium in space to talk with each other.

5. Diagrammatic questions

a. In the diagrams, the number of waves
produced in one second is shown.
Answer the following questions:

i. Write frequency of waves
produced in a and b.

ii. Find the speed of both if wavelengths of a and b are 1m and 2m respectively.

iii. Which of them has high pitch and which has high intensity?

b. Velocity of sound in three different gases A, B and C is given in the table. Study the

table and answer the following questions: Medium Velocity

i. Which gas has the highest density? A 400

ii. Which gas has the lowest density? B 900
700
iii. If a sound wave having the same frequency is C

allowed to pass through gases A, B and C separately, in which medium has the

sound wave the highest wavelength? In which medium has the sound wave

the lowest wavelength?

Classification of Elements 89

c. The diagram shows two sound waves, A and B. Answer the following questions
after studying the diagram:

i. Which wave 'A' or 'B' can give sharper
sound? Why?

ii. Is wave can produce 'A' or 'B' louder
sound? Why?

d. Frequency of some waves are shown in the table. Answer Wave F (Hz)
the following questions on the basis of it: A 6000Hz
100Hz
i. Which of the sounds can you hear? Why? B 10Hz
600Hz
ii. Which sound has the greatest wavelength? C
iii. Which sound will you hear the sharpest and why? D

iv. How many compressions and refractions are formed per second in wave 'C'?

e. Study the table given and answer the questions below.

i. Identify the wave which Wave Wavelength Frequency Amplitude
has the sharpest sound. X 3.5m 2000Hz 0.4m
Give a reason also. Y 1.5m 466.67Hz 0.8m
Z 0.5m 1400Hz 0.2m
ii. Identify the wave which D 600Hz

is the loudest? Give a

reason also.

iii. Calculate the speed of 'Y'? (Ans: 700 m/s)

f. Intensity of the sounds of three objects is given in the table. Answer the following

questions on the basis of it: Source Intensity

i. Which sound is the loudest? X 10dB
Y 20dB
ii. By how many times is the sound 'Y' louder than the Z 40dB
sound 'X'? How?

iii. By how many times is the sound 'X' fainter than the sound 'Z'? How?

90 Modern Graded Science Class 9

6. Numerical Problems

a. Calculate the frequency of sound whose speed is 350 m/s and wavelength 35 m.
(Ans: 10 Hz)

b. The audible frequency ranges for a human ear is 20 Hz - 20 kHz. Convert this into
the corresponding wavelength. (velocity of sound = 340 m/s)

(Ans: 17m, 1.7×10-4 m)

c. A source produces 20 crests and 20 troughs in 4 seconds. The second crest is 3

cm away from the first crest. Calculate (i) wavelength (ii) frequency and (iii) wave

speed. (Ans: 3×10-2m, 5Hz, 1.5×10–1ms–1)

d. Calculate the wavelength of the radio waves whose frequency is 3×109 Hz. The speed

of the radio waves is 3×108 m/s. (Ans: 10-1m)

e. The speed of sound in air is 340 m/s. If the wavelength is 2.4 cm, what will be the

frequency of the sound wave? (Ans: 1.42 Hz)

f. Find the frequency of a wave whose time period is 0.004 second.

(Ans: 2.5 ×102 Hz)

g. A boy standing 100 m from the foot of a high wall claps his hands loudly and the echo

reaches him 0.5 s later. Calculate the velocity of sound in air using this observation.

(Ans: 4×102m/s)

h. A ship receives the sound produced by its fathometer after 3.5 seconds. Calculate the

depth of the sea (speed of light in water = 1400 m/s). (Ans: 2425 m)

Tuning fork : an instrument made usually of steel and used as a source of
sound by hitting of its prongs on a rubber pad

Rheumatic pain : the pain at joints due to heart disorder

Neuralgic pain : the pain occurred due to nerve disorders

Nausea : the feeling that you want to vomit

Coagulation : similar solidification of other materials

Pattering : grouping of frequent irregularly repeated sounds of
moderate magnitude and lower than average pitch

∆∆∆

Classification of Elements 91

Chapter Light

6

Total estimated Pds: 6 (4T/2P

Competencies
On completion of this chapter, the students will be competent to:

define refraction.
explain the refraction of light with illustration.
describe the process of dispersion of light.
describe the nature of the electromagnetic spectrum.
mention the practical uses of electromagnetic spectrum.

Light is a form of energy that can be sensed by the eyes. So, we can see the things around us.
The rays of light always travel in straight lines. They travel readily in the transparent media
such as air, water and glass. They travel with different speed in different media. For instance,
the speed of light in air, water and glass is 3×108 m/s2, 2.25×108m/s and 2×108 m/s respectively.
However, the speed of light in air and vacuum is considered the same i.e. 3×108 m/s. Light
follows different phenomena such as reflection, refraction, dispersion, etc. When light travels
from one medium to another medium, it changes its direction at the boundary separating the
two media. This is called refraction of light because the light is bent or it changes the direction
on entering from one medium to another due to difference of its speed in different media.

A pencil ABC partly immersed in a trough of water appears bent upwards from the point B to
C i.e. at the surface of water as shown in the figure. A coin placed at the bottom of the beaker
containing water appears at a less depth than its really is. Similarly, a pond looks shallower
than its actual depth. These effects are caused by the bending of the rays of light when they
pass from one medium to another which is called refraction of light.

Refraction of light

Light travels on a straight line in a medium. When a beam of light passes from one medium
to other, it gets bent. The bending of light as it passes from one transparent medium to another
medium is called refraction of light.
When a ray of light AO in air is incident on the surface PQ of a glass slab, the ray bends
along OB in the glass slab as shown in the figure. MN is the normal to the glass surface at O.
The ray OB then emerges along BC in air. Here, AO is an incident ray and OB is a refracted

92 Modern Graded Science Class 9

ray. The incident ray (AO)

makes an angle AOM with

the normal MN drawn at

the point O, which is called

angle of incidence (∠i). The

refracted ray (OB) makes an

angle NOB with the normal

MN, which is called angle of

refraction (∠r). The point O Fig. 6.1 refraction of light

is called point of incidence. OB' is the original direction of the incident ray AO.

Rarer and denser media

The medium, through which the light passes is called an optical medium. The optical medium
in which the speed of light is more is called a rarer medium and the medium in which the
speed of light is comparatively less is called a denser medium. In other words, the medium
having less density is called an optically rarer medium and the medium having more density is
called an optically denser medium. If the pair of media are air and water, air is a rarer medium
and water is a denser medium but in the case of water and glass, water is rarer medium and
glass is the denser one. Thus, the rarer and denser media are relative terms.

In refraction, the angle of incidence is not equal to the angle of refraction. The angle of
refraction is smaller than the angle of incidence if a ray of light passes from a rarer medium to
a denser medium. While a ray of light passes from a denser medium to the rarer medium, the
angle of refraction is greater than the angle of incidence. This is because the speed of light in

two differen media is differen. For example, the speed of light is more in air than in glass

as the glass is a denser medium and the air is a rarer medium.

When the light ray passes from one medium to another along the normal i.e. at the right angle
to the surface, it passes without deviation but its speed is changed.

Laws of refraction of light

The refraction of light occurs when it travels from one Fig. 6.2 laws of refraction of light
medium to another. It obeys the following laws:
Light 93
1. The incident ray, the refracted ray and the normal
at the point of incidence all lie on the same plane.

In the figure, the incident ray AO, the refracted ray
OB and the normal MN at the point of incidence
O, all lie on the same plane.

2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is
constant for a given pair of media. This realation was propounded by Willebrord Snell.
So, this is also called Snell's law.

Mathematically,

 α ‹‹‡‡ ‘‘ˆˆ ––ŠŠ‡‡ ƒƒ‰‰ŽŽ‡‡ ‘‘ˆˆ ”‹‡ˆ…”‹ƒ†…‡–‹‘…‡

‹Ǥ ‡Ǥǡ ••‹‹ ”‹ α ȋȌ …‘•–ƒ–
This constant (µ) is called refractive index of the material of the medium. For glass

µ = 1.5 and for water µ= 1.33.
The Snell's law can be stated in the following conditions:

(a) When a light ray Fig. 6.3 (a) bending (b) bending away (c) no deviation
travels from a rarer towards the normal from the normal
to a denser medium,
it bends towards the
normal. It means the
angle of incidence is
greater than the angle
of refraction as in figure (a).

(b) When the light passes from a denser to a rarer medium, it bends away from the normal. It
means the angle of incidence (i) is smaller than the angle of refraction (r) as in figure (b).

(c) When the light passes along the normal i.e. at right angle to the surface from any medium
another medium, it passes without deviation as in figure (c).

Cause of refraction of light

The speed of light is generally different in different media. For example, the speed of light in
air or in vacuum, water and glass is 3×1018 m/s, 2.25×108 m/s and 2×108 m/s respectively.
When a light ray passes from one medium to another, the speed of light changes. This change
is the main cause of refraction of light. For example, when a light ray passes from air to water,
its speed decreases and the ray of light bends toward the normal. Thus, the slower the speed of
light ray in a medium, the ray bends more. This is the real cause of refraction of light.

Activity 6.1
To verify of the laws of refraction of light

Apparatus required: a glass slab, a pencil, a drawing board, thumb pins, pins, a geometrical
box, a white sheet of paper

94 Modern Graded Science Class 9

Procedure:
1. Fix a white sheet of paper on a drawing board using thumb pins.

Fig. 6.4 verification of the laws of refraction of light

2. Draw the outline of the glass slab in the middle of the paper.
3. Removing the slab from the paper, draw a normal MN at a point O on its one of the

outlined faces.
4. Draw ∠A1OM = 30° (say) and fix two pins at point A1 and point A2 on the line A1O at

least 8cm apart.
5. Place the slab on its outline on the paper.
6. Viewing through opposite face, fix a pin at B1 so that all three pins A1, A2 and B1 appear

on a straight line.
7. Fix another pin at B2 in the same way as described in the step 6. Mark the points of the pin.
8. Remove all the pins from point A1, point A2, point B1 and point B2. Remove the slab also

from its outline.
9. Draw a line through B1 and B2 so that the line meets the outline of the slab at P. Join P and O.
Here, A1O in air is the incident ray. The ray OP in glass is the refracted ray and the ray PB2 is
the emergent ray. OZ is the original direction of the incident ray A1O.
In the figure above, we see that when a ray passes through a rectangular glass slab, it is
not deviated at all, but simply displaced sideways. This sideway displacement is called
lateral displacement (d). The incident ray (A1O) is parallel to the emergent ray (PB2). The
perpendicular distance (YZ) between the incident ray and emergent ray measures the lateral
displacement.

Light 95

Conclusion
1. The incident ray A1O, the refracted ray OP and normal MN at the point O all lie on the

plane of the paper. Thus, the first law of refraction is verified.
2. Measure the angle of incidence ∠A1 OM = ∠i and the angle of refraction ∠NOP =

∠r and then find sin i/sin r. Repeat this procedure for different values of the angle of

incidence like 20°, 30°, 40°, etc. Each time, we = constant. Thus, the second law
of refraction is verified.

Real depth and apparent depth

To an observer standing at the side of a pond, any object under the water appears to be nearer

the surface than its realy depth. This effect is due to the refraction of light at the boundary

between the water and air media. A M air medium refracted ray
similar effect can be described when

observing any other optical media like A A r
glass. For example, when a coin is placed apparent
in a beaker full of water and observed, depth iN
we can see the coin nearer the surface of I

water than its really depth. We see the incident ray

coin only if the rays coming from it water medium beaker
reach our eyes after refraction. We see

the image (I) of the coin at a distance 'd' real depth coin

from the surface of water which is the Fig. 6.5 real depth and apparent depth

apparent depth of the coin rather than its real depth 'D'. This is due to the refraction of light.

So, in the given figure, AI is the apparent depth and AO is the real depth. The actual depth or

position of the object under water is called real depth. The virtual depth or position at which

an object is visible to an observer's eye under water due to refraction of light is called apparent

depth. The apparent depth is less than the real depth in the effect of refraction. The refractive

index in terms of real depth and apparent depth is calculated by,

Refractive Index (m) = Real depth
Apparent depth

where, m is the refractive index of the denser medium with respect to the rarer medium.

96 Modern Graded Science Class 9