Periodic motion

When an object repeats its motion after fixed

interval of time, this type of motion is

called periodic motion.

For Example: motion of planets

around the sun,

motion of hands of a clock, motion of pendulum.

Oscillatory motion

Oscillatory motion is a specific type

of periodic motion in which a body

moves back and forth about a fixed

point, called mean position.

Simple Harmonic Motion (S.H.M.)

Simple Harmonic Motion is a motion in

which the acceleration of the particle is

always directed towards a fixed point on a

straight line and is proportional to the

displacement of the particle from that point.

Examples of SHM

1.The motion of a bob of a simple pendulum.

2.The motion of the mass attached to a spring.

•The motion of liquid oscillating in a U-tube.

For Example: motion of a pendulum, the

vibrations produced in strings of a guitar.

Displacement:

The distance of a particle executing SHM

from its mean position, at a given instant is

called displacement.

OM = y is the displacement of the particle at any time t.

Few important terms

completed in one second.

n =

from the mean position is called its

amplitude.

The maximum displacement = OY

A m plitude =

ymax = OY = r

Time Period(T): The time taken to complete one

vibration is known as time period.

Amplitude:

The maximum displacement of the particle

Frequency(n): The number of vibrations

1

T

Angular velocity =

Angular velocity:

=

=

2 n

Angle described in one revolution

Time taken to complete one revolution

2

T

sin

=

Equationof simple Harmonic Motion

(expression for displacement)

OM = y

Let particle P traces an angle

at o after time t.

POX =

Also MPO =

OM = OP sin

M

O

P

yOM

OP

y = r sin

or y = r sin

t

M

y = r cos

or y = r cos t

POX = = MPO

Also NPQ =

(i)v cos along the diameter

YOY'

(ii)v sin perpendicular to the diameter YOY'

Only velocity to M is given by the component v cos

Component (v sin ) has no effecton

the motion of M.

Velocity of a particle executing SHM

Special Cases:

(a) When y = 0 i.e. displacement is zero or the

body is at mean position.

= v

= v 1

=

velocity of M, V =

velocity

of M, V= v cos

1 sin2

2

r

y

r2 y2

r

=

vr r2

y2

r

r2

y2

( y = r sin

)

This value of velocity is called velocity amplitude of SHM.

(b) When y = r i.e. displacement is maximum or

the body is at extreme position.

From Eq. (1),Vmax = r (max.

velocity)

Vmin = 0 (minimum velocity)

using velocity of M, V =

r2 y2

r

This centripetal acceleration is

resolved into

components.

two rectangular

The centripetal acceleration

acting at P is along PO

(ii) v cos perpendicular to

YOY'.

(i) v sin along PN i.e. along the diameter

YOY'

Acceleration of a particle executing SHM

v2

r

2

r

2

But the actual expression for acceleration is given by

a = – 2y

It also shows that acceleration is always directed

towards point o.

= r

sin

Acceleration of

M, a =v sin

Component (ii) has no effect on the motion of M.

2

r2 2

r

a

=

2y

= 2 r

sin

(b) If y =r i.e. displacement is maximum or the

body is at extreme position.

From Eqn. (2) acceleration, amax

(maximum acceleration)

=

2

r

Special Cases:

(a) If y = 0 i.e. displacement is zero or the

body is at mean position.

From Eqn. (2) acceleration, amin = 0

acceleration)(minimum

The magnitude of the acceleration of a particle

executing SHM is

a = 2y (neglecting negative sign)

Velocity of a particle executing SHM

Expression for the time period and frequency

of a particle executing SHM

But

=

, where T is the time period

a

acceleration

y displacement

=2

T

or frequency, n =

or Time period, T =

2

acceleration

displacement

2

T=

displacement

acceleration

1 acceleration(a)

2 displacement(y)

i.e. x Fa (Applied force = Fa = Deforming force)

Deformation Deforming force.

Hook’s Law

It states that deformation is always proportional

to the deforming force.

or

or Fa = K x where K is constant of

proportionality and is called spring factor or

or theforce constant stiffness factor of

spring.

Fa x

Definition of spring factor

It is defined as the force in newtons required

to stretch the spring through 1m.

Also we know Fa = – Fr

Fr = – K x

Since Fa =K x , If x = 1 m

Then Fa = K

Vibrations of a mass attached to a spring

(i)Vertical oscillations

•Horizontal oscillations.

(i) Oscillationsof a mass attached with

a vertical spring.

Thus Fa = – Fr

From (1) and (2) Ma = – K x

If 'a' be the acceleration produced by the force Fr

in a mass M, then

x

M

a K

Now we know Time period,

displacement

accelerationT =

2

Fr = Ma .....(1)

also by Hook's law Fr = – K x .....(2)

K

If n be the frequency of vibrations, then

1 1

n = =2

T

1 K

2 M

M

T =

2

(ii) Oscillations

horizontal spring.

of mass attached with a

M

K

T =

2

n = 1

1=

2

T

1 K

2 M

Vibrations of Loaded Beam

(a) Beam supported at one end.

Cantilever: A beam fixed horizontally at

one end and free to vibrate at the other

end is called cantilever.

T

=

2

p

g

Free vibrations:

When a body is set into vibrations and is

allowed to vibrate freely under the influence of

its own elastic forces

called free vibrations.

such vibrations are

lT =2

g

n =1

g

2 l

Damped Vibrations

Vibrations in which energy continuously goes

on dissipating and finally the motion die

out, are called damped vibrations.

Vibrations in which the body vibrate with a

frequency other than its natural frequency

under the external periodic force, are

called forced vibrations.

Example: 1.Child's swing with external force.

2. Vibrating pendulum with some force.

Resonant vibration

A special type of forced vibration in which

the frequency of applied force matches

with natural frequency of the body is

called resonant vibration.

Forced Vibrations

The phenomenon of making a body to vibrate

with its natural frequency under the influence

of another vibrating body with the same

frequency, is called resonance.

Resonance

Definition of wave or wave motion

motion is being

particle to another.

handed over from one

or wave

It is a form of disturbance which travels

through the material medium due to therepeated periodic motion of the vibrating

particles about their mean position and the

(a) Elasticity

(b) Inertia

(c) Minimum friction

Types of waves or wave motion :

1. Longitudinal wave motion

2. Transverse wave motion

Properties:

LONGITUDINAL WAVE MOTION

mean position in the

propagation of the wave.

Example:

1. Sound waves.

2. Wavesproducedinairbycompressing and

releasing spring.

C = Compression R = Rarefaction

C RC

It is that type of wave motion in which

particles of the medium vibrate about their

direction of

It is that type of wave motion in which

particles of the medium vibrate about their

mean position perpendicular to the

direction of propagation of the wave.

Examples:

1.Light waves .

2.All electro-magnetic waves are

transverse in nature i.e. Radio waves, X- rays,

- rays etc.

3.Waves produced on the surface of

water when a

piece of stone is dropped into it.

WaveParticles

TRANSVERSE WAVE MOTION

distance

crest.

Trough: The point on the wave at the

maximum distance below the mean position is

called trough.

T

Crest: The point on the wave at the maximum

from the mean position is called

C

A B

Also AB =

A FEW DEFINITIONS

(i) Wavelength ( ):

It is the distance travelled by the wave in onecomplete cycle.

C

T

A BM

It is defined as the distance travelled by the

wave per unit time.

Relation between Velocity (v),Frequency (n) and Wavelength () of the

wave.

Wave velocity (v):

Wavelength () is the distance travelled by the

wave in one time period (T).Wavelength ()

distan ce

timeVelocity =

Velocity = Time period (T) T

or v = n for light wave, c = v

Distinction Between Transverse & Longitudinal Waves

Transverse Waves Longitudinal Waves

1. Particles of the medium

vibrate perpendicular

to the wave.

2. Travels in the form of

crest and trough.

3. Transverse wave can

be polarised.

4. There is no change in

the density of the

medium.

1. P a r t i c l e s o f t h emedium vibrate parallel

to the wave.

2. Travels in the form of

compression and

rarefaction.

3 Longitudinalwaves

cannot be polarised.

4. There is change in the

density of the

medium.

2. Applications of sound waves

The branch of physics which deals with

the design and construction of halls,

theatre, auditorium etc. with best sound

effect is called acoustics of buildings.

Co-efficient of absorption of sound

An open window acts as a perfect

absorber of sound energy. The absorption co-

efficient of an open window is one i.e. 100%.

a =

Acoustics of Building:

Sound energy absorbed by the surface

Total sound energy incident upon the surface

Musical sound: It produces pleasant effect

on the ear. It’s curve is regular and has a

definite amplitude. Fig. (a)

Musical Sound And Noise

Noise: It produces unpleasant effect on the ear.

The curve is irregular and has no definite

amplitude. Noise is usually of low frequency.

Noise

The persistence sound in a room or hall after

the original sound has been stopped is

called Reverberation.

Reverberation

It is defined as the time required for the

intensity of sound to fall to one millionth

(10–6th) of its original intensity after

the source stops sounding.

Sabine's formula for reverberation time (T)

Standard Reverberation time

T= .............10.16 V

as

V = the volume of the room in cubic metres (m3).

S = area of the surfaces in square metres (m2).

a = the coefficient of absorption.

a s = the total surface absorption of materials.

Factors on Which Reverberation Time Depends

1.Size of room or hall.

2.Total absorption by the various surfaces.

Q. A cinema hall has volume of 7500 m3. It

is required to have reverberation time 1.5

sec. What would be the total absorption in the

hall ?

i.e. a s = a1 s1 + a2 s2 + a3 s3 + ...... an sn

= 800 units

0.16 V

T

0.16 7500

1.5as = =

Methods to control reverberation time

1. Covering the walls and floor with

absorbing materials.

2. By providing a few open windows.

3. By using false ceiling.

4. By increasing good number of audience.

5. By using heavy curtains with folds.

6. By using upholstered seats in the hall.

Echo

Echo is repetition of sound due to reflection

from some object.

Thus sound must travel (d = v × t) = 332 × 1

=33.2 metres, for an echo to be heard.

So that minimum distance of the large

reflecting surface from the listener should be

= 16.6 m

Remedy: To avoid confusion between

original sound and its echo the surfaces

must be covered with good absorbing

material.

10

Audio frequency range is 20Hz to 20kHz.

Infrasonics

The sound waves having frequency less than

20Hz are called as Infrasonics.

Ultrasonics

The sound waves having

frequency more

than 20kHz are called as ultrasonics.

Audible range of sound waves

Production of Ultrasonic Waves

(1) Magnetostriction Oscillator

Principle : It is based upon magnetostriction

effect.

“If a ferromagnetic material in the form of

a rod (iron or nickel), is subjected

to alternating magnetic field, the rod

expands and contracts in length alternately.”

Construction

High frequency oscillator

A rod of Nickel or Invar

( 36% Ni + 64% Fe) is

clamped in the middle. L1 and L2 are two

coils surrounding the rod XY. Coils are

connected with High frequency oscillator.

l = Length of rod, = Density of material

Y = Young’s modulus of elasticity.

1. High frequency A.C. current is

passed through coil L1.

2. As a result of this alternating magnetic field is

associated with the coil which makes the bar

magnetised and demagnetised.

3. The length of the rod changes and free ends

begin to vibrate.4. Thus high frequency ultrasonics are

produced.

Working

n =1 Y

2l

Applications of ultrasonics

1. Drilling : A ferromagnetic rod is placed in a

coil through which high frequency A.C. is

passed. At the lower end of rod a tool bit is

attached. The rod vibrates with high frequency.

The bit moves up and down very fast and thus

make a hole in the material placed below.

Rod

Tool bit

A ferromagnetic rod is placed in a coil through which

high frequency A.C. is passed. At the lower end of rod

a hammer is attached. The rod vibrates with high

frequency and hammer hits the plates. The molecules

of plates start vibrating and diffuse into each other

and thus sheets get welded.

(2) Cold Welding :

(3) Ultrasonic cleaning :

Ultrasonic waves cause violent agitation when

transmitted through a liquid. Cleaning job is put in

a detergent solution and then ultrasonic waves

are passed. Strong agitations of molecules perform a

super cleaning job on small pieces of machinery.

The principle of SONAR is same as that of

RADAR.

1. It is used to measure the depth of sea water.

2. It is also used to detect ice berg or

submarine in the sea water.

3. It helps sailor to steer ship in a safer

(4) SONAR : Sound Navigation and Ranging.

direction.

4. Knowing the velocity of ultrasonic waves

and time taken by the wave, the distance

(depth) can be determined.

d =v x t

2

1st SessionalFeb.2014

Subject : Applied Physics – II

Section –ANote : Attempt all the Questions 5×1 = 5

I.Define Acoustics of Buildings.

II.Define Noise.

III.Define Simple Harmonic Motion.

IV.Define Cantilever.

V. Define Wavelength.

Section – BNote : Attempt any four Questions 4×5 = 20

2. Explain construction and working of

Magnetostriction oscillator?

3. What are the methods to control

reverberation time?

Q.4 Explain

transverse and longitudinal waves?

5. What are free and forced vibrations?

6. Calculate the displacement and velocity

for S.H.M?

1st SessionalFeb.2015

Subject : Applied Physics – II

Section – ANote : Attempt all the Questions 5×1 = 5

I.Define wave motion by giving examples.

•Give relation between wave

velocity,

frequency and wavelength.

III.Define cantilever and give the formula of

time period of cantilever.

IV.Define What is acoustics and

acoustics of buildings.

•Give full form of SONAR.

Section – BNote : Attempt any four Questions 4×5 = 20

2. What is SHM? Derive an expression for

velocity of SHM.

3. What is Reverberation? Give methods to

control Reverberation.

Q.4 Discuss

by giving example free vibration & resonant

vibration.

5. Explain principle, construction & working of

magnetostriction oscillator.

• Give difference between transverse and

longitude wave.

1. Principles of optics

(1) Reflection :

When light is incident on the surface of an

object, some of the light is bounced back into

the same medium. This phenomenon is called

as reflection of light.

M1 M2

rayray

(i)The incident ray, the reflected ray and the

normal at the point of incidence all lie in the

same plane.

(ii)The angle of incidence is equal to the angle

of reflection.

i= r

The laws of reflection are :

Real and Virtual Objects and Images

(i)An object is said to be real when light

diverges from it.

(ii)An object is said to be virtual when light

converges towards it.

(iii)An image is said to be Real when light

converges towards it. It can be obtained on

screen.

(i)An image is said to be virtual when light

diverges from it. It can not be obtained on the

screen.

(a)All the distances along the principal axis are

measured from the pole of the spherical mirror.

(b)The distances measured in the same direction

as that of the incident light are taken as

positive, while the distances measured in the

direction opposite to that of incident light are

taken as negative.

(c)The distances perpendicular to the principal

axis (i.e. size of object and size of image) are

taken as positive if measured in upward

direction but negative if measured in downward

direction.

Sign Conventions:

Sign Conventions

Height upward

(positive)

Height downwards (negative)

In the direction of

light (positive)

Against incident light

(negative)

where v = image-distance i.e. the distance

from the pole to the image.

u =object-distancei.e.thedistancefrom

the pole to the object.

f =focallengthi.e.thedistancefromthe

pole

to the focus F.

Spherical mirror formula

1

1=

1

v u f

Also f =R

2

Linear Magnification

m =sizeof image

sizeof object

I

O

v

um = =

Uses of Spherical Mirrors

Concave mirrors

1.They are used in search lights.

2.They are used in solar cookers to focus sunlight.

3.Concave mirrors are used by doctors to focus

light on certain parts of the body.

4.It is also used as shaving mirror.

Convex mirrors

1. Widelyused as rear view mirrors in

cars, scooters etc.

2. They are used as reflectors in street lights.

Refraction of Light

The phenomenon of bending of light

rays while passing from one medium to

another is called Refraction of light.

(i)The incident ray, refracted ray and the

normal at the point of interface all lie in the

same plane.

(ii)The ratio of sine of the angle of

incidence to the sine of the angle of

refraction is constant for a given pair of media.

(This law is also known as the SNELL’s law).

The Snell’s law

The laws of refraction are :

=Constant =a g

sin i

sinr

Where a g is the refractive index of glass w.r.t.

Air.

Absolute refractive index of a medium

a m =Velocityof light in air Velocityof light inMedium

c

v

Lenses

A lens is made of a homogeneous transparent

material bounded by two spherical surfaces or

one spherical and one plane surface.

Where C = 3 x 108 m/s

Lenses are of two types :

Formation of Images by a Convex Lens

Image formation with a Concave Lens

Lens Formula

=11 1

v u f

where v = image-distance

u = object-distance

f = focal length

m =

Note: If ‘m’ is positive then image will be

virtual and erect if ‘m’ is negative, then image

will be real

lenses.

and inverted for mirrors and

It is same for both type of

lenses

Linear Magnification

image height

object height

size of image

size of object=

I vm = =

O u

It is reciprocal of the focal length measured in

metre.

Power of a Lens

P =1

f metre

The unit of the power of lens is ‘Dioptre’ and

is

indicated by the symbol ‘D’.

Thus if the focal length of a lens is 0.25 m, its

power will be ?

P is positive for a convex lens and that of a

concave lens is negative.

Q. Two lenses, one of focal length 20 cm

(convex lens) and another of focal

length

–10cm (concave lens) are placed in contact.

What is the focal length and power of the

combination?

Ans. P = - 5D, F = - 0.2 m

P = P1 + P2

Power of combination of Lenses

1 1

F f1

1

f2

(i) Simple microscope ( A convex lens of small F.L.)

(ii) Compound microscope

Near point or least distance of distinct vision (D)

It is the minimum distance from the eye at

which an object can be seen clearly.

Standard near point distance D = 25 cm.

Microscope :

It is an

instrument image

of small object.

that produces enlarged

Magnifying Power (M)

It is the ratio of the angle subtended by

the image to the angle subtended by the

object at naked eye at the near point.

(i) Simple microscope

M = 1 D

f

(ii) Compound microscope

L = Distance between two lenses.

1 fe

L D

fo

M =

Telescope

(i) Astronomical telescope :

(ii) Terresterial telescope :

(iii)Galilian telescope :

Length of tube remains fixed i.e. L= (fe+fo)

M = –fo

fe

Total Internal reflection

When the angle of incidence of a ray of light

travelling in a denser medium is greater than

the critical angle for the two media, the ray is

totally reflected back into the same

medium. This phenomenon is called total

internal reflection of light.

The critical angle for a medium is the angle of

incidence in the medium for which the angle of

refraction in air is 90°.

Conditions for Total Internal Reflection.

(i)The incident light must pass from a denser

medium into a rarer medium.

•The angle of incidence in denser medium

must be greater than critical angle (ic).

Critical angle

Refractive index,

=

1 1

sine of critical angle sin ic

1st SessionalFeb.2014

Subject : Applied Physics – II

Section –ANote : Attempt all the Questions 5×1 = 5

I.Define Acoustics of Buildings.

II.Define Noise.

III.Define Simple Harmonic Motion.

IV.Define Cantilever.

V. Define Wavelength.

Section – BNote : Attempt any four Questions 4×5 = 20

2. Explain construction and working of

Magnetostriction oscillator?

3. What are the methods to control

reverberation time?

Q.4 Explain

transverse and longitudinal waves?

5. What are free and forced vibrations?

6. Calculate the displacement and velocity

for S.H.M?

THANK YOU