SlideShare a Scribd company logo
1 of 17
Download to read offline
9011041155 / 9011031155

• Live Webinars (online lectures) with
recordings.
• Online Query Solving
• Online MCQ tests with detailed
solutions
• Online Notes and Solved Exercises
• Career Counseling

1
9011041155 / 9011031155

Stationary Waves
Stationary Waves
The resultant waves formed due to superposition of
two exactly identical progressive waves, having same
amplitude, wavelength and speed, travelling in the
same medium, along the same path, but in opposite
directions are called stationary waves.

Characteristics of Stationary waves
1. Stationary waves are formed due to superposition
of two exactly identical waves travelling through the
same medium, along the same path but, in
opposite directions.
2. When stationary waves are set up in a medium, the
particles at some points are permanently at rest
(i.e. amplitude is zero). Such points are called
2
9011041155 / 9011031155

‘nodes’. The distance between two successive
nodes is λ/2.

3. When stationary waves are set up in a medium, the
particles at some points vibrate with maximum
amplitude. Such points are called ‘antinodes’.
Distance between two successive antinodes is λ /2.
4. Nodes and antinodes are alternately situated. The
distance

between

any

node

and

successive

antinode is λ /4.
5. In stationary waves loops are formed between two
successive nodes. All the particles in one loop are
3
9011041155 / 9011031155

in the same phase, while the particles in the
successive loop are out of phase by πc.

6. Stationary waves are periodic in time and space.
7. Stationary waves do not transfer energy through
the medium.
8. In stationary waves, all the particles except those at
nodes, vibrate with same period as that of the
interfering waves.
9. The amplitude of vibration is different for different
particles and that increases from node to antinode.
10. A loop is formed between two successive nodes

4
9011041155 / 9011031155

because of two reasons. Firstly, the amplitude of
vibration of the particles increases from node to
antinode and decreases from antinode to node.
Secondly, all the particles reach their maximum
displacement at a time.
11. In case of stationary waves formed due to
interference of longitudinal waves, displacement of
the particle at the node is zero. But, pressure at the
nodes changes between maximum to minimum. At
antinodes, the displacement is maximum, but, the
pressure remains constant. Hence, displacement
nodes

are

called

pressure

antinodes

and

displacement antinodes are called pressure nodes.

5
9011041155 / 9011031155

Equation of a Stationary Wave

y

1

a sin 2

t x
T

and y

a sin 2

2

t
T

i.e. y = y1 + y2

y a sin 2

t x
T

a sin 2

t
T

x

We know that,

sin A

sin B

2 sin

A

B
2

2 t
2 x
y 2 a sin
cos
T
2 x
put, 2a cos
A
2 t
T
But,1 / T n
y A sin 2 n t
y

A sin

6

A B
cos
2

x
9011041155 / 9011031155

Hence, the resultant wave is also an S.H.M. with
same period T. But, in this equation the term ± x/λ
is absent. Thus, the resultant wave is not a
progressive wave. It is travelling neither along + ve
X - axis nor along - ve X-axis.
Such a steady or localized wave is called
Stationary Wave or Standing Wave. Transfer of
energy is 0.
Amplitude of the resultant wave varies between
± 2a
1. At nodes, i.e. A = 0

2 x

2 a cos
2 x
x

2

0

, 3 ,5 ,.......
2 2 2
,3

, 5 ,........
2 2
7
9011041155 / 9011031155

distance between two successive nodes is,

3

2

2

2

OR 5

3

2

2 x
x

2 x

0,
0,

2

i.e. A = ± 2a

2. At antinodes,

2a cos

2

and so on

2a i.e. cos

2 x

1

, 2 ,3 , ......

, 2 ,3 ,.......
2 2 2

Distance between two successive antinodes is,

2

0

2

or 2

2

2

2

and so on

Hence, distance between successive nodes
and antinodes is

2

or the nodes and antinodes

are equidistant. Also, the distance between
consecutive node and antinode is λ / 4.
8
9011041155 / 9011031155

M.C.Q.
Q.1

The phase difference between the particles in successive loops of a stationary wave is
(a.1) 90°

Q.9

(b.1) 45°

(c.1) 180°

(d.1) zero

Find the ‘wrong’ statement from the following:

The equation of a stationary wave is given by

, where y and x are in

cm and t is in second.
Then for the stationary wave,
(a.9) Amplitude=3 cm

(b.9) Wavelength=5cm

(c.9) Frequency=20 Hz

(d.9) Velocity=2 m/s

Harmonics and Overtones
The

fundamental

frequency

along

with

its

integral multiples are called harmonics. The
fundamental

frequency

itself

is

the

first

than

the

harmonic.

Vibrations
fundamental

of

frequencies
frequency

which

present are called overtones.
9

higher
are

actually
9011041155 / 9011031155

Free Oscillations
The body starts oscillating about its mean position,
on its own. Such vibrations are called free
oscillations. The frequency of vibrations of the body
is called ‘natural frequency of vibrations’ of the
material of the body.

Examples
1.

Simple pendulum

2.

Tuning fork
10
9011041155 / 9011031155

3.

Stretched string

11
9011041155 / 9011031155

Damped oscillations
Amplitude of free oscillations decreases because in
every oscillation a little amount of energy is utilized to
overcome the air resistance. So, the oscillations are
called ‘damped oscillations’.

Forced oscillations
the body is forced to oscillate with a new frequency.
Hence,

such

oscillations

are

called

‘forced

oscillations’.
The oscillations in the body due to an external
periodic force whose frequency is different from
natural frequency of vibration of the body are
called forced vibrations.
e.g.
1.
12
9011041155 / 9011031155

2.

13
9011041155 / 9011031155

Resonance
Amplitude of forced vibrations is inversely proportional
to the difference between the natural frequency of
vibrations of the body and the frequency of the external
force (called forcing frequency or driving frequency).
Thus, as the driving frequency approaches the natural
frequency,

the

amplitude

of

vibration

goes

on

increasing. Finally when the driving frequency matches
exactly with the natural frequency, we get maximum
amplitude of vibration. This effect is called resonance.
Getting

maximum

amplitude

of

forced

vibrations due to synchronization or matching
between natural frequency and driving frequency is
called resonance.

14
9011041155 / 9011031155

e.g.
1.

2.

15
9011041155 / 9011031155

3.

16
9011041155 / 9011031155
Q.65 In the experiment of a simple pendulum, the oscillations of the simple pendulum are actually
(a.65) Free oscillations
(c.65) Damped harmonic oscillations

(b.65) Forced oscillation
(d.65) Resonant oscillations

Q.66 When a regiment of soldiers have to cross a suspension bridge, they are ordered to
(a.66) March in steps

(b.66) Break the steps

(c.66) Stand in attention

(d.66) Stand at ease

Q.67 In the case of forced vibrations, the resonance becomes very sharp, when the
(a.67) Restoring force is very small

(b.67) Applied periodic force is small

(c.67) Damping force is small

(d.67) Quality factor is small

•

Ask Your Doubts

•

For inquiry and registration, call 9011041155 /
9011031155.

17

More Related Content

What's hot

LO4 - Sound Waves
LO4 - Sound WavesLO4 - Sound Waves
LO4 - Sound WavesCeleste Ng
 
Standing Waves on a String
Standing Waves on a StringStanding Waves on a String
Standing Waves on a Stringayshaab
 
Standing waves
Standing wavesStanding waves
Standing wavesannayys
 
Standing waves final ppt
Standing waves final pptStanding waves final ppt
Standing waves final pptarbinddhaliwal
 
STATIONARY WAVES
STATIONARY WAVESSTATIONARY WAVES
STATIONARY WAVESKANNAN
 
Lecture 06 wave energy. interference. standing waves.
Lecture 06   wave energy. interference. standing waves.Lecture 06   wave energy. interference. standing waves.
Lecture 06 wave energy. interference. standing waves.Albania Energy Association
 
Grade 11, U4 L3-Superposition of Waves
Grade 11, U4 L3-Superposition of WavesGrade 11, U4 L3-Superposition of Waves
Grade 11, U4 L3-Superposition of Wavesgruszecki1
 
The wave eqution presentation
The wave eqution presentationThe wave eqution presentation
The wave eqution presentationMuhammad Saqib
 
Standing Waves on Strings
Standing Waves on StringsStanding Waves on Strings
Standing Waves on Stringsjjsoroka
 
Grade 11, U4 L2-Waves
Grade 11, U4 L2-WavesGrade 11, U4 L2-Waves
Grade 11, U4 L2-Wavesgruszecki1
 
Damped Oscillations
Damped Oscillations Damped Oscillations
Damped Oscillations Hantao Mai
 
PHYS101 Learning Object (LO6)
PHYS101 Learning Object (LO6)PHYS101 Learning Object (LO6)
PHYS101 Learning Object (LO6)CurryJam
 
2D wave interference
2D wave interference 2D wave interference
2D wave interference shikhak12
 
Learning objective -- Beats
Learning objective -- BeatsLearning objective -- Beats
Learning objective -- BeatsHedy Liang
 
Phase and phase difference LO3
Phase and phase difference LO3Phase and phase difference LO3
Phase and phase difference LO3Vivian Tsang
 
Topic 7 wave_interference(latest)
Topic 7 wave_interference(latest)Topic 7 wave_interference(latest)
Topic 7 wave_interference(latest)Gabriel O'Brien
 

What's hot (20)

LO4 - Sound Waves
LO4 - Sound WavesLO4 - Sound Waves
LO4 - Sound Waves
 
Standing Waves on a String
Standing Waves on a StringStanding Waves on a String
Standing Waves on a String
 
Standing waves
Standing wavesStanding waves
Standing waves
 
Standing waves final ppt
Standing waves final pptStanding waves final ppt
Standing waves final ppt
 
STATIONARY WAVES
STATIONARY WAVESSTATIONARY WAVES
STATIONARY WAVES
 
Lecture 06 wave energy. interference. standing waves.
Lecture 06   wave energy. interference. standing waves.Lecture 06   wave energy. interference. standing waves.
Lecture 06 wave energy. interference. standing waves.
 
Grade 11, U4 L3-Superposition of Waves
Grade 11, U4 L3-Superposition of WavesGrade 11, U4 L3-Superposition of Waves
Grade 11, U4 L3-Superposition of Waves
 
The wave eqution presentation
The wave eqution presentationThe wave eqution presentation
The wave eqution presentation
 
Lo8 upload
Lo8 uploadLo8 upload
Lo8 upload
 
GENERAL DYNAMICS
GENERAL DYNAMICSGENERAL DYNAMICS
GENERAL DYNAMICS
 
Standing Waves on Strings
Standing Waves on StringsStanding Waves on Strings
Standing Waves on Strings
 
Sound waves
Sound wavesSound waves
Sound waves
 
Grade 11, U4 L2-Waves
Grade 11, U4 L2-WavesGrade 11, U4 L2-Waves
Grade 11, U4 L2-Waves
 
Damped Oscillations
Damped Oscillations Damped Oscillations
Damped Oscillations
 
PHYS101 Learning Object (LO6)
PHYS101 Learning Object (LO6)PHYS101 Learning Object (LO6)
PHYS101 Learning Object (LO6)
 
2D wave interference
2D wave interference 2D wave interference
2D wave interference
 
Vibrations
VibrationsVibrations
Vibrations
 
Learning objective -- Beats
Learning objective -- BeatsLearning objective -- Beats
Learning objective -- Beats
 
Phase and phase difference LO3
Phase and phase difference LO3Phase and phase difference LO3
Phase and phase difference LO3
 
Topic 7 wave_interference(latest)
Topic 7 wave_interference(latest)Topic 7 wave_interference(latest)
Topic 7 wave_interference(latest)
 

Similar to JEE Main 2014 Physics Syllabus - Stationary Waves

Ch 7 physical optics final
Ch 7 physical optics finalCh 7 physical optics final
Ch 7 physical optics finalanimesh samundh
 
04 UNIT-4 (WAVES) .pptx
04 UNIT-4 (WAVES) .pptx04 UNIT-4 (WAVES) .pptx
04 UNIT-4 (WAVES) .pptxFatimaAfzal56
 
Introduction to Waves Notes2.pptx
Introduction to Waves Notes2.pptxIntroduction to Waves Notes2.pptx
Introduction to Waves Notes2.pptxElezabeth Vashini
 
Notes for Atoms Molecules and Nuclei - Part III
Notes for Atoms Molecules and Nuclei - Part IIINotes for Atoms Molecules and Nuclei - Part III
Notes for Atoms Molecules and Nuclei - Part IIIEdnexa
 
Standing waves
Standing wavesStanding waves
Standing wavesMidoOoz
 
Phy exppp chap11
Phy exppp chap11Phy exppp chap11
Phy exppp chap11hmsoh
 
Chapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptxChapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptxPooja M
 
Waves in 2 Dimensions
Waves in 2 DimensionsWaves in 2 Dimensions
Waves in 2 DimensionsBruce Coulter
 
Wave Optics Class 12 Part-2
Wave Optics Class 12 Part-2Wave Optics Class 12 Part-2
Wave Optics Class 12 Part-2Self-employed
 
Ir spectroscopy by Bhavana P Khobragade
Ir spectroscopy by Bhavana P KhobragadeIr spectroscopy by Bhavana P Khobragade
Ir spectroscopy by Bhavana P KhobragadeBhavanaKhobragade
 
Waves unit (1)
Waves unit (1)Waves unit (1)
Waves unit (1)taddlaton
 
3.1 form 4 general wave properties
3.1 form 4 general wave properties3.1 form 4 general wave properties
3.1 form 4 general wave propertieschris lembalemba
 

Similar to JEE Main 2014 Physics Syllabus - Stationary Waves (20)

Ch 7 physical optics final
Ch 7 physical optics finalCh 7 physical optics final
Ch 7 physical optics final
 
04 UNIT-4 (WAVES) .pptx
04 UNIT-4 (WAVES) .pptx04 UNIT-4 (WAVES) .pptx
04 UNIT-4 (WAVES) .pptx
 
Introduction to Waves Notes2.pptx
Introduction to Waves Notes2.pptxIntroduction to Waves Notes2.pptx
Introduction to Waves Notes2.pptx
 
Notes for Atoms Molecules and Nuclei - Part III
Notes for Atoms Molecules and Nuclei - Part IIINotes for Atoms Molecules and Nuclei - Part III
Notes for Atoms Molecules and Nuclei - Part III
 
Standing waves
Standing wavesStanding waves
Standing waves
 
Wave motion
Wave motionWave motion
Wave motion
 
Wave properties
Wave propertiesWave properties
Wave properties
 
Phy exppp chap11
Phy exppp chap11Phy exppp chap11
Phy exppp chap11
 
Physics form 5 chapter 1
Physics form 5 chapter 1Physics form 5 chapter 1
Physics form 5 chapter 1
 
Chapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptxChapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptx
 
Physics 17-2
Physics 17-2Physics 17-2
Physics 17-2
 
Waves in 2 Dimensions
Waves in 2 DimensionsWaves in 2 Dimensions
Waves in 2 Dimensions
 
4.4
4.44.4
4.4
 
Wave Optics Class 12 Part-2
Wave Optics Class 12 Part-2Wave Optics Class 12 Part-2
Wave Optics Class 12 Part-2
 
Waves
WavesWaves
Waves
 
Ir spectroscopy by Bhavana P Khobragade
Ir spectroscopy by Bhavana P KhobragadeIr spectroscopy by Bhavana P Khobragade
Ir spectroscopy by Bhavana P Khobragade
 
4.4
4.44.4
4.4
 
4_wave_optics_2.ppt
4_wave_optics_2.ppt4_wave_optics_2.ppt
4_wave_optics_2.ppt
 
Waves unit (1)
Waves unit (1)Waves unit (1)
Waves unit (1)
 
3.1 form 4 general wave properties
3.1 form 4 general wave properties3.1 form 4 general wave properties
3.1 form 4 general wave properties
 

More from Ednexa

Recommendation letters
Recommendation lettersRecommendation letters
Recommendation lettersEdnexa
 
Physics Measurements Notes for JEE Main 2015
Physics Measurements Notes for JEE Main 2015 Physics Measurements Notes for JEE Main 2015
Physics Measurements Notes for JEE Main 2015 Ednexa
 
Important Points on Elasticity for JEE Main 2015
Important Points on Elasticity for JEE Main 2015 Important Points on Elasticity for JEE Main 2015
Important Points on Elasticity for JEE Main 2015 Ednexa
 
Important points on Gravitation for JEE Main 2015
Important points on Gravitation for JEE Main 2015Important points on Gravitation for JEE Main 2015
Important points on Gravitation for JEE Main 2015Ednexa
 
Current Electricity Notes for JEE Main 2015 - Part II
Current Electricity Notes for JEE Main 2015 - Part IICurrent Electricity Notes for JEE Main 2015 - Part II
Current Electricity Notes for JEE Main 2015 - Part IIEdnexa
 
Aldehydes Ketones and Carboxylic Acids - JEE Main 2015
Aldehydes Ketones and Carboxylic Acids - JEE Main 2015Aldehydes Ketones and Carboxylic Acids - JEE Main 2015
Aldehydes Ketones and Carboxylic Acids - JEE Main 2015Ednexa
 
Physics - Current Electricity Notes for JEE Main 2015
Physics - Current Electricity Notes for JEE Main 2015Physics - Current Electricity Notes for JEE Main 2015
Physics - Current Electricity Notes for JEE Main 2015Ednexa
 
Enhancement in Food Production Exercises - MH-CET 2015
Enhancement in Food Production Exercises - MH-CET 2015 Enhancement in Food Production Exercises - MH-CET 2015
Enhancement in Food Production Exercises - MH-CET 2015 Ednexa
 
Properties of Solids and Liquids Notes - JEE Main 2015
Properties of Solids and Liquids Notes - JEE Main 2015Properties of Solids and Liquids Notes - JEE Main 2015
Properties of Solids and Liquids Notes - JEE Main 2015Ednexa
 
12th Chemistry P-block elements Notes for JEE Main 2015
12th Chemistry P-block elements Notes for JEE Main 2015 12th Chemistry P-block elements Notes for JEE Main 2015
12th Chemistry P-block elements Notes for JEE Main 2015 Ednexa
 
Organisms and Environment Exercise - MH-CET 2015
Organisms and Environment Exercise - MH-CET 2015Organisms and Environment Exercise - MH-CET 2015
Organisms and Environment Exercise - MH-CET 2015Ednexa
 
Communication System Theory for JEE Main 2015
Communication System Theory for JEE Main 2015 Communication System Theory for JEE Main 2015
Communication System Theory for JEE Main 2015 Ednexa
 
Genetic Engineering and Genomics Notes - MH-CET 2015
Genetic Engineering and Genomics Notes - MH-CET 2015 Genetic Engineering and Genomics Notes - MH-CET 2015
Genetic Engineering and Genomics Notes - MH-CET 2015 Ednexa
 
Notes and Important Points on Circular Motion for JEE Main 2015
Notes and Important Points on Circular Motion for JEE Main 2015Notes and Important Points on Circular Motion for JEE Main 2015
Notes and Important Points on Circular Motion for JEE Main 2015Ednexa
 
Notes and Important Points on Electrochemistry - JEE Main 2015
Notes and Important Points on Electrochemistry - JEE Main 2015Notes and Important Points on Electrochemistry - JEE Main 2015
Notes and Important Points on Electrochemistry - JEE Main 2015Ednexa
 
Physics Sound and Waves for JEE Main 2015 - Part I
Physics Sound and Waves for JEE Main 2015 - Part IPhysics Sound and Waves for JEE Main 2015 - Part I
Physics Sound and Waves for JEE Main 2015 - Part IEdnexa
 
Notes and Important Points on Solid State - JEE Main 2015
Notes and Important Points on Solid State - JEE Main 2015 Notes and Important Points on Solid State - JEE Main 2015
Notes and Important Points on Solid State - JEE Main 2015 Ednexa
 
Study material 12th Physics - Wave Theory of Light Part II
 Study material 12th Physics - Wave Theory of Light Part II  Study material 12th Physics - Wave Theory of Light Part II
Study material 12th Physics - Wave Theory of Light Part II Ednexa
 
Physics in day to day life Notes for JEE Main 2015
Physics in day to day life Notes for JEE Main 2015 Physics in day to day life Notes for JEE Main 2015
Physics in day to day life Notes for JEE Main 2015 Ednexa
 
Summarized notes on Interference and Diffraction for JEE Main
Summarized notes on Interference and Diffraction for JEE MainSummarized notes on Interference and Diffraction for JEE Main
Summarized notes on Interference and Diffraction for JEE MainEdnexa
 

More from Ednexa (20)

Recommendation letters
Recommendation lettersRecommendation letters
Recommendation letters
 
Physics Measurements Notes for JEE Main 2015
Physics Measurements Notes for JEE Main 2015 Physics Measurements Notes for JEE Main 2015
Physics Measurements Notes for JEE Main 2015
 
Important Points on Elasticity for JEE Main 2015
Important Points on Elasticity for JEE Main 2015 Important Points on Elasticity for JEE Main 2015
Important Points on Elasticity for JEE Main 2015
 
Important points on Gravitation for JEE Main 2015
Important points on Gravitation for JEE Main 2015Important points on Gravitation for JEE Main 2015
Important points on Gravitation for JEE Main 2015
 
Current Electricity Notes for JEE Main 2015 - Part II
Current Electricity Notes for JEE Main 2015 - Part IICurrent Electricity Notes for JEE Main 2015 - Part II
Current Electricity Notes for JEE Main 2015 - Part II
 
Aldehydes Ketones and Carboxylic Acids - JEE Main 2015
Aldehydes Ketones and Carboxylic Acids - JEE Main 2015Aldehydes Ketones and Carboxylic Acids - JEE Main 2015
Aldehydes Ketones and Carboxylic Acids - JEE Main 2015
 
Physics - Current Electricity Notes for JEE Main 2015
Physics - Current Electricity Notes for JEE Main 2015Physics - Current Electricity Notes for JEE Main 2015
Physics - Current Electricity Notes for JEE Main 2015
 
Enhancement in Food Production Exercises - MH-CET 2015
Enhancement in Food Production Exercises - MH-CET 2015 Enhancement in Food Production Exercises - MH-CET 2015
Enhancement in Food Production Exercises - MH-CET 2015
 
Properties of Solids and Liquids Notes - JEE Main 2015
Properties of Solids and Liquids Notes - JEE Main 2015Properties of Solids and Liquids Notes - JEE Main 2015
Properties of Solids and Liquids Notes - JEE Main 2015
 
12th Chemistry P-block elements Notes for JEE Main 2015
12th Chemistry P-block elements Notes for JEE Main 2015 12th Chemistry P-block elements Notes for JEE Main 2015
12th Chemistry P-block elements Notes for JEE Main 2015
 
Organisms and Environment Exercise - MH-CET 2015
Organisms and Environment Exercise - MH-CET 2015Organisms and Environment Exercise - MH-CET 2015
Organisms and Environment Exercise - MH-CET 2015
 
Communication System Theory for JEE Main 2015
Communication System Theory for JEE Main 2015 Communication System Theory for JEE Main 2015
Communication System Theory for JEE Main 2015
 
Genetic Engineering and Genomics Notes - MH-CET 2015
Genetic Engineering and Genomics Notes - MH-CET 2015 Genetic Engineering and Genomics Notes - MH-CET 2015
Genetic Engineering and Genomics Notes - MH-CET 2015
 
Notes and Important Points on Circular Motion for JEE Main 2015
Notes and Important Points on Circular Motion for JEE Main 2015Notes and Important Points on Circular Motion for JEE Main 2015
Notes and Important Points on Circular Motion for JEE Main 2015
 
Notes and Important Points on Electrochemistry - JEE Main 2015
Notes and Important Points on Electrochemistry - JEE Main 2015Notes and Important Points on Electrochemistry - JEE Main 2015
Notes and Important Points on Electrochemistry - JEE Main 2015
 
Physics Sound and Waves for JEE Main 2015 - Part I
Physics Sound and Waves for JEE Main 2015 - Part IPhysics Sound and Waves for JEE Main 2015 - Part I
Physics Sound and Waves for JEE Main 2015 - Part I
 
Notes and Important Points on Solid State - JEE Main 2015
Notes and Important Points on Solid State - JEE Main 2015 Notes and Important Points on Solid State - JEE Main 2015
Notes and Important Points on Solid State - JEE Main 2015
 
Study material 12th Physics - Wave Theory of Light Part II
 Study material 12th Physics - Wave Theory of Light Part II  Study material 12th Physics - Wave Theory of Light Part II
Study material 12th Physics - Wave Theory of Light Part II
 
Physics in day to day life Notes for JEE Main 2015
Physics in day to day life Notes for JEE Main 2015 Physics in day to day life Notes for JEE Main 2015
Physics in day to day life Notes for JEE Main 2015
 
Summarized notes on Interference and Diffraction for JEE Main
Summarized notes on Interference and Diffraction for JEE MainSummarized notes on Interference and Diffraction for JEE Main
Summarized notes on Interference and Diffraction for JEE Main
 

Recently uploaded

LEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudLEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudDr. Bruce A. Johnson
 
3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptx3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptxmary850239
 
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...Nguyen Thanh Tu Collection
 
3.14.24 Gender Discrimination and Gender Inequity.pptx
3.14.24 Gender Discrimination and Gender Inequity.pptx3.14.24 Gender Discrimination and Gender Inequity.pptx
3.14.24 Gender Discrimination and Gender Inequity.pptxmary850239
 
PHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdf
PHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdfPHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdf
PHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdfSumit Tiwari
 
Quantitative research methodology and survey design
Quantitative research methodology and survey designQuantitative research methodology and survey design
Quantitative research methodology and survey designBalelaBoru
 
2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...Sandy Millin
 
Awards Presentation 2024 - March 12 2024
Awards Presentation 2024 - March 12 2024Awards Presentation 2024 - March 12 2024
Awards Presentation 2024 - March 12 2024bsellato
 
The basics of sentences session 8pptx.pptx
The basics of sentences session 8pptx.pptxThe basics of sentences session 8pptx.pptx
The basics of sentences session 8pptx.pptxheathfieldcps1
 
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in PharmacyASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in PharmacySumit Tiwari
 
25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...
25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...
25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...Nguyen Thanh Tu Collection
 
UNIT I Design Thinking and Explore.pptx
UNIT I  Design Thinking and Explore.pptxUNIT I  Design Thinking and Explore.pptx
UNIT I Design Thinking and Explore.pptxGOWSIKRAJA PALANISAMY
 
How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17
How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17
How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17Celine George
 
ICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdfICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdfVanessa Camilleri
 
LEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudLEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudDr. Bruce A. Johnson
 
The First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdfThe First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdfdogden2
 

Recently uploaded (20)

LEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudLEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced Stud
 
3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptx3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptx
 
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
 
t-test Parametric test Biostatics and Research Methodology
t-test Parametric test Biostatics and Research Methodologyt-test Parametric test Biostatics and Research Methodology
t-test Parametric test Biostatics and Research Methodology
 
3.14.24 Gender Discrimination and Gender Inequity.pptx
3.14.24 Gender Discrimination and Gender Inequity.pptx3.14.24 Gender Discrimination and Gender Inequity.pptx
3.14.24 Gender Discrimination and Gender Inequity.pptx
 
PHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdf
PHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdfPHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdf
PHARMACOGNOSY CHAPTER NO 5 CARMINATIVES AND G.pdf
 
Quantitative research methodology and survey design
Quantitative research methodology and survey designQuantitative research methodology and survey design
Quantitative research methodology and survey design
 
2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...
 
Awards Presentation 2024 - March 12 2024
Awards Presentation 2024 - March 12 2024Awards Presentation 2024 - March 12 2024
Awards Presentation 2024 - March 12 2024
 
The basics of sentences session 8pptx.pptx
The basics of sentences session 8pptx.pptxThe basics of sentences session 8pptx.pptx
The basics of sentences session 8pptx.pptx
 
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in PharmacyASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
 
25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...
25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...
25 CHUYÊN ĐỀ ÔN THI TỐT NGHIỆP THPT 2023 – BÀI TẬP PHÁT TRIỂN TỪ ĐỀ MINH HỌA...
 
UNIT I Design Thinking and Explore.pptx
UNIT I  Design Thinking and Explore.pptxUNIT I  Design Thinking and Explore.pptx
UNIT I Design Thinking and Explore.pptx
 
How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17
How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17
How to Customise Quotation's Appearance Using PDF Quote Builder in Odoo 17
 
ICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdfICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdf
 
Least Significance Difference:Biostatics and Research Methodology
Least Significance Difference:Biostatics and Research MethodologyLeast Significance Difference:Biostatics and Research Methodology
Least Significance Difference:Biostatics and Research Methodology
 
LEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudLEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced Stud
 
The First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdfThe First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdf
 
ANOVA Parametric test: Biostatics and Research Methodology
ANOVA Parametric test: Biostatics and Research MethodologyANOVA Parametric test: Biostatics and Research Methodology
ANOVA Parametric test: Biostatics and Research Methodology
 
Problems on Mean,Mode,Median Standard Deviation
Problems on Mean,Mode,Median Standard DeviationProblems on Mean,Mode,Median Standard Deviation
Problems on Mean,Mode,Median Standard Deviation
 

JEE Main 2014 Physics Syllabus - Stationary Waves

  • 1. 9011041155 / 9011031155 • Live Webinars (online lectures) with recordings. • Online Query Solving • Online MCQ tests with detailed solutions • Online Notes and Solved Exercises • Career Counseling 1
  • 2. 9011041155 / 9011031155 Stationary Waves Stationary Waves The resultant waves formed due to superposition of two exactly identical progressive waves, having same amplitude, wavelength and speed, travelling in the same medium, along the same path, but in opposite directions are called stationary waves. Characteristics of Stationary waves 1. Stationary waves are formed due to superposition of two exactly identical waves travelling through the same medium, along the same path but, in opposite directions. 2. When stationary waves are set up in a medium, the particles at some points are permanently at rest (i.e. amplitude is zero). Such points are called 2
  • 3. 9011041155 / 9011031155 ‘nodes’. The distance between two successive nodes is λ/2. 3. When stationary waves are set up in a medium, the particles at some points vibrate with maximum amplitude. Such points are called ‘antinodes’. Distance between two successive antinodes is λ /2. 4. Nodes and antinodes are alternately situated. The distance between any node and successive antinode is λ /4. 5. In stationary waves loops are formed between two successive nodes. All the particles in one loop are 3
  • 4. 9011041155 / 9011031155 in the same phase, while the particles in the successive loop are out of phase by πc. 6. Stationary waves are periodic in time and space. 7. Stationary waves do not transfer energy through the medium. 8. In stationary waves, all the particles except those at nodes, vibrate with same period as that of the interfering waves. 9. The amplitude of vibration is different for different particles and that increases from node to antinode. 10. A loop is formed between two successive nodes 4
  • 5. 9011041155 / 9011031155 because of two reasons. Firstly, the amplitude of vibration of the particles increases from node to antinode and decreases from antinode to node. Secondly, all the particles reach their maximum displacement at a time. 11. In case of stationary waves formed due to interference of longitudinal waves, displacement of the particle at the node is zero. But, pressure at the nodes changes between maximum to minimum. At antinodes, the displacement is maximum, but, the pressure remains constant. Hence, displacement nodes are called pressure antinodes and displacement antinodes are called pressure nodes. 5
  • 6. 9011041155 / 9011031155 Equation of a Stationary Wave y 1 a sin 2 t x T and y a sin 2 2 t T i.e. y = y1 + y2 y a sin 2 t x T a sin 2 t T x We know that, sin A sin B 2 sin A B 2 2 t 2 x y 2 a sin cos T 2 x put, 2a cos A 2 t T But,1 / T n y A sin 2 n t y A sin 6 A B cos 2 x
  • 7. 9011041155 / 9011031155 Hence, the resultant wave is also an S.H.M. with same period T. But, in this equation the term ± x/λ is absent. Thus, the resultant wave is not a progressive wave. It is travelling neither along + ve X - axis nor along - ve X-axis. Such a steady or localized wave is called Stationary Wave or Standing Wave. Transfer of energy is 0. Amplitude of the resultant wave varies between ± 2a 1. At nodes, i.e. A = 0 2 x 2 a cos 2 x x 2 0 , 3 ,5 ,....... 2 2 2 ,3 , 5 ,........ 2 2 7
  • 8. 9011041155 / 9011031155 distance between two successive nodes is, 3 2 2 2 OR 5 3 2 2 x x 2 x 0, 0, 2 i.e. A = ± 2a 2. At antinodes, 2a cos 2 and so on 2a i.e. cos 2 x 1 , 2 ,3 , ...... , 2 ,3 ,....... 2 2 2 Distance between two successive antinodes is, 2 0 2 or 2 2 2 2 and so on Hence, distance between successive nodes and antinodes is 2 or the nodes and antinodes are equidistant. Also, the distance between consecutive node and antinode is λ / 4. 8
  • 9. 9011041155 / 9011031155 M.C.Q. Q.1 The phase difference between the particles in successive loops of a stationary wave is (a.1) 90° Q.9 (b.1) 45° (c.1) 180° (d.1) zero Find the ‘wrong’ statement from the following: The equation of a stationary wave is given by , where y and x are in cm and t is in second. Then for the stationary wave, (a.9) Amplitude=3 cm (b.9) Wavelength=5cm (c.9) Frequency=20 Hz (d.9) Velocity=2 m/s Harmonics and Overtones The fundamental frequency along with its integral multiples are called harmonics. The fundamental frequency itself is the first than the harmonic. Vibrations fundamental of frequencies frequency which present are called overtones. 9 higher are actually
  • 10. 9011041155 / 9011031155 Free Oscillations The body starts oscillating about its mean position, on its own. Such vibrations are called free oscillations. The frequency of vibrations of the body is called ‘natural frequency of vibrations’ of the material of the body. Examples 1. Simple pendulum 2. Tuning fork 10
  • 12. 9011041155 / 9011031155 Damped oscillations Amplitude of free oscillations decreases because in every oscillation a little amount of energy is utilized to overcome the air resistance. So, the oscillations are called ‘damped oscillations’. Forced oscillations the body is forced to oscillate with a new frequency. Hence, such oscillations are called ‘forced oscillations’. The oscillations in the body due to an external periodic force whose frequency is different from natural frequency of vibration of the body are called forced vibrations. e.g. 1. 12
  • 14. 9011041155 / 9011031155 Resonance Amplitude of forced vibrations is inversely proportional to the difference between the natural frequency of vibrations of the body and the frequency of the external force (called forcing frequency or driving frequency). Thus, as the driving frequency approaches the natural frequency, the amplitude of vibration goes on increasing. Finally when the driving frequency matches exactly with the natural frequency, we get maximum amplitude of vibration. This effect is called resonance. Getting maximum amplitude of forced vibrations due to synchronization or matching between natural frequency and driving frequency is called resonance. 14
  • 17. 9011041155 / 9011031155 Q.65 In the experiment of a simple pendulum, the oscillations of the simple pendulum are actually (a.65) Free oscillations (c.65) Damped harmonic oscillations (b.65) Forced oscillation (d.65) Resonant oscillations Q.66 When a regiment of soldiers have to cross a suspension bridge, they are ordered to (a.66) March in steps (b.66) Break the steps (c.66) Stand in attention (d.66) Stand at ease Q.67 In the case of forced vibrations, the resonance becomes very sharp, when the (a.67) Restoring force is very small (b.67) Applied periodic force is small (c.67) Damping force is small (d.67) Quality factor is small • Ask Your Doubts • For inquiry and registration, call 9011041155 / 9011031155. 17