Study guide H C Verma JEE Physics Ch. 15 WAVE MOTION AND WAVES ON A STRING

JEE Syllabus

Wave motion (plane waves only) 15.1,
longitudinal and transverse waves 15.13, 15.14,
superposition of waves; 15.6
Progressive and stationary waves(15.9 ,10);
Vibration of strings 15.11, 12, 13

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Sections of the chapter

15.1 Wave motion
15.2 Wave pulse on a string
15.3 Sine wave travelling on a string
15.4 Velocity of a wave on a string
15.5 Power transmitted along the string by a sine wave
15.6 Interference and the Principle of Superposition
15.7 Interference of waves going in same direction
15.8 reflection and tramission of waves
15.9 Standing waves
15.10 Standing waves on a string fixed at both ends
15.11 analytic treatment of vibration of string fixed at both ends
15.12 Vibration of string fixed at both ends
15.13 Laws of Transverse vibrations of a string; Sonometer
15.14 Transverse and Longitudinal waves
15.15 Polarisation of waves
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Study Plan

Day 1

Concept review Ch.15 Wave Motion and Waves on a String

Study sections
15.1 and 15.2

       Video Lectures 15.1 Wave motion
       Video Lectures 15.2 Wave pulse on a string

Day 2

Study sections
15.3 and 15.4

Study sections
15.5 and 15.6

Day 3

Study sections
15.5 and 15.6
Do worked out examples 1,2,3

Day 4

Study sections
15.7 Interference of waves going the same direction
and
15.8 Reflection and transmission of waves

Read example 15.5

Study worked out examples 4 and 5

Day 5

Study sections
15.9 and 15.10

Day 6

Study sections
15.11 and 15.12
15,11 Analytical treatment of vibration of a string fixed at both end.
15.12 Vibration of a string fixed at one end

Study worked out examples 6 and 7

Day 7

Study 15.13 and 15.14

15.13 Laws of Transverse Vibrations of a string: Sonometer
15.14 Transverse and Longitudinal waves

Study example 15.8

Study worked out examples 7,8,9

Do exercise problems 1,2,3

Day 8

Study 15.15 Polarization of waves



Study worked out examples 10

Do exercise problems 4 to 10

Day 9

Revision
Concept review Ch.15 Wave Motion and Waves on a String
Wave Motion - Waves on a String - Laws
Formula Revision 15. Wave motion and waves on a string
     

Do exercise problems 11 to 20

Day 10

Do exercise problems 21 to 30

Day 11

Do exercise problems 31 - 35

Day 12

Do exercise problems 36 - 40


Day 13

Do exercise problems 41 - 45

Day 14

Do exercise problems 46 - 50

Day 15

Do exercise problems 51 - 55

Day 16

Do exercise problems 56 - 57

Day 17
Objective I 1 to 12

Day 18
Objective I 13 to 22

Day 19
Objective II

Day 20
Questions for short answer 1 to 8
















Concepts covered

Wave motion
Way of transporting energy from part of space to the other without any bulk motion of material together with it is wave motion. Sound is transmitted in air in this manner.

Waves that require a medium to travel are called mechanical waves and those which do not require a medium are called nonmechanical waves.

Travelling wave or progressive wave







---------------
Audiovisual lectures
Lesson 42: Wave Basics
www.curriki.org/nroc/Introductory_Physics_2/lesson42/Container.html

Lesson 43: Properties of Traveling Waves
www.curriki.org/nroc/Introductory_Physics_2/lesson43/Container.html

Lesson 44: Properties of Standing Waves
www.curriki.org/nroc/Introductory_Physics_2/lesson44/Container.html





Web sites

http://physics.pdx.edu/~larosaa/Ph-223/larosa_lecture_3.pdfnte

CBSE - JEE - Chapters from H C Verma - Study Guides, Revision Notes, Revision Questions and Problems, Lecture Videos

Concepts of Physics Part I by H C Verma




Chapters

1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity



H C Verma Book  Chapters - Study Guides

1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity




Chapters

1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity




Chapters

1. Introduction to physics
2. Physics and mathematics
3. Rest and motion :kinematics
4. The forces
5. Newtons law of motion
6. Friction
7. Circular motion
8. Work and energy
9. Centre of mass,linear momentum,collision
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity



Updated 11 Feb 2016, 16 May 2007

General Theory of Relativity in Hindi

जनरल थ्‍योरी ऑफ रिलेटिविटी  -  अल्‍बर्ट आइन्स्टीन (Albert Einstein)


कल्पना कीजिए एक  बिन्दु में विस्फोट होता है और वह कई भागों में बंट जाता है और भाग एक दूसरे से दूर जाने लगेंगे। और इसके लिये ये जगह को भी खुद से पैदा करेंगे।  सभी भाग विस्फोट हुए बिन्दु से बाहर की ओर सीढ़ी रेखा में चलते जायेंगे। किन्तु अगर ये भाग एक दूसरे को परस्पर किसी कमजोर बल द्वारा आकर्षित करें ? तो  इनकी गति सीढ़ी रेखा में नहीं रह जायेगी। अगर इन बिन्दुओं के समूह को आकाश माना जाये तो यह आकाश सीधा न होकर वक्र (curve) होगा


http://blog.scientificworld.in/2016/02/general-theory-of-relativity-in-hindi.html

JEE - CBSE - Physics Ch. 1 INTRODUCTION TO PHYSICS - Revision Questions

This blog was started along with my blog. Still being updated.

http://physicsgoeasy.blogspot.in/



Test on all chapters

http://www.mtel.nesinc.com/pdfs/ma_fld011_practice_test.pdf


http://www.topperlearning.com/study/cbse/class-11/physics/multiple-choice-questions/units-and-measurement/b101c3s4e23ch121#begin-test

Concept Review - Chapter 9 Centre of Mass, Collision

Centre of mass

Definition

Centre of mass of several groups of particles

Centre of mass of continuous bodies

Motion of centre of mass


Linear momentum

Principle of conservation of linear momentum

Collision

Elastic collision

Inelastic collision

Coefficient of restitution

Impulse

Impulse force




Centre of mass - Linear momentum - Videos



Updated 10 Jan 2016, 7 May 2008

Concept Review - Chapter 10 Rotational Mechanics

Rotation of a rigid body
Kinematics of rotation of rigid body
Torque of a force about the axis of rotation
Angular momentum
Conservation of angular momentum


Work done by a torque
Power delivered by a torque

Moment of inertia


Moment of inertia theorems
Theorem of parallel axes
Theorem of perpendicular axes
Combined rotation and translation
Rolling

Rotation of a rigid body

If each particle of a rigid body moves in a circle, with centres of all the circles on a straight line and with planes of the circles perpendicular to this line we say that the body is rotating about this line. The straight line is called the axis of rotation. (Particle makes circular motion. Rigid body makes rotation.)

Kinematics of rotation of rigid body

For a rigid body let the axis of rotation be Z-axis.
At time t =0, let particle P be at P₀.
Perpendicular to axis of rotation from P₀ be PQ. (Q is on the axis)
If at time t Particle P moves P₁ and angle P₀Q P₁ = θ.
Hence the particle has rotated through θ.
All particles have rotated through θ.
We can say the whole rigid body has rotated through angle θ.
The angular position of the body at time t is θ.
If P has made a complete revolution its circular path, every particle will do so and hence rigid body has done so. We can say rigid body made a complete revolution and it has rotated through an angle of 2 π radians.
Hence, rotation of a rigid body is measured by the rotation of a line PQ (P is a particle on the rigid body and Q is a point on the axis of rotation and PQ is perpendicular from P to the axis of rotation).

As the rotation of rigid body is defined in terms of the circular motion of a particle on the rigid body, kinematics of circular motion of particle becomes applicable to rotation.

Angular variables

θ = angular position of the particle

ω = angular velocity = d θ/dt = lim∆t→0 ∆θ/∆t

α = angular acceleration = d ω/dt = d²θ/dt²

If the angular acceleration is constant, formulas similar in form to linear formulas can be used to find the angular variables:

θ = ω₀t + ½ αt²

ω = ω₀ + αt

ω² = ω₀² + 2 α θ

Where

ω₀ is velocity at time t = 0.

Given the axis of rotation, the body can rotate in two directions – clockwise or anticlockwise. One of the directions has to be defined as positive direction according to the convenience of the problem.

The SI unit for angular velocity is radian/sec (rad/s).
One revolution/sec = 2 π radian/sec

Similar to the circular motion of the particle, in rotation for a particle P

s = Linear distance traveled by the particle in circular motion

∆s = Linear distance traveled by the particle in circular motion in time ∆t


∆s = r∆θ

Where
r = radius of the circle over which the particle is moving
∆θ = angular displacement in time ∆t

∆s/∆t = r∆θ/∆t

v = r ω
where
v = linear speed of the particle

a_t = rate of change of speed of the particle in circular motion

a_t = dv/dt = rdω/dt = r α




Rotational dynamics

In rotation of a body the resultant force due to external forces is zero, but the resultant of
Torque produced by the external forces is nonzero and this torque produces rotation motion.

Torque of a force about the axis of rotation

First we define torque a force about a point.
For a force F acting on a particle P, to find torque about a point O, define the position vector of P with respect to O. Let this position vector be r.

Torque of force F about O = Γ = F × r.
This is vector product of two vectors hence a vector quantity, as per the rules of vector product, the direction of Γ will be perpendicular to to F and r.

When the torque about an axis of rotation is to be determined, select a point on the axis of the rotation and find the torque of the force acting on a particle about this point. Find the angle between the axis and the line joining the point on axis (about which the torque is calculated) and the particle (one which the force is acting). Let the angle be θ.

Torque about the axis due to a force is the component along the axis, of the torque of the force about a point on the axis.

Magnitude of the torque = | F × r | cos θ

The torque about the axis is same, even if different points are chosen along the axis for determining the torque of the force about those points.

Some special cases of relation between force and the axis of rotation.

1. Force is parallel to the axis of rotation.
Torque along the axis is zero.

2. F and r are collinear. The torque about O is zero and the torque about axis is zero.

3. Force and axis are perpendicular but they do not intersect. In three dimensions, two lines may be perpendicular without intersecting. Example: A vertical line on
a wall and a horizontal line on the opposite wall.

In this case torque about the axis is equal to Force multiplied by the perpendicular to axis from the force direction (line along which the force is acting).


Torque produced by forces on a particle

A particle having circular motion will have two forces acting on it.
One force produces tangential acceleration dv/dt in it. Hence the force named tangential force is 'ma' = mdv/dt = mrα
This force creates a torque of mr²α

the other force creates radial acceleration or centripetal acceleration ω²r. Hence the force named radial force is mω²r
As intersects the axis of rotation, the torque produced by it is zero.

Hence total torque produced by a rigid body consisting of n particles is

Г(total) = Σm_ir_i²α

= αΣm_ir_i² as α is same for all particles

Let I = Σm_ir_i²

Г(total) = Iα

Quantity I is called moment of inertia of the body about the axis of rotation.

I = Σm_ir_i²

where

m_i = mass of the ith particle
r_i = perpendicular distance of ith particle from the axis of rotation.




Angular momentum

Conservation of angular momentum


Work done by a torque

Power delivered by a torque

Moment of inertia

Moment of Inertia

Torque created by external forces in rotating motion

When a particle is rotating it has tangential acceleration and radial acceleration.

Radial acceleration = ω²r

Hence radial force acting on it = m ω²r

Tangential acceleration = dv/dt = rdω/dt = r α
ω = angular velocity
α = angular acceleration
Tangential force = mrα

Torque created by radial force is zero as the force intersects the axis of rotation.
Tangential force and axis are skew (they do not intersect) and they are perpendicular. Thus the resultant torque is Force*radius = mr²α

In the case of a body having ‘n’ particles and rotating, the total torque is equal to torque acting on each of the particles

Total torque on the body = Γ(total) = Σ m_ir_i²α
Σ m_ir_i² is called as moment of inertia.

Moment of inertia can be calculated using the above formula for collection of discrete particles.

If the body is a continuous, the technique of integration needs to be used. We consider a small element of the body with mass dm and having a perpendicular distance from the axis or line about which moment of inertial is to be calculated.

We find ∫ r²dm under proper limits to get the moment of inertia of the body.

r²dm is the moment of inertia of the small element.

Determination of moment of inertia of representative bodies.

1. Uniform rod about a perpendicular

M = total mass of the body
l = length of the body
I = Ml²/12

I is obtained by taking a small element dx at a distance x from the centre of the rod.
Mass dm of the element = (M/l)*dx (M/l give mass per unit length)

dI = (M/l)*dx*x²
I = ∫(M/l)*dx*x² (limits are from –l/2 to l/2: these limits cover the entire rod).
= M/l[x³/3] from –l/2 to l/2
= M/3l[l³/8 + l³/8] = M/3l(l³/40) = Ml²/12

2. Moment of inertia of uniform rectangular plate about a line parallel to an edge and passing through the centre.

M = total mass of the body
Plate measurements l,b
Axis or line is parallel to b

I = Ml²/12

If the axis of line is parallel to l

I = Mb²/12



3. Circular ring
M = total mass of the body
R = radius

I = MR²

4. Uniform circular plate
M = total mass of the body
R = radius

I = MR²/2

5. Hollow cylinder about its axis

M = total mass of the body
R = radius

I = MR²


6. Uniform solid cylinder about its axis.

M = total mass of the body
R = radius

I = MR²/2

7. Hollow sphere about a diameter

M = total mass of the body
R = radius

I =(2/3) MR²

8. Uniform solid sphere about a diameter

M = total mass of the body
R = radius

I = (2/5) MR²


Moment of inertia theorems

Theorem of parallel axes

Thoerem of perpendicular axes

Combined rotation and translation

Rolling

Formula Sheet – Rotational Mechanics

Rotational kinematics

Angular variables

θ = angular position of the particle

ω = angular velocity = dθ/dt = lim∆t→0 ∆θ/∆t

α = angular acceleration = dω/dt = d²θ/dt²

If the angular acceleration is constant, formulas similar in form to linear formulas can be used to find the angular variables:

θ = ω₀t + ½ αt²

ω = ω₀ + αt

ω² = ω₀² + 2 α θ

where
ω₀ = angular velocity at the beginning

Relation between the linear motion of a particle of a rigid body and rotation of the rigid body

v = r ω
where
v = linear speed of the particle

a_t = rate of change of speed of the particle in circular motion

a_t = dv/dt = rdω/dt = r α (These relations are from the chapter of circular motion)

Updated 10 Jan 2016, 7 May 2008

Concept Review - Chapter 8 Work and Energy

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Physics Pathasala upload


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Updated 9 Jan 2016, 7 May 2008