The book consists of twelve chapters that include the explanations of the properties of materials in details with fairness. This volume has study of Elasticity, Cantilever, Viscosity, Fluid dynamics, Surface Tension, Gravitation, Simple Harmonic Motion, Oscillations, Forced Oscillation, Damped Oscillation, Sound Waves and Doppler Effect is made to fulfill the requirements of different kinds of readers. This volume has to present illustrative examples of both the ideas and the methods. The book is intended as a text book on Properties of Matter, Waves and Oscillations for undergraduate levels and also as a reference book for anyone who is interested in this field of enquiry.
A lot of books on this topic are available in the market. Sometimes students are facing serious obstacles in their learning process due to their unavoidable situations and no previous much study of Properties of Matter, Waves and Oscillations. The book is comprehensive enough to cover all the topics that are usually taught to the upper undergraduate students of Physics. But because of the above mentioned features, this book will entertain students and teachers alike who have no previous much study of Properties of Matter, Waves and Oscillations. Hence, teachers of courses on Properties of Matter, Waves and Oscillations can use the book as their own lecture plans without any modification.
It is to be noted that the purpose of this book is to cover the basic principles and methods of Properties of Matter, Waves and Oscillations which are usually included in the course of teaching physics at the undergraduate levels. I hope that this book will be useful to the students and teachers in the different universities around the world.
Table of Contents
1. Elasticity
1.1 Elasticity and Coefficient of Elasticity [Modulus of Elasticity]
1.2 Hooke's law: Its application and importance
1.3 Stress: Its dimension, units and Elastic limit
1.4 Strain: A short description of different types of strain
1.5 Strain: A board description of different types of strain
1.6 Different types of modulus of elasticity
1.7 Poisson's Ratio and its limiting value from Young's modulus (Y) and Bulk modulus (K)
1.8 Experimental facts of Poisson's ratio: Maximum possible value of Poisson's ratio
1.9 The Work done during the three cases of strain
1.10 Shear is equivalent to compression and extension
1.11 Relation between Young modulus [Y], Bulk modulus [K] and Poisson ratio [ σ]
1.12 Establish the relation between Young's modulus [Y], rigidity modulus [η] and Poisson's ratio
1.13 Establish some important relations among Young modulus, Bulk modulus and rigidity modulus
1.14 Some important solved problems relevant to the chapter
1.15 Review and Summary
2. Cantilever
2.1 A concrete idea, advantages and disadvantages of cantilever
2.2 An Expression for the Bending Moment of a Beam
2.3 An expression for the depression of the free end of a cantilever fixed at one end and loaded at the other end
2.4 Determination for the bending of a bar supported at the two ends and loaded in the middle
2.5 When the beam is loaded uniformly
2.6 When the weight of the beam is effective
2.7 Cantilever loaded uniformly
2.8 Torsional rigidity of the cylinder or wire
2.9 Determination of the spring constant and effective mass of a spiral spring, and hence to determine the rigidity modulus of the material of the spring
2.10 Determination of the rigidity modulus of a wire by statical method
2.11 Determination of the Modulus of Rigidity of a Wire by the Method of Oscillations (Dynamic Method)
2.12 Conical Pendulum: A simple pendulum
2.13 Searle's Method for the Comparison of Young's Modulus and Coefficient of Rigidity for a given material
2.14 Some important solved problems are relevant to the chapter
2.15 Review and Summary
3. Viscosity
3.1 Viscosity: A recommence
3.2 Coefficient of viscosity and its dimension and units
3.3 Torricelli's Theorem: An acute recommence
3.4 Derivation of Torricelli's Theorem
3.5 Poiseuille's Equation: A brief description
3.6 Derivation of Poiseuille's Equation
3.7 Derivation of Stoke's Law
3.8 Stoke's law, its application and validity condition
3.9 Coefficient of viscosity of a liquid can be determined by Stoke's formula
3.10 Critical Velocity and explain Reynold's law on the basis of critical velocity
3.11 Some important problems are relevant to the chapters
3.12 Review and Summary
4. Fluid dynamics
4.1 Some general characteristics of fluid flow
4.2 Bernoulli's Theorem
4.3 Derivation of Bernoulli's Theorem
4.4 Applications of Bernoulli's equation
4.5 Equation of Continuity
4.6 Equation of Continuity: Quantum mechanical treatment
4.7 Some important solved problems relevant to the chapter
4.8 Review and Summary
5. Surface Tension
5.1 Surface Tension: A recommence
5.2 Acute comparison between molecular forces of cohesion and adhesion
5.3 Molecular Theory of Surface Tension
5.4 Surface Energy
5.5 Excess Pressure inside a Soap Bubble and Excess Pressure inside a Liquid Drop
5.6 Capillarity and Angle of Contact
5.7 Surface tension of water by capillary rise method
5.8 The excess of pressure inside a curved liquid surface is
5.9 Determination of surface tension and angle of contact of mercury: Quincke's method
5.10 Relation between surface tension and free surface energy of a surface
5.11 Some important solved problems relevant to the chapter
5.12 Review and Summary
6. Gravitation
6.1 State Newton's law of gravitation and gravitational constant
6.2 Difference between gravitational constant and acceleration due to gravity
6.3 Gravitational constant and it is called universal constant
6.4 Determination of gravitational constant G [universal constant] by Cavendish method
6.5 Inertial mass, Gravitational mass and Relativistic mass
6.6 Gravitational field and Gravitational intensity
6.7 The weights of bodies at the same place on the earth surface are exactly proportional to their inertial masses
6.8 Escape velocity and an expression of the escape velocity of a body from the surface of the earth
6.9 Kepler's Law of planetary motion
6.10 Mathematical expressions of Kepler's law of planetary motion: The law of areas
6.11 Mathematical expressions of Kepler's law of planetary motion: The law of orbits
6.12 Mathematical expressions of Kepler's law of planetary motion: The law of periods
6.13 The square of the period of revolution of any planet about the Sun is proportional to the cube of its mean distance from the Sun
6.14 Gravitational potential at a point distant r from a body of mass m
6.15 The gravitational potential and gravitational attraction due to a spherical shell bounded by spheres of radio a and b at a point
6.16 An expression for the gravitational potential and field due to uniform solid sphere
6.17 Gravitational potential and field at a point due to spherical shell
6.18 The potential and field (intensity) due to the circular plate or disc at a point P distance R from the center of the disc
6.19 Some important solved relevant problems of the chapter
6.20 Review and Summary
7. Simple Harmonic Motion
7.1 Simple Harmonic Motion and Characteristics of Simple Harmonic Motion
7.2 Harmonic motion and Simple Harmonic Motion: A rigid difference
7.3 Simple Harmonic Motion: Mathematical ground with Hooke's Law
7.4 Derivation of the Equation of Motion of SHM
7.5 Solution of the Equation of Motion of Simple Harmonic Oscillator [SHO]
7.6 Energy in Simple Harmonic Motion
7.7 Solution of Simple Harmonic Motion in Exponential Form
7.8 Time period and frequency of a body executing Simple Harmonic Motion [SHM]
7.9 Relation between simple harmonic motion and uniform circular motion
7.10 Composition of two simple harmonic vibrations at right angles to each other having equal frequencies but differing in phases and amplitudes
7.11 Lissajous' figures
7.12 Composition of two simple harmonic motions at right angles to each other and having time periods in the ratio 1:2
7.13 Some important problems of Simple Harmonic Motion
7.14 Review and summary
8. Oscillations
8.1 Oscillation and causes the oscillation
8.2 The Simple Pendulum
8.3 The Physical Pendulum
8.4 The Torsional Pendulum
8.5 Electromagnetic Oscillations: Analogy to Simple Harmonic Motion
8.6 Electromagnetic oscillation: A brief description
8.7 Electromagnetic Oscillations: Quantitative
8.8 Some important solved problems relevant to the chapter
8.9 Review and Summary
9. Forced Oscillations
9.1 Some important terms on Forced oscillations:
9.2 Harmonic Oscillator, Oscillatory Motion and example of Oscillatory Motion
9.3 Bound states and free states
9.4 Linear Harmonic Oscillator [L.H.O.] and interesting of Linear Harmonic Oscillator
9.5 Two-body Oscillation
9.6 Problem of an undamped oscillator with harmonic forcing: the amplitude and phase of the motion change with the frequency of the applied force
9.7 The general solution of forced oscillations of a system with a damping force undergoing forced oscillations at an angular frequency [ω]
9.8 A brief resume on damping and different types of damping expresses their property with suitable diagram
9.9 A system with a damping force undergoing forced oscillation at an angular frequency ω. The total energy of the system varies with time exponentially for an arbitrary value of ω. At resonance, the total energy is constant in time
9.10 Some important solved problems relevant to the chapter
9.11 Review and Summary
10. Damped Oscillations
10.1 Some important phenomenon regarding damped Oscillations:
10.2 Resonance and Resonant Frequency: A resume of description
10.3 Damped harmonic motion: Solution of Damped harmonic motion for different conditions
10.4 Energy of the damped system
10.5 Determination of the steady state motion of a forced oscillator if the driving force is of the form F = F0 sin ωt instead of F0 cos ωt
10.6 Some important solved problems relevant to the chapter
10.7 Review and Summary
11. Sound Waves
11.1 Introduction: Sound Waves
11.2 Some important phenomenon that are describing the sound waves acutely
11.3 Relation between Frequency and Time Period
11.4 Relation between Frequency and Wavelength
11.5 Sound Waves and Types of Sound Waves
11.6 Distinction between Transverse Wave and Longitudinal Wave
11.7 Distinction between Progressive Wave and Stationary Wave
11.8 Equation of motion of progressive wave
11.9 Interference of waves: Physical effects of superimposing two or more wave trains
11.10 Standing waves: Two wavetrains of the same frequency, speed and amplitude which are traveling in opposite directions along a string
11.11 Beats phenomenon: Two waves of slightly different frequencies combine to give a resultant wave whose amplitude varies periodically a time
11.12 Concept of a wave function and different types of simple harmonic wave
11.13 Physical significance [Interpretation] of Wave function
11.14 Some citations that be explained the physical meaning of wave function significantly
11.15 Limitations of Wave function
11.16 Matter Wave
11.17 Some important solved problems relevant to the chapter
11.18 Review and Summary
12. Doppler Effect
12.1 The Doppler Effect: Definition and a brief discussion
12.2 Common Example, reason and needs the observer and the source of Doppler Effect
12.3 Application of Doppler Effect
12.4 Observer is Moving but Source is at Rest
12.5 Source is moving but Observer is at Rest
12.6 When both Source and Observer are Moving
12.7 Concept of Doppler Effect
12.8 Travelling wave concepts
12.9 Various types of travelling waves
12.10 Some important solved problems relevant to the chapter
12.11 Review and Summary
Objectives and Scope
This textbook provides a comprehensive guide for upper-level undergraduate students to the fundamental principles of physics, specifically focusing on the properties of matter, waves, and oscillations. It aims to bridge the gap between theoretical understanding and practical application through detailed physical models, illustrative examples, and problem-solving exercises.
- Exploration of material properties, including elasticity, viscosity, and surface tension.
- In-depth analysis of fluid dynamics and wave motion, including sound and Doppler effects.
- Study of mechanical oscillations, covering simple harmonic, forced, and damped systems.
- Gravitational physics, including laws of motion, fields, and potential theories.
- Practical training through numerous solved problems and numerical examples.
Excerpt from the Book
1.1 Elasticity and Coefficient of Elasticity [Modulus of Elasticity]
When an external force acts on a body, there is change in its length, shape and volume. If the body retains its deformed shape and size when the deforming force is withdrawn, it is called a perfectly plastic body. On the other hand, if the body recovers its original shape and size when this external force is removed, it is said to be perfectly elastic. Therefore, elasticity is that property by virtue of which a deformed body tends to return to its original shape and size when he deforming force is removed.
Coefficient of Elasticity [Modulus of Elasticity]: Within the elastic limit, the stress developed is proportional to its corresponding strain. Mathematical
Stress ∝ Strain
Or, F = -kx
Or, Stress/Strain = Constant
The ratio stress/strain is constant and is known as coefficient of elasticity or modulus of elasticity. It depends upon the material and state of the body.
Summary of Chapters
Chapter 1: Covers the fundamental concepts of elasticity, Hooke's Law, and various moduli of elasticity.
Chapter 2: Discusses the mechanics of cantilevers, bending moments, and beam deflections.
Chapter 3: Details the theory of viscosity, Poiseuille’s equation, and Stokes' Law.
Chapter 4: Provides an overview of fluid dynamics, focusing on Bernoulli’s theorem and the equation of continuity.
Chapter 5: Explores surface tension, capillary rise, and the molecular theory of surfaces.
Chapter 6: Examines gravitation, Kepler’s laws, and gravitational potential.
Chapter 7: Explains simple harmonic motion, energy in oscillators, and Lissajous figures.
Chapter 8: Analyzes various forms of oscillations, including simple, physical, and torsional pendulums.
Chapter 9: Investigates forced oscillations, resonance, and the impact of driving frequencies.
Chapter 10: Covers damped oscillations, focusing on different damping conditions and energy decay.
Chapter 11: Discusses sound waves, interference, beats, and wave function concepts.
Chapter 12: Explains the Doppler Effect and its applications in light and sound.
Keywords
Elasticity, Hooke's Law, Viscosity, Fluid Dynamics, Bernoulli's Theorem, Surface Tension, Gravitation, Kepler's Laws, Simple Harmonic Motion, Oscillations, Damped Oscillations, Forced Oscillations, Doppler Effect, Sound Waves, Wave Function
Frequently Asked Questions
What is the primary focus of this textbook?
The book focuses on the study of the properties of matter, wave phenomena, and various types of oscillatory motion at an undergraduate physics level.
Who is the intended audience for this publication?
It is primarily designed for upper-level undergraduate students of physics, engineering, and applied sciences.
What research methodology does the author employ?
The author uses a structured pedagogical approach, combining theoretical derivation of physical laws with illustrative examples and practical solved numerical problems.
What are the core topics covered in the later chapters?
The latter part of the book focuses on sound wave propagation, the Doppler Effect, and an introduction to the physical significance of wave functions.
Does the book include practice material?
Yes, each of the twelve chapters concludes with an extensive exercise section containing theoretical and numerical problems.
What is the significance of the "Solved Problems" section?
These sections provide step-by-step guidance on how to apply the theoretical concepts covered in each chapter to real-world calculations, reinforcing understanding.
How is the Doppler Effect utilized in this text?
The text explains the Doppler Effect as a fundamental change in frequency due to relative motion, with applications ranging from simple acoustic examples to astronomical observations like red shift.
What is the relevance of studying Damped Oscillations?
Damped oscillations are critical for understanding how real-world systems lose energy over time, which is essential for the design of instruments and mechanical systems.
- Citation du texte
- Dr Alauddin Khan (Auteur), 2021, Properties of Matter, Waves and Oscillations. An Introduction to Basic Mechanics, Munich, GRIN Verlag, https://www.grin.com/document/984772
