Introduction to Vibrations and Waves

Based on the successful multi-edition book "The Physics of Vibrations and Waves" by John Pain, the authors carry over the simplicity and logic of the approach taken in the original first edition with its focus on the patterns underlying and connecting so many aspects of physical behavior, whilst bringing the subject up-to-date so it is relevant to teaching in the 21st century.
The transmission of energy by wave propagation is a key concept that has applications in almost every branch of physics with transmitting mediums essentially acting as a continuum of coupled oscillators. The characterization of these simple oscillators in terms of three parameters related to the storage, exchange, and dissipation of energy forms the basis of this book. The text moves naturally on from a discussion of basic concepts such as damped oscillations, diffraction and interference to more advanced topics such as transmission lines and attenuation, wave guides, diffusion, Fourier series, and electromagnetic waves in dielectrics and conductors. Throughout the text the emphasis on the underlying principles helps readers to develop their physics insight as an aid to problem solving.
This book provides undergraduate students of physics and engineering with the mathematical tools required for full mastery of the concepts. With worked examples presented throughout the text, as well as the Problem sets concluding each chapter, this textbook will enable students to develop their skills and measure their understanding of each topic step-by-step.
 
A companion website is also available, which includes solutions to chapter problems and PowerPoint slides.
Review of "The Physics of Vibrations and Waves 6e"
This is an excellent textbook, full of interesting material clearly explained and fully worthy of being studied by future contributors ..." Journal of Sound and Vibration

List of contents

Acknowledgement x
 
About the companion website xi
 
Preface xii
 
Introduction xiii
 
Table of Constants xiv
 
Table of Energy Storing Processes xv
 
1 Simple Harmonic Motion 1
 
1.1 Displacement in Simple Harmonic Motion 4
 
1.2 Velocity and Acceleration in Simple Harmonic Motion 7
 
1.2.1 Non-linearity 8
 
1.3 Energy of a Simple Harmonic Oscillator 8
 
1.4 Simple Harmonic Oscillations in an Electrical System 12
 
1.5 Superposition of Two Simple Harmonic Vibrations in One Dimension 14
 
2 Damped Simple Harmonic Motion 21
 
2.1 Complex Numbers 22
 
2.2 The Exponential Series 22
 
2.2.1 The Exponential Series and the Law of Compound Interest 23
 
2.2.2 Note on the Binomial Theorem 25
 
2.2.3 Region 1. Heavy Damping (r2/4m2 > omega2 0) 28
 
2.2.4 Region 2. Critical Damping (r2/4m2 = omega2 0) 30
 
2.2.5 Region 3. Damped Simple Harmonic Motion (r2/4m2
 
2.3 Methods of Describing the Damping of an Oscillator 33
 
2.3.1 Logarithmic Decrement 33
 
2.3.2 Relaxation Time or Modulus of Decay 35
 
2.3.3 The Quality Factor or Q-value of a Damped Simple Harmonic Oscillator 35
 
2.3.4 Energy Dissipation 37
 
2.3.5 Damped SHM in an Electrical Circuit 38
 
3 The Forced Oscillator 41
 
3.1 The Operation of i upon a Vector 41
 
3.2 Vector Form of Ohm's Law 43
 
3.3 The Tuned LCR Circuit 45
 
3.4 Power Supplied to Oscillator by the Input Voltage 47
 
3.5 The Q-Value in Terms of the Resonance Absorption Bandwidth 48
 
3.6 The Forced Mechanical Oscillator 50
 
3.7 Behaviour of Velocity v in Magnitude and Phase versus Driving Force Frequency omega 56
 
3.8 Behaviour of Displacement x versus Driving Force Frequency omega 57
 
3.9 The Q-Value as an Amplification Factor 59
 
3.10 Significance of the Two Components of the Displacement Curve 60
 
3.11 Problem on Vibration Insulation 63
 
3.12 The Effect of the Transient Term 65
 
4 Coupled Oscillations 69
 
4.1 Stiffness (or Capacitance) Coupled Oscillators 69
 
4.2 Normal Modes of Vibration, Normal Coordinates and Degrees of Freedom 72
 
4.3 Mass or Inductance Coupling 77
 
4.4 Coupled Oscillations of a Loaded String 81
 
4.5 The Wave Equation 87
 
5 Transverse Wave Motion (1) 95
 
5.1 Partial Differentiation 95
 
5.2 Waves 98
 
5.3 Velocities in Wave Motion 99
 
5.4 The Wave Equation 99
 
5.5 Solution of the Wave Equation 101
 
5.6 Characteristic Impedance of a String (the String as a Forced Oscillator) 105
 
5.7 Reflection and Transmission of Waves on a String at a Boundary 108
 
5.8 Reflection and Transmission of Energy 112
 
5.9 The Reflected and Transmitted Intensity Coefficients 113
 
5.10 Matching of Impedances 113
 
5.11 Standing Waves on a String of Fixed Length 113
 
5.12 Standing Wave Ratio 116
 
5.13 Energy in Each Normal Mode of a Vibrating String 116
 
6 Transverse Wave Motion (2) 121
 
6.1 Wave Groups, Group Velocity and Dispersion 121
 
6.1.1 Superposition of Two Waves of Almost Equal Frequencies 121
 
6.1.2 Wave Groups, Group Velocity and Dispersion 123
 
6.2 Wave Group of Many Components. The Bandwidth Theorem 125
 
6.3 Heisenberg's Uncertainty Principle 128
 
6.4 Transverse Waves in Periodic Structures (1) Waves in a Crystal 129
 
6.5 Linear Array of Two Kinds of Atoms in an Ionic Crystal 132
 
6.6 Transverse Waves in Periodic Structures (2) The Di

About the author

H. J. Pain
Emeritus, Department of Physics, Imperial College London, UK
Patricia Rankin
Department of Physics, University of Colorado, USA

Summary

Based on the successful multi-edition book "The Physics of Vibrations and Waves" by John Pain, the authors carry over the simplicity and logic of the approach taken in the original first edition with its focus on the patterns underlying and connecting so many aspects of physical behavior, whilst bringing the subject up-to-date so it is relevant to teaching in the 21st century.
The transmission of energy by wave propagation is a key concept that has applications in almost every branch of physics with transmitting mediums essentially acting as a continuum of coupled oscillators. The characterization of these simple oscillators in terms of three parameters related to the storage, exchange, and dissipation of energy forms the basis of this book. The text moves naturally on from a discussion of basic concepts such as damped oscillations, diffraction and interference to more advanced topics such as transmission lines and attenuation, wave guides, diffusion, Fourier series, and electromagnetic waves in dielectrics and conductors. Throughout the text the emphasis on the underlying principles helps readers to develop their physics insight as an aid to problem solving.
This book provides undergraduate students of physics and engineering with the mathematical tools required for full mastery of the concepts. With worked examples presented throughout the text, as well as the Problem sets concluding each chapter, this textbook will enable students to develop their skills and measure their understanding of each topic step-by-step.

A companion website is also available, which includes solutions to chapter problems and PowerPoint slides.
Review of "The Physics of Vibrations and Waves 6e"
This is an excellent textbook, full of interesting material clearly explained and fully worthy of being studied by future contributors ..." Journal of Sound and Vibration

Product details

• Authors: H Joh Pain, H John Pain, H. J. Pain, H. J. Rankin Pain, H. John Pain, H. John (Emeritus Reader Pain, H. John Rankin Pain, Hj Pain, Pain H. John, Patricia Rankin, Rankin Patricia
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 27.03.2015
• EAN: 9781118441107
• ISBN: 978-1-118-44110-7
• No. of pages: 368
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Electricity, magnetism, optics; Physik, Schwingung, Welle, Theoretische Physik, Physics, Industrial Engineering, Industrielle Verfahrenstechnik, Theoretical Physics, Allg. Physik, Allg. Industrielle Verfahrenstechnik