Introduction to Vibrations and Waves

ISBN-13: 9781118441084 / Angielski / Miękka / 2015 / 368 str.

H. J. Pain; Patricia Rankin

Opis

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 21^st 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

Spis treści

Acknowledgement xAbout the companion website xiPreface xiiIntroduction xiiiTable of Constants xivTable of Energy Storing Processes xv1 Simple Harmonic Motion 11.1 Displacement in Simple Harmonic Motion 41.2 Velocity and Acceleration in Simple Harmonic Motion 71.2.1 Non-linearity 81.3 Energy of a Simple Harmonic Oscillator 81.4 Simple Harmonic Oscillations in an Electrical System 121.5 Superposition of Two Simple Harmonic Vibrations in One Dimension 142 Damped Simple Harmonic Motion 212.1 Complex Numbers 222.2 The Exponential Series 222.2.1 The Exponential Series and the Law of Compound Interest 232.2.2 Note on the Binomial Theorem 252.2.3 Region 1. Heavy Damping (r2/4m2 > omega2 0) 282.2.4 Region 2. Critical Damping (r2/4m2 = omega2 0) 302.2.5 Region 3. Damped Simple Harmonic Motion (r2/4m22.3 Methods of Describing the Damping of an Oscillator 332.3.1 Logarithmic Decrement 332.3.2 Relaxation Time or Modulus of Decay 352.3.3 The Quality Factor or Q-value of a Damped Simple Harmonic Oscillator 352.3.4 Energy Dissipation 372.3.5 Damped SHM in an Electrical Circuit 383 The Forced Oscillator 413.1 The Operation of i upon a Vector 413.2 Vector Form of Ohm's Law 433.3 The Tuned LCR Circuit 453.4 Power Supplied to Oscillator by the Input Voltage 473.5 The Q-Value in Terms of the Resonance Absorption Bandwidth 483.6 The Forced Mechanical Oscillator 503.7 Behaviour of Velocity v in Magnitude and Phase versus Driving Force Frequency omega 563.8 Behaviour of Displacement x versus Driving Force Frequency omega 573.9 The Q-Value as an Amplification Factor 593.10 Significance of the Two Components of the Displacement Curve 603.11 Problem on Vibration Insulation 633.12 The Effect of the Transient Term 654 Coupled Oscillations 694.1 Stiffness (or Capacitance) Coupled Oscillators 694.2 Normal Modes of Vibration, Normal Coordinates and Degrees of Freedom 724.3 Mass or Inductance Coupling 774.4 Coupled Oscillations of a Loaded String 814.5 The Wave Equation 875 Transverse Wave Motion (1) 955.1 Partial Differentiation 955.2 Waves 985.3 Velocities in Wave Motion 995.4 The Wave Equation 995.5 Solution of the Wave Equation 1015.6 Characteristic Impedance of a String (the String as a Forced Oscillator) 1055.7 Reflection and Transmission of Waves on a String at a Boundary 1085.8 Reflection and Transmission of Energy 1125.9 The Reflected and Transmitted Intensity Coefficients 1135.10 Matching of Impedances 1135.11 Standing Waves on a String of Fixed Length 1135.12 Standing Wave Ratio 1165.13 Energy in Each Normal Mode of a Vibrating String 1166 Transverse Wave Motion (2) 1216.1 Wave Groups, Group Velocity and Dispersion 1216.1.1 Superposition of Two Waves of Almost Equal Frequencies 1216.1.2 Wave Groups, Group Velocity and Dispersion 1236.2 Wave Group of Many Components. The Bandwidth Theorem 1256.3 Heisenberg's Uncertainty Principle 1286.4 Transverse Waves in Periodic Structures (1) Waves in a Crystal 1296.5 Linear Array of Two Kinds of Atoms in an Ionic Crystal 1326.6 Transverse Waves in Periodic Structures (2) The Diffusion Equation, Energy Loss from Wave Systems 1357 Longitudinal Waves 1417.1 Sound Waves in Gases 1417.2 Energy Distribution in Sound Waves 1457.3 Intensity of Sound Waves 1487.4 Longitudinal Waves in a Solid 1497.5 Application to Earthquakes 1517.6 Reflection and Transmission of Sound Waves at Boundaries 1527.7 Reflection and Transmission of Sound Intensity 1547.8 Water Waves 1547.9 Doppler Effect 1568 Waves on Transmission Lines 1618.1 Ideal or Lossless Transmission Line 1638.2 Coaxial Cables 1648.3 Characteristic Impedance of a Transmission Line 1658.4 Reflections from the End of a Transmission Line 1678.5 Short Circuited Transmission Line (ZL =0) 1678.6 The Transmission Line as a Filter 1698.7 Effect of Resistance in a Transmission Line 1728.8 Characteristic Impedance of a Transmission Line with Resistance 1768.9 Matching Impedances 1789 Electromagnetic Waves 1839.1 Maxwell's Equations 1839.2 Electromagnetic Waves in a Medium having Finite Permeability mu and Permittivity but with Conductivity sigma =0 1869.3 The Wave Equation for Electromagnetic Waves 1889.4 Illustration of Poynting Vector 1899.5 Impedance of a Dielectric to Electromagnetic Waves 1919.6 Electromagnetic Waves in a Medium of Properties mu, and sigma (where sigma = 0) 1939.7 Skin Depth 1969.8 Electromagnetic Wave Velocity in a Conductor and Anomalous Dispersion 1979.9 When is a Medium a Conductor or a Dielectric? 1989.10 Why will an Electromagnetic Wave not Propagate into a Conductor? 1999.11 Impedance of a Conducting Medium to Electromagnetic Waves 2009.12 Reflection and Transmission of Electromagnetic Waves at a Boundary 2039.12.1 Normal Incidence 2039.13 Reflection from a Conductor (Normal Incidence) 20510 Waves in More Than One Dimension 20910.1 Plane Wave Representation in Two and Three Dimensions 20910.2 Wave Equation in Two Dimensions 21010.3 Wave Guides 21210.3.1 Reflection of a 2D Wave at Rigid Boundaries 21210.4 Normal Modes and the Method of Separation of Variables 21610.5 Two-Dimensional Case 21710.6 Three-Dimensional Case 21810.7 Normal Modes in Two Dimensions on a Rectangular Membrane 21910.8 Normal Modes in Three Dimensions 22110.9 3D Normal Frequency Modes and the de Broglie Wavelength 22310.10 Frequency Distribution of Energy Radiated from a Hot Body. Planck's Law 22310.11 Debye Theory of Specific Heats 22511 Fourier Methods 22911.1 Fourier Series 22911.1.1 Worked Example of Fourier Series 23311.1.2 Fourier Series for any Interval 23311.2 Application of Fourier Sine Series to a Triangular Function 23611.3 Application to the Energy in the Normal Modes of a Vibrating String 23711.4 Fourier Series Analysis of a Rectangular Velocity Pulse on a String 24011.5 Three-Phase Full Wave Rectification 24311.6 The Spectrum of a Fourier Series 24412 Waves in Optics (1) Interference 24912.1 Light. Waves or Rays? 24912.2 Fermat's Principle 25012.3 The Laws of Reflection 25112.4 The Law of Refraction 25312.5 Interference and Diffraction 25412.6 Interference 25412.7 Division of Amplitude 25412.8 Newton's Rings 25712.9 Michelson's Spectral Interferometer 25912.10 The Structure of Spectral Lines 26112.11 Fabry-Pérot Interferometer 26212.12 Resolving Power of the Fabry-Pérot Interferometer 26412.12.1 Resolving Power 26612.12.2 Finesse 26612.12.3 Free Spectral Range 26712.12.4 The Laser Cavity 26812.12.5 Total Internal Reflection 27012.12.6 The Thin Film Optical Wave Guide 27012.13 Division of Wavefront 27212.13.1 Interference between Waves from Two Slits or Sources 27212.14 Interference from Two Equal Sources of Separation f 27412.14.1 Separation f lambda. Young's Slit Experiment 27412.14.2 Separation f lambda (kf 1 where k = 2pi/lambda) 27912.14.3 Dipole Radiation (f lambda) 27912.15 Interference from Linear Array of N Equal Sources 28013 Waves in Optics (2) Diffraction 28713.1 Diffraction 28713.1.1 Fraunhofer Diffraction 28713.2 Scale of the Intensity Distribution 29013.3 Intensity Distribution for Interference with Diffraction from N Identical Slits 29013.4 Fraunhofer Diffraction for Two Equal Slits (N = 2) 29213.5 Transmission Diffraction Grating (N Large) 29313.6 Resolving Power of Diffraction Grating 29413.7 Resolving Power in Terms of the Bandwidth Theorem 29613.8 Fraunhofer Diffraction from a Rectangular Aperture 29713.9 Fraunhofer Diffraction from a Circular Aperture 29913.10 The Airy Disc and Resolving Power 30113.11 The Michelson Stellar Interferometer 30113.12 Fresnel Diffraction 30313.12.1 The Straight Edge and Slit 30313.12.2 Circular Aperture (Fresnel Diffraction) 30913.13 Zone Plate 31113.14 Electron Diffraction and Brillouin Zones 31214 Non-linear Oscillations 31714.1 Free Vibrations of an Anharmonic Oscillator - Large Amplitude Motion of a Simple Pendulum 31714.2 Forced Oscillations - Non-linear Restoring Force 31814.3 Thermal Expansion of a Crystal 32114.4 Non-linear Acoustic Waves and Shocks 32314.5 Mach Number 327Appendix 1 The Binomial Theorem 329Appendix 2 Taylor's and the Exponential Series 331Appendix 3 Superposition of a Large Number n of Simple Harmonic Vibrations of Equal Amplitude a and Equal Successive Phase Difference delta 333Appendix 4 Superposition of n Equal SHM Vectors of Length a with Random Phase phi 337Appendix 5 Electromagnetic Wave Equations: Vector Method 341Appendix 6 Planck's Radiation Law 343Appendix 7 Fraunhofer Diffraction from a Rectangular Aperture 345Appendix 8 Reflection and Transmission Coefficients for aWave Meeting a Boundary 347Index 349

O autorze

H. J. PainEmeritus, Department of Physics, Imperial College London, UKPatricia RankinDepartment of Physics, University of Colorado, USA