{"product_id":"introduction-to-vibrations-and-waves-isbn-9781118441084","title":"Introduction to Vibrations and Waves","description":"\u003cp\u003eBased 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\u003csup\u003est\u003c\/sup\u003e century.\u003cbr\u003e \u003cbr\u003e 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.\u003cbr\u003e \u003cbr\u003e 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.\u003cbr\u003e\u003cbr\u003eA companion website is also available, which includes solutions to chapter problems and PowerPoint slides.\u003cbr\u003e \u003cbr\u003e Review of “The Physics of Vibrations and Waves 6e“\u003cbr\u003e This is an excellent textbook, full of interesting material clearly explained and fully worthy of being studied by future contributors ...\" \u003ci\u003eJournal of Sound and Vibration\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eAcknowledgement x\u003c\/p\u003e \u003cp\u003eAbout the companion website xi\u003c\/p\u003e \u003cp\u003ePreface xii\u003c\/p\u003e \u003cp\u003eIntroduction xiii\u003c\/p\u003e \u003cp\u003eTable of Constants xiv\u003c\/p\u003e \u003cp\u003eTable of Energy Storing Processes xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Simple Harmonic Motion 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Displacement in Simple Harmonic Motion 4\u003c\/p\u003e \u003cp\u003e1.2 Velocity and Acceleration in Simple Harmonic Motion 7\u003c\/p\u003e \u003cp\u003e1.2.1 Non-linearity 8\u003c\/p\u003e \u003cp\u003e1.3 Energy of a Simple Harmonic Oscillator 8\u003c\/p\u003e \u003cp\u003e1.4 Simple Harmonic Oscillations in an Electrical System 12\u003c\/p\u003e \u003cp\u003e1.5 Superposition of Two Simple Harmonic Vibrations in One Dimension 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Damped Simple Harmonic Motion 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Complex Numbers 22\u003c\/p\u003e \u003cp\u003e2.2 The Exponential Series 22\u003c\/p\u003e \u003cp\u003e2.2.1 The Exponential Series and the Law of Compound Interest 23\u003c\/p\u003e \u003cp\u003e2.2.2 Note on the Binomial Theorem 25\u003c\/p\u003e \u003cp\u003e2.2.3 \u003ci\u003eRegion 1\u003c\/i\u003e. \u003ci\u003eHeavy Damping \u003c\/i\u003e(r\u003csup\u003e2\u003c\/sup\u003e\u003ci\u003e\/\u003c\/i\u003e4m\u003csup\u003e2\u003c\/sup\u003e \u003ci\u003e\u0026gt; ω\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e\u003csub\u003e0\u003c\/sub\u003e) 28\u003c\/p\u003e \u003cp\u003e2.2.4 \u003ci\u003eRegion 2\u003c\/i\u003e. \u003ci\u003eCritical Damping \u003c\/i\u003e(r\u003csup\u003e2\u003c\/sup\u003e\u003ci\u003e\/\u003c\/i\u003e4m\u003csup\u003e2\u003c\/sup\u003e = \u003ci\u003eω\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e\u003csub\u003e0\u003c\/sub\u003e) 30\u003c\/p\u003e \u003cp\u003e2.2.5 \u003ci\u003eRegion 3\u003c\/i\u003e. \u003ci\u003eDamped Simple Harmonic Motion \u003c\/i\u003e(r\u003csup\u003e2\u003c\/sup\u003e\u003ci\u003e\/\u003c\/i\u003e4m\u003csup\u003e2\u003c\/sup\u003e \u003ci\u003e\u0026lt; ω\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e\u003csub\u003e0\u003c\/sub\u003e) 31\u003c\/p\u003e \u003cp\u003e2.3 Methods of Describing the Damping of an Oscillator 33\u003c\/p\u003e \u003cp\u003e2.3.1 Logarithmic Decrement 33\u003c\/p\u003e \u003cp\u003e2.3.2 Relaxation Time or Modulus of Decay 35\u003c\/p\u003e \u003cp\u003e2.3.3 The Quality Factor or Q-value of a Damped Simple Harmonic Oscillator 35\u003c\/p\u003e \u003cp\u003e2.3.4 Energy Dissipation 37\u003c\/p\u003e \u003cp\u003e2.3.5 Damped SHM in an Electrical Circuit 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Forced Oscillator 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Operation of i upon a Vector 41\u003c\/p\u003e \u003cp\u003e3.2 Vector Form of Ohm’s Law 43\u003c\/p\u003e \u003cp\u003e3.3 The Tuned LCR Circuit 45\u003c\/p\u003e \u003cp\u003e3.4 Power Supplied to Oscillator by the Input Voltage 47\u003c\/p\u003e \u003cp\u003e3.5 The \u003ci\u003eQ\u003c\/i\u003e-Value in Terms of the Resonance Absorption Bandwidth 48\u003c\/p\u003e \u003cp\u003e3.6 The Forced Mechanical Oscillator 50\u003c\/p\u003e \u003cp\u003e3.7 Behaviour of Velocity \u003ci\u003ev \u003c\/i\u003ein Magnitude and Phase versus Driving Force Frequency \u003ci\u003eω \u003c\/i\u003e56\u003c\/p\u003e \u003cp\u003e3.8 Behaviour of Displacement \u003ci\u003ex \u003c\/i\u003eversus Driving Force Frequency \u003ci\u003eω \u003c\/i\u003e57\u003c\/p\u003e \u003cp\u003e3.9 The \u003ci\u003eQ\u003c\/i\u003e-Value as an Amplification Factor 59\u003c\/p\u003e \u003cp\u003e3.10 Significance of the Two Components of the Displacement Curve 60\u003c\/p\u003e \u003cp\u003e3.11 Problem on Vibration Insulation 63\u003c\/p\u003e \u003cp\u003e3.12 The Effect of the Transient Term 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Coupled Oscillations 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Stiffness (or Capacitance) Coupled Oscillators 69\u003c\/p\u003e \u003cp\u003e4.2 Normal Modes of Vibration, Normal Coordinates and Degrees of Freedom 72\u003c\/p\u003e \u003cp\u003e4.3 Mass or Inductance Coupling 77\u003c\/p\u003e \u003cp\u003e4.4 Coupled Oscillations of a Loaded String 81\u003c\/p\u003e \u003cp\u003e4.5 The Wave Equation 87\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Transverse Wave Motion (1) 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Partial Differentiation 95\u003c\/p\u003e \u003cp\u003e5.2 Waves 98\u003c\/p\u003e \u003cp\u003e5.3 Velocities in Wave Motion 99\u003c\/p\u003e \u003cp\u003e5.4 The Wave Equation 99\u003c\/p\u003e \u003cp\u003e5.5 Solution of the Wave Equation 101\u003c\/p\u003e \u003cp\u003e5.6 Characteristic Impedance of a String (the String as a Forced Oscillator) 105\u003c\/p\u003e \u003cp\u003e5.7 Reflection and Transmission of Waves on a String at a Boundary 108\u003c\/p\u003e \u003cp\u003e5.8 Reflection and Transmission of Energy 112\u003c\/p\u003e \u003cp\u003e5.9 The Reflected and Transmitted Intensity Coefficients 113\u003c\/p\u003e \u003cp\u003e5.10 Matching of Impedances 113\u003c\/p\u003e \u003cp\u003e5.11 Standing Waves on a String of Fixed Length 113\u003c\/p\u003e \u003cp\u003e5.12 Standing Wave Ratio 116\u003c\/p\u003e \u003cp\u003e5.13 Energy in Each Normal Mode of a Vibrating String 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Transverse Wave Motion (2) 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Wave Groups, Group Velocity and Dispersion 121\u003c\/p\u003e \u003cp\u003e6.1.1 Superposition of Two Waves of Almost Equal Frequencies 121\u003c\/p\u003e \u003cp\u003e6.1.2 Wave Groups, Group Velocity and Dispersion 123\u003c\/p\u003e \u003cp\u003e6.2 Wave Group of Many Components. The Bandwidth Theorem 125\u003c\/p\u003e \u003cp\u003e6.3 Heisenberg’s Uncertainty Principle 128\u003c\/p\u003e \u003cp\u003e6.4 Transverse Waves in Periodic Structures (1) Waves in a Crystal 129\u003c\/p\u003e \u003cp\u003e6.5 Linear Array of Two Kinds of Atoms in an Ionic Crystal 132\u003c\/p\u003e \u003cp\u003e6.6 Transverse Waves in Periodic Structures (2) The Diffusion Equation, Energy Loss from Wave Systems 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Longitudinal Waves 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Sound Waves in Gases 141\u003c\/p\u003e \u003cp\u003e7.2 Energy Distribution in Sound Waves 145\u003c\/p\u003e \u003cp\u003e7.3 Intensity of Sound Waves 148\u003c\/p\u003e \u003cp\u003e7.4 Longitudinal Waves in a Solid 149\u003c\/p\u003e \u003cp\u003e7.5 Application to Earthquakes 151\u003c\/p\u003e \u003cp\u003e7.6 Reflection and Transmission of Sound Waves at Boundaries 152\u003c\/p\u003e \u003cp\u003e7.7 Reflection and Transmission of Sound Intensity 154\u003c\/p\u003e \u003cp\u003e7.8 Water Waves 154\u003c\/p\u003e \u003cp\u003e7.9 Doppler Effect 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Waves on Transmission Lines 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Ideal or Lossless Transmission Line 163\u003c\/p\u003e \u003cp\u003e8.2 Coaxial Cables 164\u003c\/p\u003e \u003cp\u003e8.3 Characteristic Impedance of a Transmission Line 165\u003c\/p\u003e \u003cp\u003e8.4 Reflections from the End of a Transmission Line 167\u003c\/p\u003e \u003cp\u003e8.5 Short Circuited Transmission Line (\u003ci\u003eZ\u003csub\u003eL\u003c\/sub\u003e \u003c\/i\u003e=0) 167\u003c\/p\u003e \u003cp\u003e8.6 The Transmission Line as a Filter 169\u003c\/p\u003e \u003cp\u003e8.7 Effect of Resistance in a Transmission Line 172\u003c\/p\u003e \u003cp\u003e8.8 Characteristic Impedance of a Transmission Line with Resistance 176\u003c\/p\u003e \u003cp\u003e8.9 Matching Impedances 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Electromagnetic Waves 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Maxwell’s Equations 183\u003c\/p\u003e \u003cp\u003e9.2 Electromagnetic Waves in a Medium having Finite Permeability \u003ci\u003eμ \u003c\/i\u003eand Permittivity\u003ci\u003e ε \u003c\/i\u003ebut with Conductivity \u003ci\u003eσ \u003c\/i\u003e= 0 186\u003c\/p\u003e \u003cp\u003e9.3 The Wave Equation for Electromagnetic Waves 188\u003c\/p\u003e \u003cp\u003e9.4 Illustration of Poynting Vector 189\u003c\/p\u003e \u003cp\u003e9.5 Impedance of a Dielectric to Electromagnetic Waves 191\u003c\/p\u003e \u003cp\u003e9.6 Electromagnetic Waves in a Medium of Properties \u003ci\u003eμ\u003c\/i\u003e, \u003ci\u003eε \u003c\/i\u003eand \u003ci\u003eσ \u003c\/i\u003e(where \u003ci\u003eσ \u003c\/i\u003e\u003ci\u003e≠ \u003c\/i\u003e0) 193\u003c\/p\u003e \u003cp\u003e9.7 Skin Depth 196\u003c\/p\u003e \u003cp\u003e9.8 Electromagnetic Wave Velocity in a Conductor and Anomalous Dispersion 197\u003c\/p\u003e \u003cp\u003e9.9 When is a Medium a Conductor or a Dielectric? 198\u003c\/p\u003e \u003cp\u003e9.10 Why will an Electromagnetic Wave not Propagate into a Conductor? 199\u003c\/p\u003e \u003cp\u003e9.11 Impedance of a Conducting Medium to Electromagnetic Waves 200\u003c\/p\u003e \u003cp\u003e9.12 Reflection and Transmission of Electromagnetic Waves at a Boundary 203\u003c\/p\u003e \u003cp\u003e9.12.1 Normal Incidence 203\u003c\/p\u003e \u003cp\u003e9.13 Reflection from a Conductor (Normal Incidence) 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Waves in More Than One Dimension 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Plane Wave Representation in Two and Three Dimensions 209\u003c\/p\u003e \u003cp\u003e10.2 Wave Equation in Two Dimensions 210\u003c\/p\u003e \u003cp\u003e10.3 Wave Guides 212\u003c\/p\u003e \u003cp\u003e10.3.1 Reflection of a 2D Wave at Rigid Boundaries 212\u003c\/p\u003e \u003cp\u003e10.4 Normal Modes and the Method of Separation of Variables 216\u003c\/p\u003e \u003cp\u003e10.5 Two-Dimensional Case 217\u003c\/p\u003e \u003cp\u003e10.6 Three-Dimensional Case 218\u003c\/p\u003e \u003cp\u003e10.7 Normal Modes in Two Dimensions on a Rectangular Membrane 219\u003c\/p\u003e \u003cp\u003e10.8 Normal Modes in Three Dimensions 221\u003c\/p\u003e \u003cp\u003e10.9 3D Normal Frequency Modes and the de Broglie Wavelength 223\u003c\/p\u003e \u003cp\u003e10.10 Frequency Distribution of Energy Radiated from a Hot Body. Planck’s Law 223\u003c\/p\u003e \u003cp\u003e10.11 Debye Theory of Specific Heats 225\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Fourier Methods 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Fourier Series 229\u003c\/p\u003e \u003cp\u003e11.1.1 Worked Example of Fourier Series 233\u003c\/p\u003e \u003cp\u003e11.1.2 Fourier Series for any Interval 233\u003c\/p\u003e \u003cp\u003e11.2 Application of Fourier Sine Series to a Triangular Function 236\u003c\/p\u003e \u003cp\u003e11.3 Application to the Energy in the Normal Modes of a Vibrating String 237\u003c\/p\u003e \u003cp\u003e11.4 Fourier Series Analysis of a Rectangular Velocity Pulse on a String 240\u003c\/p\u003e \u003cp\u003e11.5 Three-Phase Full Wave Rectification 243\u003c\/p\u003e \u003cp\u003e11.6 The Spectrum of a Fourier Series 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Waves in Optics (1) Interference 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Light. Waves or Rays? 249\u003c\/p\u003e \u003cp\u003e12.2 Fermat’s Principle 250\u003c\/p\u003e \u003cp\u003e12.3 The Laws of Reflection 251\u003c\/p\u003e \u003cp\u003e12.4 The Law of Refraction 253\u003c\/p\u003e \u003cp\u003e12.5 Interference and Diffraction 254\u003c\/p\u003e \u003cp\u003e12.6 Interference 254\u003c\/p\u003e \u003cp\u003e12.7 Division of Amplitude 254\u003c\/p\u003e \u003cp\u003e12.8 Newton’s Rings 257\u003c\/p\u003e \u003cp\u003e12.9 Michelson’s Spectral Interferometer 259\u003c\/p\u003e \u003cp\u003e12.10 The Structure of Spectral Lines 261\u003c\/p\u003e \u003cp\u003e12.11 Fabry–Pérot Interferometer 262\u003c\/p\u003e \u003cp\u003e12.12 Resolving Power of the Fabry–Pérot Interferometer 264\u003c\/p\u003e \u003cp\u003e12.12.1 Resolving Power 266\u003c\/p\u003e \u003cp\u003e12.12.2 Finesse 266\u003c\/p\u003e \u003cp\u003e12.12.3 Free Spectral Range 267\u003c\/p\u003e \u003cp\u003e12.12.4 The Laser Cavity 268\u003c\/p\u003e \u003cp\u003e12.12.5 Total Internal Reflection 270\u003c\/p\u003e \u003cp\u003e12.12.6 The Thin Film Optical Wave Guide 270\u003c\/p\u003e \u003cp\u003e12.13 Division of Wavefront 272\u003c\/p\u003e \u003cp\u003e12.13.1 Interference between Waves from Two Slits or Sources 272\u003c\/p\u003e \u003cp\u003e12.14 Interference from Two Equal Sources of Separation \u003ci\u003ef \u003c\/i\u003e274\u003c\/p\u003e \u003cp\u003e12.14.1 Separation \u003ci\u003ef \u0026gt;\u0026gt; λ\u003c\/i\u003e. Young’s Slit Experiment 274\u003c\/p\u003e \u003cp\u003e12.14.2 Separation \u003ci\u003ef \u0026lt;\u0026lt; λ \u003c\/i\u003e(\u003ci\u003ekf \u0026lt;\u0026lt; \u003c\/i\u003e1 where \u003ci\u003ek \u003c\/i\u003e= 2\u003ci\u003eπ\/λ\u003c\/i\u003e) 279\u003c\/p\u003e \u003cp\u003e12.14.3 Dipole Radiation (\u003ci\u003ef \u0026lt;\u0026lt; λ\u003c\/i\u003e) 279\u003c\/p\u003e \u003cp\u003e12.15 Interference from Linear Array of \u003ci\u003eN \u003c\/i\u003eEqual Sources 280\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Waves in Optics (2) Diffraction 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Diffraction 287\u003c\/p\u003e \u003cp\u003e13.1.1 Fraunhofer Diffraction 287\u003c\/p\u003e \u003cp\u003e13.2 Scale of the Intensity Distribution 290\u003c\/p\u003e \u003cp\u003e13.3 Intensity Distribution for Interference with Diffraction from \u003ci\u003eN \u003c\/i\u003eIdentical Slits 290\u003c\/p\u003e \u003cp\u003e13.4 Fraunhofer Diffraction for Two Equal Slits (\u003ci\u003eN \u003c\/i\u003e= 2) 292\u003c\/p\u003e \u003cp\u003e13.5 Transmission Diffraction Grating (\u003ci\u003eN \u003c\/i\u003eLarge) 293\u003c\/p\u003e \u003cp\u003e13.6 Resolving Power of Diffraction Grating 294\u003c\/p\u003e \u003cp\u003e13.7 Resolving Power in Terms of the Bandwidth Theorem 296\u003c\/p\u003e \u003cp\u003e13.8 Fraunhofer Diffraction from a Rectangular Aperture 297\u003c\/p\u003e \u003cp\u003e13.9 Fraunhofer Diffraction from a Circular Aperture 299\u003c\/p\u003e \u003cp\u003e13.10 The Airy Disc and Resolving Power 301\u003c\/p\u003e \u003cp\u003e13.11 The Michelson Stellar Interferometer 301\u003c\/p\u003e \u003cp\u003e13.12 Fresnel Diffraction 303\u003c\/p\u003e \u003cp\u003e13.12.1 The Straight Edge and Slit 303\u003c\/p\u003e \u003cp\u003e13.12.2 Circular Aperture (Fresnel Diffraction) 309\u003c\/p\u003e \u003cp\u003e13.13 Zone Plate 311\u003c\/p\u003e \u003cp\u003e13.14 Electron Diffraction and Brillouin Zones 312\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Non-linear Oscillations 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Free Vibrations of an Anharmonic Oscillator – Large Amplitude Motion of a Simple Pendulum 317\u003c\/p\u003e \u003cp\u003e14.2 Forced Oscillations – Non-linear Restoring Force 318\u003c\/p\u003e \u003cp\u003e14.3 Thermal Expansion of a Crystal 321\u003c\/p\u003e \u003cp\u003e14.4 Non-linear Acoustic Waves and Shocks 323\u003c\/p\u003e \u003cp\u003e14.5 Mach Number 327\u003c\/p\u003e \u003cp\u003eAppendix 1 The Binomial Theorem 329\u003c\/p\u003e \u003cp\u003eAppendix 2 Taylor’s and the Exponential Series 331\u003c\/p\u003e \u003cp\u003eAppendix 3 Superposition of a Large Number \u003ci\u003en \u003c\/i\u003eof Simple Harmonic Vibrations of Equal Amplitude \u003ci\u003ea \u003c\/i\u003eand Equal Successive Phase Difference \u003ci\u003eδ \u003c\/i\u003e333\u003c\/p\u003e \u003cp\u003eAppendix 4 Superposition of \u003ci\u003en \u003c\/i\u003eEqual SHM Vectors of Length \u003ci\u003ea \u003c\/i\u003ewith Random Phase \u003ci\u003eφ \u003c\/i\u003e337\u003c\/p\u003e \u003cp\u003eAppendix 5 Electromagnetic Wave Equations: Vector Method 341\u003c\/p\u003e \u003cp\u003eAppendix 6 Planck’s Radiation Law 343\u003c\/p\u003e \u003cp\u003eAppendix 7 Fraunhofer Diffraction from a Rectangular Aperture 345\u003c\/p\u003e \u003cp\u003eAppendix 8 Reflection and Transmission Coefficients for a Wave Meeting a Boundary 347\u003c\/p\u003e \u003cp\u003eIndex 349\u003c\/p\u003e  \u003cp\u003e\u003cb\u003e\u003ci\u003eH. J. Pain\u003c\/i\u003e\u003c\/b\u003e Emeritus, Department of Physics, Imperial College London, UK \u003c\/p\u003e\u003cp\u003e\u003cb\u003e\u003ci\u003ePatricia Rankin\u003c\/i\u003e\u003c\/b\u003e Department of Physics, University of Colorado, USA   \u003c\/p\u003e\u003cp\u003eIntroduction to \u003cb\u003eVibrations and Waves\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003eBased on the successful multi-edition book, \u003ci\u003eThe Physics of Vibrations and Waves\u003c\/i\u003e, by John Pain. Here 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 behaviour, whilst bringing the subject up to date so it is relevant to teaching in the 21st century. \u003c\/p\u003e\u003cp\u003eThe 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 characterisation 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 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. \u003c\/p\u003e\u003cp\u003eThis 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. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eReview of\u003c\/b\u003e \u003cb\u003e\u003ci\u003eThe Physics of Vibrations and Waves,\u003c\/i\u003e\u003c\/b\u003e \u003cb\u003eSixth Edition\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003e'This is an excellent textbook, full of interesting material clearly explained and fully worthy of being studied by future contributors ...'\u003c\/i\u003e Journal of Sound and Vibration\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989469249765,"sku":"NP9781118441084","price":56.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118441084.jpg?v=1761784224","url":"https:\/\/k12savings.com\/es\/products\/introduction-to-vibrations-and-waves-isbn-9781118441084","provider":"K12savings","version":"1.0","type":"link"}