Transcription of THE PHYSICS OF WAVES Version date - February 15, 2015
1 THE PHYSICS OF WAVESV ersion date - February 15, 2015 THE PHYSICS OF WAVESHOWARD GEORGIH arvard UniversityOriginally published byPRENTICE HALLE nglewood Cliffs, New Jersey 07632c 1993 by Prentice-Hall, Simon & Schuster CompanyEnglewood Cliffs, New Jersey 07632 All rights reserved. No part of this book may bereproduced, in any form or by any means,without permission in writing from the in the United States of America10 9 8 7 6 5 4 3 Prentice-Hall International (UK) Limited,LondonPrentice-Hall of Australia Pty. Limited,SydneyPrentice-Hall Canada Inc.,TorontoPrentice-Hall Hispanoamericana, ,MexicoPrentice-Hall of India Private Limited,New DelhiPrentice-Hall of Japan, Inc.
2 ,TokyoSimon & Schuster Asia Pte. Ltd.,SingaporeEditora Prentice-Hall do Brasil, Ltda.,Rio de JaneiroContents1 Harmonic Oscillation1 Preview.. The Harmonic Oscillator.. Small Oscillations and Linearity.. Time Translation Invariance.. Uniform Circular Motion.. Complex Numbers.. Some Definitions.. Arithmetic.. Complex Exponentials.. Notation.. Exponential Solutions.. *Building Up The Exponential.. What isH?.. Units Displacement and Energy.. Constant Energy.. The Torsion Pendulum.. A Simple Nonlinear Oscillator.
3 30 Chapter Checklist.. 32 Problems.. 332 Forced Oscillation and Resonance37 Preview.. Damped Oscillators.. Overdamped Oscillators.. Underdamped Oscillators.. Critically Damped Oscillators.. Forced Oscillations.. Resonance.. Work.. Resonance Width and Lifetime.. Phase Lag.. An Example.. Feeling It In Your Bones.. 48 Chapter Checklist.. 51 Problems.. 513 Normal Modes53 Preview.. More than One Degree of Freedom.. Two Coupled Oscillators.. Linearity and Normal Modes.. Oscillators.. Matrices.. *Inverse and Determinant.
4 More Useful Facts about Matrices.. Eigenvalue Equations.. The Matrix Equation of Motion.. Normal Modes.. Normal Modes and Frequencies.. Back to the 2 2 Example.. the General Case.. The Initial Value Problem.. *Normal Coordinates and Initial Values.. More on the Initial Value Problem.. *Matrices from Vectors.. *!2is Real.. *Forced Oscillations and Resonance.. Example.. 83 Chapter Checklist.. 86 Problems.. 874 Symmetries93 Preview.. Symmetries.. Beats.. A Less Trivial Example.. 99 Chapter Checklist.
5 104 CONTENTSviiProblems.. 1045 Waves107 Preview.. Space Translation Invariance.. The Infinite System.. Boundary Conditions.. Dispersion Relations.. The Dispersion Relation.. WAVES .. The Beaded String.. Fixed Ends.. Free Ends.. Normal Modes for Free Ends.. Forced Oscillations and Boundary Conditions.. Forced Oscillations with a Free End.. Generalization.. CoupledLCCircuits.. An Example of CoupledLCCircuits.. A Forced Oscillation Problem for CoupledLCCircuits.. 133 Chapter Checklist.. 134 Problems.. 1356 Continuum Limit and Fourier Series139 Preview.
6 The Continuum Limit.. Philosophy and Speculation.. Fourier series.. The String with Fixed Ends.. Free Ends.. Examples of Fourier Series.. Plucking a String.. 148 Chapter Checklist.. 149 Problems.. 1497 Longitudinal Oscillations and Sound153 Preview.. Longitudinal Modes in a Massive Spring.. Fixed Ends.. Free Ends.. A Mass on a Light Spring.. The Speed of Sound.. The Helmholtz Approximation.. Corrections to Helmholtz.. 165 Chapter Checklist.. 166 Problems.. 1678 Traveling Waves171 Preview.. Standing and Traveling WAVES .
7 What is It That is Moving?.. Boundary Conditions.. Force, Power and Impedance.. *Complex Impedance.. Light.. Plane WAVES .. Interferometers.. Quantum Interference.. Transmission Lines.. Parallel Plate Transmission Line.. WAVES in the Transmission Line.. Damping.. Free Oscillations.. Forced Oscillation.. High and Low Frequency Cut-Offs.. More on Coupled Pendulums.. 193 Chapter Checklist.. 197 Problems.. 1989 The Boundary at Infinity201 Preview.. Reflection and Transmission.. Forced Oscillation.. Infinite Systems.
8 Impedance Matching.. Looking at Reflected WAVES .. Power and Reflection.. Mass on a String.. Index of Refraction.. Reflection from a Dielectric Boundary.. *Transfer Matrices.. Two Masses on a String.. Reflection from a Thin Film.. Nonreflective Coating.. 219 Chapter Checklist.. 220 Problems.. 22110 Signals and Fourier Analysis225 Preview.. Signals in Forced Oscillation.. A Pulse on a String.. Fourier integrals.. Dispersive Media and Group Velocity.. Group Velocity.. Bandwidth, Fidelity, and Uncertainty.. A Solvable Example.
9 Broad Generalities.. Scattering of Wave Packets.. Scattering from a Boundary.. A Mass on a String.. Iscthe Speed of Light?.. 246 Chapter Checklist.. 250 Problems.. 25011 Two and Three Dimensions253 Preview.. The kVector.. The Difference between One and Two Dimensions.. Three Dimensions.. Sound WAVES .. Plane Boundaries.. Snell s Law the Translation Invariant Boundary.. Prisms.. Total Internal Reflection.. Tunneling.. Chladni Plates.. Waveguides.. Water.. Mathematics of Water WAVES .. Depth.. Lenses and Geometrical Optics.
10 Rainbows.. Spherical WAVES .. Chapter Checklist.. 316 Chapter Checklist.. 316 Problems.. 31712 Polarization333 Preview.. The String in Three Dimensions.. Polarization.. Electromagnetic WAVES .. General Electromagnetic Plane WAVES .. Energy and Intensity.. Circular Polarization and Spin.. Wave Plates and Polarizers.. Unpolarized Light.. Polarizers.. Wave Plates.. Matrices.. Optical Activity.. Crossed Polarizers and Quantum Mechanics.. Boundary between Dielectrics.. Polarization Perpendicular to the Scattering Plane.. Polarization in the Scattering Plane.
