THE PHYSICS OF WAVES
CONTENTS 1 THE ESSENCE OF WAVE MOTION INTRODUCTION A LOCAL VIEW OF WAVE PROPAGATION CAUSE AND EFFECT EXAMPLES OF WAVE DISTURBANCE EXERCISES 2 WAVE EQUATIONS AND THEIR SOLUTION WAVE EQUATIONS WAVES ON LONG STRINGS 3 FURTHER WAVE EQUATIONS WAVES ALONG A COAXIAL CABLE ELECTROMAGNETIC WAVES OCEAN WAVES CAPILLARY WAVES GRAVITY WAVES IN COMPRESSIBLE ?UIDS WAVES AND WEATHER 4 SINUSOIDAL WAVEFORMS SINUSOIDAL SOLUTIONS ENERGY OF A WAVE MOTION THE TSUNAMI NORMAL MODES, STANDING WAVES AND ORTHOGONALITY 5 COMPLEX WAVEFUNCTIONS COMPLEX HARMONIC WAVES DISPERSION IN DISSIPATIVE SYSTEMS PHASORS AND GEOMETRIC SERIES 6 HUYGENS WAVE PROPAGATION HUYGENS’ MODEL OF WAVE PROPAGATION PROPAGATION IN FREE SPACE RE?ECTION AT AN INTERFACE REFRACTION AT AN INTERFACE FERMAT’S PRINCIPLE OF LEAST TIME 7 GEOMETRICAL OPTICS RAY OPTICS REFRACTION AT A SPHERICAL SURFACE THE THIN LENS FERMAT’S PRINCIPLE IN IMAGING 8 INTERFERENCE WAVE PROPAGATION AROUND OBSTRUCTIONS YOUNG’S DOUBLE-SLIT EXPERIMENT WAVEFRONT DIVIDERS THE MICHELSON INTERFEROMETER 9 FRAUNHOFER DIFFRACTION MORE WAVE PROPAGATION AROUND OBSTRUCTIONS DIFFRACTION BY A SINGLE SLIT BABINET’S PRINCIPLE THE DIFFRACTION GRATING WAVEFRONT RECONSTRUCTION AND HOLOGRAPHY DE?NITION OF FRAUNHOFER DIFFRACTION THE RESOLUTION OF AN IMAGING SYSTEM 10 LONGITUDINAL WAVES FURTHER EXAMPLES OF WAVE PROPAGATION SOUND WAVES IN AN ELASTIC MEDIUM THERMAL WAVES 11 CONTINUITY CONDITIONS WAVE PROPAGATION IN CHANGING MEDIA THE FRAYED GUITAR STRING GENERAL CONTINUITY CONDITIONS AND CHARACTERISTIC IMPEDANCE RE?ECTION AND TRANSMISSION BY MULTIPLE INTERFACES TOTAL INTERNAL RE?ECTION FRUSTRATED TOTAL INTERNAL RE?ECTION APPLICATIONS OF INTERNAL RE?ECTION AND EVANESCENT ?ELDS EVANESCENT-WAVE CONFUSIONS AND CONUNDRUMS 12 BOUNDARY CONDITIONS THE IMPOSITION OF EXTERNAL CONSTRAINTS THE GUITAR AND OTHER STRINGED MUSICAL INSTRUMENTS ORGAN PIPES AND WIND INSTRUMENTS BOUNDARY CONDITIONS IN OTHER SYSTEMS DRIVEN BOUNDARIES CYCLIC BOUNDARY CONDITIONS 13 LINEARITY AND SUPERPOSITIONS WAVE MOTIONS IN LINEAR SYSTEMS LINEARITY AND THE SUPERPOSITION PRINCIPLE WAVEPACKETS DISPERSION AND THE GROUP VELOCITY 14 FOURIER SERIES AND TRANSFORMS FOURIER SYNTHESIS AND ANALYSIS FOURIER SERIES AND THE ANALYSIS OF A PERIODIC FUNCTION ALTERNATIVE FORMS OF THE FOURIER TRANSFORM MATHEMATICAL JUSTI?CATION OF FOURIER’S PRINCIPLE THE SPECTRUM ORTHOGONALITY, POWER CALCULATIONS AND SPECTRAL INTENSITIES FOURIER ANALYSIS OF DISPERSIVE PROPAGATION THE CONVOLUTION OF WAVEFORMS FOURIER ANALYSIS OF FRAUNHOFER DIFFRACTION 14 10 FOURIER-TRANSFORM SPECTROSCOPY 15 WAVES IN THREE DIMENSIONS WAVES IN MULTIPLE DIMENSIONS WAVE EQUATIONS IN TWO AND THREE DIMENSIONS PLANE WAVES AND THE WAVEVECTOR FOURIER TRANSFORMS IN TWO AND THREE DIMENSIONS DIFFRACTION IN THREE DIMENSIONS WAVE RADIATION IN THREE DIMENSIONS POLARIZATION 16 OPERATORS FOR WAVE MOTIONS THE MATHEMATICAL OPERATOR OPERATORS FOR FREQUENCY AND WAVENUMBER THE EXPECTATION VALUE: THE MEAN VALUE OF AN OBSERVABLE THE UNCERTAINTY: THE STANDARD DEVIATION OF AN OBSERVABLE OPERATOR ANALYSIS OF A GAUSSIAN WAVEPACKET COMPLEX ELECTRICAL IMPEDANCES 17 UNCERTAINTY AND QUANTUM MECHANICS THE BANDWIDTH THEOREM WAVE–PARTICLE DUALITY THE QUANTUM-MECHANICAL WAVEFUNCTION MEASUREMENT OF THE QUANTUM WAVEFUNCTION 18 WAVES FROM MOVING SOURCES WAVES FROM SLOWLY MOVING SOURCES WAVES FROM QUICKLY MOVING SOURCES THE WAKE OF A SHIP UNDER WAY 19 RADIATION FROM MOVING CHARGES SOLUTION OF THE ELECTROMAGNETIC WAVE EQUATION RETARDED ELECTROMAGNETIC POTENTIALS RETARDED ELECTROMAGNETIC ?ELDS RADIATION FROM MOVING CHARGES