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Introduction to the Physics of Waves

Book Description

Balancing concise mathematical analysis with the real-world examples and practical applications that inspire students, this textbook provides a clear and approachable introduction to the physics of waves. The author shows through a broad approach how wave phenomena can be observed in a variety of physical situations and explains how their characteristics are linked to specific physical rules, from Maxwell's equations to Newton's laws of motion. Building on the logic and simple physics behind each phenomenon, the book draws on everyday, practical applications of wave phenomena, ranging from electromagnetism to oceanography, helping to engage students and connect core theory with practice. Mathematical derivations are kept brief and textual commentary provides a non-mathematical perspective. Optional sections provide more examples along with higher-level analyses and discussion. This textbook introduces the physics of wave phenomena in a refreshingly approachable way, making it ideal for first- and second-year undergraduate students in the physical sciences.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Preface
  6. Acknowledgements
  7. Symbols
  8. 1 The Essence of Wave Motion
    1. 1.1 - Introduction
    2. 1.2 - A Local View of Wave Propagation
    3. 1.3 - Cause and Effect
    4. 1.4 - Examples of Wave Disturbance
    5. Exercises
  9. 2 Wave Equations and their Solution
    1. 2.1 - Wave Equations
    2. 2.2 - Waves on Long Strings
    3. Exercises
  10. 3 Further Wave Equations
    1. 3.1 - Waves Along a Coaxial Cable
    2. 3.2 - Electromagnetic Waves
    3. 3.3 - Ocean Waves
    4. 3.4 - Capillary Waves
    5. 3.5 - Gravity Waves in Compressible Fluids
    6. 3.6 - Waves and Weather
    7. Exercises
  11. 4 Sinusoidal Waveforms
    1. 4.1 - Sinusoidal Solutions
    2. 4.2 - Energy of a Wave Motion
    3. 4.3 - The Tsunami
    4. 4.4 - Normal Modes, Standing Waves and Orthogonality
    5. Exercises
  12. 5 Complex Wavefunctions
    1. 5.1 - Complex Harmonic Waves
    2. 5.2 - Dispersion in Dissipative Systems
    3. 5.3 - Phasors and Geometric Series
    4. Exercises
  13. 6 Huygens Wave Propagation
    1. 6.1 - Huygens’ Model of Wave Propagation
    2. 6.2 - Propagation in Free Space
    3. 6.3 - Reflection at an Interface
    4. 6.4 - Refraction at an Interface
    5. 6.5 - Fermat’s Principle of Least Time
    6. Exercises
  14. 7 Geometrical Optics
    1. 7.1 - Ray Optics
    2. 7.2 - Refraction at a Spherical Surface
    3. 7.3 - The Thin Lens
    4. 7.4 - Fermat’s Principle in Imaging
    5. Exercises
  15. 8 Interference
    1. 8.1 - Wave Propagation Around Obstructions
    2. 8.2 - Young’s Double-slit Experiment
    3. 8.3 - Wavefront Dividers
    4. 8.4 - The Michelson Interferometer
    5. Exercises
  16. 9 Fraunhofer Diffraction
    1. 9.1 - More Wave Propagation Around Obstructions
    2. 9.2 - Diffraction by a Single Slit
    3. 9.3 - Babinet’s Principle
    4. 9.4 - The Diffraction Grating
    5. 9.5 - Wavefront Reconstruction and Holography
    6. 9.6 - Definition of Fraunhofer Diffraction
    7. 9.7 - The Resolution of an Imaging System
    8. Exercises
  17. 10 Longitudinal Waves
    1. 10.1 - Further Examples of Wave Propagation
    2. 10.2 - Sound waves in an Elastic Medium
    3. 10.3 - Thermal Waves
    4. Exercises
  18. 11 Continuity Conditions
    1. 11.1 - Wave Propagation in Changing Media
    2. 11.2 - The Frayed Guitar String
    3. 11.3 - General Continuity Conditions and Characteristic Impedance
    4. 11.4 - Reflection and Transmission by Multiple Interfaces
    5. 11.5 - Total Internal Reflection
    6. 11.6 - Frustrated Total Internal Reflection
    7. 11.7 - Applications of Internal Reflection and Evanescent Fields
    8. 11.8 - Evanescent-Wave Confusions and Conundrums
    9. Exercises
  19. 12 Boundary Conditions
    1. 12.1 - The Imposition of External Constraints
    2. 12.2 - The Guitar and Other Stringed Musical Instruments
    3. 12.3 - Organ Pipes and Wind Instruments
    4. 12.4 - Boundary Conditions in Other Systems
    5. 12.5 - Driven Boundaries
    6. 12.6 - Cyclic Boundary Conditions
    7. Exercises
  20. 13 Linearity and Superpositions
    1. 13.1 - Wave Motions in Linear Systems
    2. 13.2 - Linearity and the Superposition Principle
    3. 13.3 - Wavepackets
    4. 13.4 - Dispersion and the Group Velocity
    5. Exercises
  21. 14 Fourier Series and Transforms
    1. 14.1 - Fourier Synthesis and Analysis
    2. 14.2 - Fourier Series and the Analysis of a Periodic Function
    3. 14.3 - Alternative Forms of the Fourier Transform
    4. 14.4 - Mathematical Justification of Fourier’s Principle
    5. 14.5 - The Spectrum
    6. 14.6 - Orthogonality, Power Calculations and Spectral Intensities
    7. 14.7 - Fourier Analysis of Dispersive Propagation
    8. 14.8 - The convolution of waveforms
    9. 14.9 - Fourier Analysis of Fraunhofer Diffraction
    10. 14.10 - Fourier-Transform Spectroscopy
    11. Exercises
  22. 15 Waves in Three Dimensions
    1. 15.1 - Waves in Multiple Dimensions
    2. 15.2 - Wave Equations in two and Three Dimensions
    3. 15.3 - Plane waves and the wavevector
    4. 15.4 - Fourier Transforms in Two and Three Dimensions
    5. 15.5 - Diffraction in Three Dimensions
    6. 15.6 - Wave Radiation in Three Dimensions
    7. 15.7 - Polarization
  23. 16 Operators for Wave Motions
    1. 16.1 - The Mathematical Operator
    2. 16.2 - Operators for Frequency and Wavenumber
    3. 16.3 - The Expectation Value: The Mean Value of an Observable
    4. 16.4 - The Uncertainty: The Standard Deviation of an Observable
    5. 16.5 - Operator Analysis of a Gaussian Wavepacket
    6. 16.6 - Complex Electrical Impedances
    7. Exercises
  24. 17 Uncertainty and Quantum Mechanics
    1. 17.1 - The Bandwidth Theorem
    2. 17.2 - Wave-Particle Duality
    3. 17.3 - The Quantum-Mechanical Wavefunction
    4. 17.4 - Measurement of the Quantum Wavefunction
    5. Exercises
  25. 18 Waves From Moving Sources
    1. 18.1 - Waves from Slowly Moving Sources
    2. 18.2 - Waves from Quickly Moving Sources
    3. 18.3 - The Wake of a Ship Under Way
    4. Exercises
  26. 19 Radiation from Moving Charges
    1. 19.1 - Solution of the Electromagnetic Wave Equation
    2. 19.2 - Retarded Electromagnetic Potentials
    3. 19.3 - Retarded Electromagnetic Fields
    4. 19.4 - Radiation from Moving Charges
    5. Exercises
  27. Appendix: Vector Mathematics
    1. A.1 - Cartesian Coordinates
    2. A.2 - Spherical Polar Coordinates
  28. References
  29. Index