Oscillations and Waves: An Introduction

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Features

  • Guides students through the subject of oscillations and waves in physical systems using a unified approach
  • Provides complete coverage of advanced topics in waves, such as electromagnetic wave propagation through the ionosphere
  • Offers examples from mechanical systems, elastic solids, electronic circuits, optical systems, and other areas
  • Includes numerous end-of-chapter exercises to test understanding

Solutions manual and figure slides available upon qualifying course adoption

Summary

Bridging lower-division physics survey courses with upper-division physics courses, Oscillations and Waves: An Introduction develops a unified mathematical theory of oscillations and waves in physical systems. Emphasizing physics over mathematics, the author includes many examples from discrete mechanical, optical, and quantum mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; and electromagnetic waves.

Assuming familiarity with the laws of physics and college-level mathematics, the book focuses on oscillations and waves whose governing differential equations are linear. The author covers aspects of optics that crucially depend on the wave-like nature of light, such as wave optics. He also introduces the conventional complex representation of oscillations and waves later in the text during the discussion of quantum mechanical waves. This helps students thoroughly understand how to represent oscillations and waves in terms of regular trigonometric functions before using the more convenient, but much more abstract, complex representation.

Based on the author’s longstanding course at the University of Texas at Austin, this classroom-tested text helps students acquire a sound physical understanding of wave phenomena. It eases students’ difficult transition between lower-division courses that mostly encompass algebraic equations and upper-division courses that rely on differential equations.

Table of Contents

Simple Harmonic Oscillation
Massona Spring
Simple Harmonic Oscillator Equation
LC Circuits
Simple Pendula
Compound Pendula

Damped and Driven Harmonic Oscillation
Damped Harmonic Oscillation
Quality Factor
LCR Circuits
Driven Damped Harmonic Oscillation
Driven LCR Circuits
Transient Oscillator Response

Coupled Oscillations
Two Spring-Coupled Masses
Two Coupled LC Circuits
Three Spring-Coupled Masses

Transverse Standing Waves
Normal Modes of a Beaded String
Normal Modes of a Uniform String
General Time Evolution of a Uniform String

Longitudinal Standing Waves
Spring-Coupled Masses
Longitudinal Waves on a Thin Elastic Rod
Sound Waves in an Ideal Gas
Fourier Analysis

Traveling Waves
Standing Waves in a Finite Continuous Medium
Traveling Waves in an Infinite Continuous Medium
Wave Interference
Energy Conservation
Transmission Lines
Normal Reflection and Transmission at Interfaces
Electromagnetic Waves
Doppler Effect
Wave Propagation in Inhomogeneous Media

Multi-Dimensional Waves
Plane Waves
Three-Dimensional Wave Equation
Cylindrical Waves
Spherical Waves
Oscillation of an Elastic Sheet
Polarization of Electromagnetic Waves
Laws of Geometric Optics
Fresnel Relations
Total Internal Reflection
Sound Waves in Fluids

Wave Pulses
Fourier Transforms
General Solution of One-Dimensional Wave Equation
Bandwidth

Dispersive Waves
Pulse Propagation
Electromagnetic Waves in Unmagnetized Plasmas
Faraday Rotation
Electromagnetic Wave Propagation in Conductors
Waveguides
Pulse Propagation in Two Dimensions
Gravity Waves
Wave Dragon Ships
Ship Wakes
Capillary Waves

Wave Optics
Introduction
Two-Slit Interference
Coherence
Multi-Slit Interference
Thin Film Interference
One-Dimensional Fourier Optics
Single-Slit Diffraction
Multi-Slit Diffraction
Two-Dimensional Fourier Optics

Wave Mechanics
Introduction
Photoelectric Effect
Electron Diffraction
Representation of Waves via Complex Numbers
Schrödinger’s Equation
Probability Interpretation of Wavefunction
Wave Packets
Heisenberg’s Uncertainty Principle
Wavefunction Collapse
Stationary States
Three-Dimensional Wave Mechanics
Particle in Finite Square Potential Well
Square Potential Barrier

Appendix A: Physical Constants
Appendix B: Useful Mathematics

Appendix C: Electromagnetic Theory

Bibliography

Index

Exercises appear at the end of each chapter.

Author Bio(s)

Richard Fitzpatrick is a professor of physics at the University of Texas at Austin, where he has been a faculty member since 1994. He is a member of the Royal Astronomical Society, a fellow of the American Physical Society, and the author of Maxwell’s Equations and the Principles of Electromagnetism and An Introduction to Celestial Mechanics. He earned a Master’s degree in physics from the University of Cambridge and a DPhil in astronomy from the University of Sussex.

Editorial Reviews

Oscillations and waves are ubiquitous in many physical situations. Universities now realise that instead of discussing these phenomena in different branches of physics, it is much more productive to have a core physics undergraduate course which encapsulates the reach physical phenomena such as advection, dispersion, diffraction, as well as non-linearity (solitons, shocks and chaos) in a single, generic course that encompasses the relevant elements of fluid dynamics, mechanics, optics, plasmas and quantum mechanics. There are surprisingly few good and more importantly recent, up-to-date textbooks available on the subject of Oscillations and Waves. Richard Fitzpatrick's Oscillations and Waves: An Introduction is an excellent addition to the existing literature on the subject. The book provides a clear, systematic, comprehensive and yet concise treatment of the subject. The emphasis is placed on physical interpretation rather than mathematical rigour, although the author certainly presents the material at the right mathematical level, commensurate with an advanced undergraduate course. The book will be equally useful for physics and engineering students, as well as mathematics students who want to get physical insight beyond the mathematical equations. The book benefits from very useful exercises which are accompanied by a solutions manual. As a physics educator, I would recommend this book without a reservation to both lecturers as excellent teaching material and to students as a learning resource which will guide them through the exciting world of waves, oscillations and patterns that are all around us.
—David Tsiklauri, Senior Lecturer in Astronomy, School of Physics and Astronomy, Queen Mary University of London, UK

"… The treatment is thorough … An unusual approach of the book is to postpone any use of complex representations until they are needed under the topic of quantum mechanics. The author argues that this allows the text to stress physical interpretations over mathematical solutions. Each chapter includes homework problems. Summing Up: Recommended. Lower- and upper-division undergraduates.
—E. Kincanon, Gonzaga University, in CHOICE Magazine, June 2013