Oscillations and waves : an introduction / Richard Fitzpatrick
- Fitzpatrick, Richard, 1963-
- Boca Raton, FL : Taylor & Francis, 
- Copyright Date:
- Physical Description:
- viii, 287 pages : illustrations ; 24 cm
- Machine generated contents note: 1.Simple Harmonic Oscillation -- 1.1.Mass on a Spring -- 1.2.Simple Harmonic Oscillator Equation -- 1.3.LC Circuits -- 1.4.Simple Pendula -- 1.5.Compound Pendula -- Exercises -- 2.Damped and Driven Harmonic Oscillation -- 2.1.Damped Harmonic Oscillation -- 2.2.Quality Factor -- 2.3.LCR Circuits -- 2.4.Driven Damped Harmonic Oscillation -- 2.5.Driven LCR Circuits -- 2.6.Transient Oscillator Response -- Exercises -- 3.Coupled Oscillations -- 3.1.Two Spring-Coupled Masses -- 3.2.Two Coupled LC Circuits -- 3.3.Three Spring-Coupled Masses -- Exercises -- 4.Transverse Standing Waves -- 4.1.Normal Modes of a Beaded String -- 4.2.Normal Modes of a Uniform String -- 4.3.General Time Evolution of a Uniform String -- Exercises -- 5.Longitudinal Standing Waves -- 5.1.Spring-Coupled Masses -- 5.2.Longitudinal Waves on a Thin Elastic Rod -- 5.3.Sound Waves in an Ideal Gas -- 5.4.Fourier Analysis -- Exercises -- 6.Traveling Waves -- 6.1.Standing Waves in a Finite Continuous Medium -- 6.2.Traveling Waves in an Infinite Continuous Medium -- 6.3.Wave Interference -- 6.4.Energy Conservation -- 6.5.Transmission Lines -- 6.6.Normal Reflection and Transmission at Interfaces -- 6.7.Electromagnetic Waves -- 6.8.Doppler Effect -- 6.9.Wave Propagation in Inhomogeneous Media -- Exercises -- 7.Multi-Dimensional Waves -- 7.1.Plane Waves -- 7.2.Three-Dimensional Wave Equation -- 7.3.Cylindrical Waves -- 7.4.Spherical Waves -- 7.5.Oscillation of an Elastic Sheet -- 7.6.Polarization of Electromagnetic Waves -- 7.7.Laws of Geometric Optics -- 7.8.Fresnel Relations -- 7.9.Total Internal Reflection -- 7.10.Sound Waves in Fluids -- Exercises -- 8.Wave Pulses -- 8.1.Fourier Transforms -- 8.2.General Solution of ID Wave Equation -- 8.3.Bandwidth -- Exercises -- 9.Dispersive Waves -- 9.1.Pulse Propagation -- 9.2.Electromagnetic Waves in Unmagnetized Plasmas -- 9.3.Faraday Rotation -- 9.4.Electromagnetic Wave Propagation in Conductors -- 9.5.Waveguides -- 9.6.Pulse Propagation in Two Dimensions -- 9.7.Gravity Waves -- 9.8.Wave Drag on Ships -- 9.9.Ship Wakes -- 9.10.Capillary Waves -- Exercises -- 10.Wave Optics -- 10.1.Introduction -- 10.2.Two-Slit Interference -- 10.3.Coherence -- 10.4.Multi-Slit Interference -- 10.5.Thin Film Interference -- 10.6.One-Dimensional Fourier Optics -- 10.7.Single-Slit Diffraction -- 10.8.Multi-Slit Diffraction -- 10.9.Two-Dimensional Fourier Optics -- Exercises -- 11.Wave Mechanics -- 11.1.Introduction -- 11.2.Photoelectric Effect -- 11.3.Electron Diffraction -- 11.4.Representation of Waves via Complex Numbers -- 11.5.Schrodinger's Equation -- 11.6.Probability Interpretation of Wavefunction -- 11.7.Wave Packets -- 11.8.Heisenberg's Uncertainty Principle -- 11.9.Wavefunction Collapse -- 11.10.Stationary States -- 11.11.Three-Dimensional Wave Mechanics -- 11.12.Particle in Finite Square Potential Well -- 11.13.Square Potential Barrier -- Exercises -- A.Physical Constants -- B.Useful Mathematics -- B.1.Calculus -- B.2.Series Expansions -- B.3.Trigonometric Identities -- C.Electromagnetic Theory.
- "Preface Oscillations and waves are ubiquitous phenomena in the world around us. An oscillation is defined as a disturbance in a physical system that is repetitive in time. A wave is defined as a disturbance in a continuous, spatially extended, physical system that is both repetitive in time and periodic in space. In general, an oscillation involves a continual back and forth flow between two different energy types. For example, in the case of a pendulum, the two energy types are kinetic and gravitational potential energy. A wave involves similar repetitive energy flows to an oscillation, but, in addition, is capable of transmitting energy (and information) from one place to another. Although sound waves and electromagnetic waves, for example, rely on quite distinct physical mechanisms, they, nevertheless, share many common properties. This is also true of different types of oscillation. It turns out that the common factor linking the various types of wave and oscillation is that they are all described by the same mathematical equations. The aim of this textbook is to develop a unified mathematical theory of oscillations and waves. Examples are drawn from the physics of discrete mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; electromagnetic waves; optical systems; and, finally, quantum mechanical systems. It is assumed that readers of this book possess a basic familiarity with the laws of physics, such as might be obtained from a standard two-semester introductory college-level survey course. Readers are also assumed to be conversant with collegelevel mathematics up to and including algebra, trigonometry, linear algebra, ordinary differential equations, and partial differential equations"--
- 9781466566088 (pbk.) and 1466566086 (pbk.)
- Bibliography Note:
- Includes bibliographical references (pages 281-282) and index.
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