Wave mechanics Books

305 products


  • Springer Nature Switzerland AG Acoustics: An Introduction to Its Physical Principles and Applications

    15 in stock

    Book SynopsisThis corrected version of the landmark 1981 textbook introduces the physical principles and theoretical basis of acoustics with deep mathematical rigor, concentrating on concepts and points of view that have proven useful in applications such as noise control, underwater sound, architectural acoustics, audio engineering, nondestructive testing, remote sensing, and medical ultrasonics.Since its publication, this text has been used as part of numerous acoustics-related courses across the world, and continues to be used widely today. During its writing, the book was fine-tuned according to insights gleaned from a broad range of classroom settings. Its careful design supports students in their pursuit of a firm foundation while allowing flexibility in course structure. The book can easily be used in single-term or full-year graduate courses and includes problems and answers. This rigorous and essential text is a must-have for any practicing or aspiring acoustician.Table of ContentsPreface List of Symbols Chapter 1 The Wave Theory of Sound 1-1 A Little History 1-2 The Conservation of Mass 1-3 Euler's Equation of Motion for a Fluid 1-4 Pressure-Density Relations 1-5 Equations of Linear Acoustics 1-6 The Wave Equation 1-7 Plane Traveling Waves 1-8 Waves of Constant Frequency 1-9 Speed of Sound and Ambient Density 1-10 Adiabatic versus Isothermal Sound Speeds 1-11 Acoustic Energy, Intensity, and Source Power 1-12 Spherical Waves Problems Chapter 2 Quantitative Measures of Sound 2-1 Frequency Content of Sounds 2-2 Proportional Frequency Bands 2-3 Levels and the Decibel 2-4 Frequency Weighting and Filters 2-5 Combining of Levels 2-6 Mutually Incoherent Sound Sources 2-7 Fourier Series and Long-Duration Sounds 2-8 Transient Waveforms 2-9 Transfer Functions 2-10 Stationary Ergodic Processes 2-11 Bias and Variance Problems Chapter 3 Reflection, Transmission, and Excitation of Plane Waves 3-1 Boundary Conditions at Impenetrable Surfaces 3-2 Plane-Wave Reflection at a Flat Rigid Surface 3-3 Specific Acoustic Impedance 3-4 Radiation of Sound by a Vibrating Piston within a Tube 3-5 Sound Radiation by Traveling Flexural Waves 3-6 Reflection and Transmission at an Interlace between Two Fluids 3-7 Multilayer Transmission and Reflection 3-8 Transmission through Thin Solid Slabs, Plates, and Blankets Problems Chapter 4 Radiation from Vibrating Bodies 4-1 Radially Oscillating Sphere 4-2 Transversely Oscillating Rigid Sphere 4-3 Monopoles and Green's Functions 4-4 Dipoles and Quadrupoles 4-5 Uniqueness of Solutions of Acoustic Boundary-Value Problems 4-6 The Kirchhoff-Helmholtz Integral Theorem 4-7 Sound Radiation from Small Vibrating Bodies 4-8 Radiation from a Circular Disk 4-9 Reciprocity in Acoustics 4-10 Transducers and Reciprocity Problems Chapter 5 Radiation from Sources Near and on Solid Surfaces 5-1 Sources near Plane Rigid Boundaries 5-2 Sources Mounted on Walls: The Rayleigh Integral; Fresnel-Kirchhoff Theory of Diffraction by an Aperture 5-3 Low-Frequency Radiation from Sources Mounted on Walls 5-4 Radiation Impedance of Baffled-Piston Radiators 5-5 Far-Field Radiation from Localized Wall Vibrations 5-6 Transient Solution for Baffled Circular Piston 5-7 Field on and near the Symmetry Axis 5-8 Transition to the Far Field Problems Chapter 6 Room Acoustics 6-1 The Sabine-Franklin-Jaeger Theory of Reverberant Rooms 6-2 Some Modifications 6-3 Applications of the Sabine-Franklin-Jaeger Theory 6-4 Coupled Rooms and Large Enclosures 6-5 The Modal Theory of Room Acoustics 6-6 High-Frequency Approximations 6-7 Statistical Aspects of Room Acoustics 6-8 Spatial Correlations in Diffuse Sound Fields Problems Chapter 7 Low-Frequency Models of Sound Transmission 7-1 Guided Waves 7-2 Lumped-Parameter Models 7-3 Guidelines for Selecting Lumped-Parameter Models 7-4 Helmholtz Resonators and Other Examples 7-5 Orifices 7-6 Estimation of Acoustic Inertances and End Corrections 7-7 Mufflers and Acoustic Filters 7-8 Homs Problems Chapter 8 Ray Acoustics 8-1 Wavefronts, Rays, and Fermat's Principle 8-2 Rectilinear Sound Propagation 8-3 Refraction in Inhomogeneous Media 8-4 Rays in Stratified Media 8-5 Amplitude Variation along Rays 8-6 Wave Amplitudes in Moving Media 8-7 Source above an Interface 8-8 Reflection from Curved Surfaces Problems Chapter 9 Scattering and Diffraction 9-1 Basic Scattering Concepts 9-2 Monostatic and Bistatic Scattering-Measurement Configurations 9-3 The Doppler Effect 9-4 Acoustic Fields near Caustics 9-5 Shadow Zones and Creeping Waves 9-6 Source or Listener on the Edge of a Wedge 9-7 Contour-Integral Solution for Diffraction by a Wedge 9-8 Geometrical-Acoustic and Diffracted-Wave Contributions for the Wedge Problem 9-9 Applications of Wedge-Diffraction Theory Problems Chapter 10 Effects of Viscosity and Other Dissipative Processes 10-1 The Navier-Stokes-Fourier Model 10-2 Linear Acoustic Equations and Energy Dissipation 10-3 Vorticity, Entropy, and Acoustic Modes 10-4 Acoustic Boundary-Layer Theory 10-5 Attenuation and Dispersion in Ducts and Thin Tubes 10-6 Viscosity Effects on Sound Radiation 10-7 Relaxation Processes 10-8 Absorption of Sound Problems Chapter 11 Nonlinear Effects in Sound Propagation 11-1 Nonlinear Steepening 11-2 Generation of Harmonics 11-3 Weak-Shock Theory 11-4 N Waves and Anomalous Energy Dissipation 11-5 Evolution of Sawtooth Waveforms 11-6 Nonlinear Dissipative Waves 11-7 Transition to Old Age 11-8 Nonlinear Effects in Converging and Diverging Waves 11-9 N Waves in Inhomogeneous Media; Spherical Waves 11-10 Ballistic Shocks; Sonic Booms Problems Indexes Name Index Subject Index

    15 in stock

    £44.99

  • The Physics of Music and Color: Sound and Light

    Springer Nature Switzerland AG The Physics of Music and Color: Sound and Light

    1 in stock

    Book SynopsisThis undergraduate textbook aids readers in studying music and color, which involve nearly the entire gamut of the fundamental laws of classical as well as atomic physics. The objective bases for these two subjects are, respectively, sound and light. Their corresponding underlying physical principles overlap greatly: Both music and color are manifestations of wave phenomena. As a result, commonalities exist as to the production, transmission, and detection of sound and light. Whereas traditional introductory physics textbooks are styled so that the basic principles are introduced first and are then applied, this book is based on a motivational approach: It introduces a subject with a set of related phenomena, challenging readers by calling for a physical basis for what is observed. A novel topic in the first edition and this second edition is a non-mathematical study of electric and magnetic fields and how they provide the basis for the propagation of electromagnetic waves, of light in particular. The book provides details for the calculation of color coordinates and luminosity from the spectral intensity of a beam of light as well as the relationship between these coordinates and the color coordinates of a color monitor. The second edition contains corrections to the first edition, the addition of more than ten new topics, new color figures, as well as more than forty new sample problems and end-of-chapter problems. The most notable additional topics are: the identification of two distinct spectral intensities and how they are related, beats in the sound from a Tibetan bell, AM and FM radio, the spectrogram, the short-time Fourier transform and its relation to the perception of a changing pitch, a detailed analysis of the transmittance of polarized light by a Polaroid sheet, brightness and luminosity, and the mysterious behavior of the photon.The Physics of Music and Color is written at a level suitable for college students without any scientific background, requiring only simple algebra and a passing familiarity with trigonometry. The numerous problems at the end of each chapter help the reader to fully grasp the subject.Table of ContentsChapter1: Introductory Remarks.- Chapter2: The Vibrating String.- Chapter3: The Nature of Sound; The Vibrating Air Column.- Chapter4: Energy.- Chapter5: Electricity & Magnetism.- Chapter6: The Atom as a Source of Light.- Chapter7: The Principle of Superposition.- Chapter 8: Complex Waves.- Chapter9: Propagation Phenomena.- Chapter10: The Ear.- Chapter11: Psychoacoustics.- Chapter12: Tuning, Intonation, and Temperament - Choosing Frequencies for Musical Notes.- Chapter13: The Eye.- Chapter14: Characterizing Light Sources, Color Filters, and Pigments.-Chapter15: Theory of Color Vision.- Appendices.

    1 in stock

    £49.49

  • Classical Guitar Design

    Springer Nature Switzerland AG Classical Guitar Design

    1 in stock

    Book SynopsisThis book describes the entire process of designing guitars, including the theory and guidelines for implementing it in practice. It discusses areas from acoustics and resonators to new tools and how they assist traditional construction techniques. The book begins by discussing the fundamentals of the sounds of a guitar, strings, and oscillating systems. It then moves on to resonators and acoustics within the guitar, explaining the analysis systems and evaluation methods, and comparing classic and modern techniques. Each area of the guitar is covered, from the soundboard and the back, to the process of closing the instrument. The book concludes with an analysis of historic and modern guitars. This book is of interest to luthiers wanting to advance their practice, guitar players wishing to learn more about their instruments, and academics in engineering and physics curious about the principles of acoustics when applied to musical instruments.Table of ContentsThe Sound.- The String.- Oscillating Systems.- The Resonator Components.- The Resonator as a Global System.- Upper Resonances.- Analysis Systems.- Quality and Evaluation Methods.- The Modern Guitar.- Building and Using the Mould.- The Soundboard on the Mould.- The Soundboard on the Frame.- The Back.- Closing the Instrument. Final Tuning.- Analysis of Historic and Modern Guitars

    1 in stock

    £113.99

  • Springer Nature Switzerland AG Auralization: Fundamentals of Acoustics, Modelling, Simulation, Algorithms and Acoustic Virtual Reality

    15 in stock

    Book SynopsisAuralization is the technique of creation and reproduction of sound on the basis of computer data. With this tool it is possible to predict the character of sound signals which are generated at the source and modified by reinforcement, propagation and transmission in systems such as rooms, buildings, vehicles or other technical devices. This book is organized as a comprehensive collection of the basics of sound and vibration, acoustic modelling, simulation, signal processing and audio reproduction. With some mathematical prerequisites, the readers will be able to follow the main strategy of auralization easily and work out their own implementations of auralization in various fields of application in architectural acoustics, acoustic engineering, sound design and virtual reality. For readers interested in basic research, the technique of auralization may be useful to create sound stimuli for specific investigations in linguistic, medical, neurological and psychological research, and in the field of human-machine interaction.Table of ContentsChapter1: Fundamentals of acoustics.- Chapter2: Sound sources.- Chapter3: Sound propagation.- Chapter4: Sound fields in cavities and in rooms.- Chapter5: Structure-borne sound.- Chapter6: Psychoacoustics.- Chapter7: Signal processing for auralization.- Chapter8: Characterization of sources.- Chapter9: Convolution and binaural sound synthesis.- Chapter10: Simulation methods.- Chapter11: Simulation of sound in rooms.- Chapter12: Simulation and auralization of outdoor sound propagation.- Chapter13: Simulation and auralization of airborne sound insulation.- Chapter14: Simulation and auralization of structure-borne sound.- Chapter15: Transfer path analysis and synthesis.- Chapter16: Filter construction for real-time processing.- Chapter17: 3D sound reproduction.- Chapter18: Acoustic Virtual Reality systems.

    15 in stock

    £113.99

  • Thermoacoustic Instability: A Complex Systems

    Springer Nature Switzerland AG Thermoacoustic Instability: A Complex Systems

    1 in stock

    Book SynopsisThis book systematically presents the consolidated findings of the phenomenon of self-organization observed during the onset of thermoacoustic instability using approaches from dynamical systems and complex systems theory. Over the last decade, several complex dynamical states beyond limit cycle oscillations such as quasiperiodicity, frequency-locking, period-n, chaos, strange non-chaos, and intermittency have been discovered in thermoacoustic systems operated in laminar and turbulent flow regimes. During the onset of thermoacoustic instability in turbulent systems, an ordered acoustic field and large coherent vortices emerge from the background of turbulent combustion. This emergence of order from disorder in both temporal and spatiotemporal dynamics is explored in the contexts of synchronization, pattern formation, collective interaction, multifractality, and complex networks. For the past six decades, the spontaneous emergence of large amplitude, self-sustained, tonal oscillations in confined combustion systems, characterized as thermoacoustic instability, has remained one of the most challenging areas of research. The presence of such instabilities continues to hinder the development and deployment of high-performance combustion systems used in power generation and propulsion applications. Even with the advent of sophisticated measurement techniques to aid experimental investigations and vast improvements in computational power necessary to capture flow physics in high fidelity simulations, conventional reductionist approaches have not succeeded in explaining the plethora of dynamical behaviors and the associated complexities that arise in practical combustion systems. As a result, models and theories based on such approaches are limited in their application to mitigate or evade thermoacoustic instabilities, which continue to be among the biggest concerns for engine manufacturers today. This book helps to overcome these limitations by providing appropriate methodologies to deal with nonlinear thermoacoustic oscillations, and by developing control strategies that can mitigate and forewarn thermoacoustic instabilities. The book is also beneficial to scientists and engineers studying the occurrence of several other instabilities, such as flow-induced vibrations, compressor surge, aeroacoustics and aeroelastic instabilities in diverse fluid-mechanical environments, to graduate students who intend to apply dynamical systems and complex systems approach to their areas of research, and to physicists who look for experimental applications of their theoretical findings on nonlinear and complex systems.Table of Contents1 Introduction 1.1 Introduction to thermoacoustic instability and its consequences 1.2 Mechanisms that cause thermoacoustic instability 1.2.1 Flame surface area modulations 1.2.2 Equivalence ratio fluctuations 1.2.3 Coherent structures in the flow 1.2.4 Entropy waves 1.3 Mechanisms that damp thermoacoustic instability 1.4 Current approaches: Acoustic oscillations driven by unsteady combustion, network modelling, and eigenvalues 1.5 Why do we need a nonlinear description? 1.6 Nonlinearities in a thermoacoustic system 1.7 Thermoacoustic stability analysis: Acoustic vs dynamical systems approach 1.8 Beyond limit cycles 1.9 Thermoacoustic instability in turbulent combustors 1.10 Transition to thermoacoustic instability in turbulent reacting flow systems 1.10.1 Is combustion noise deterministic or stochastic? 1.10.2 Studying the transition to thermoacoustic instability in “noisy” systems 1.10.3 Noise induced transition, stochastic bifurcation and Fokker-Planck equation 1.10.4 Is ‘signal plus noise’ paradigm the right way to go about? 1.11 Alternate perspectives 1.11.1 Combustion noise is chaos 1.11.2 Intermittency presages the onset of thermoacoustic instability 1.11.3 Multifractal description of combustion noise and its transition to thermoacoustic instability 1.11.4 Complex networks 1.11.5 On the importance of being nonlinear 1.11.6 Reductionist vs complex systems approach 1.12 References 2 Introduction to Dynamical Systems Theory 2.1 Dynamical system 2.1.1 Conservative and dissipative dynamical systems 2.1.2 Modeling dynamical systems as discrete and continuous functions of time 2.2 Linear approximation of one-dimensional systems 2.2.1 Two-dimensional linear systems 2.3 Bifurcations and their classification 2.3.1 Saddle-node bifurcation 2.3.2 Transcritical bifurcation 2.3.3 Pitchfork bifurcation 2.3.4 Hopf bifurcation 2.4 Signals and their classification 2.4.1 Limit cycle oscillations 2.4.2 Period-= oscillations 2.4.3 Quasiperiodic oscillations 2.4.4 Chaotic oscillations 2.4.5 Difference between strange chaotic, strange nonchaotic, and chaotic nonstrange attractors 2.4.6 Intermittency 2.5 Routes to chaos 2.5.1 Period-doubling route to chaos 2.5.2 Quasiperiodic route to chaos 2.5.3 Intermittency route to chaos 2.6 Phase space reconstruction 2.6.1 Selection of optimum time delay () 2.6.2 Selection of the minimum emending dimension (d) 2.7 Poincaré map (or Poincaré section or return map) 2.8 Recurrence plots 2.8.1 Cross recurrence plots 2.8.2 Joint recurrence plot 2.8.3 Recurrence quantification analysis 2.9 References 3 Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems 3.1 A brief history of Rijke-type thermoacoustic systems 3.2 Bifurcation characteristics of a deterministic thermoacoustic system 3.3 Noise-induced transition, triggering, and stochastic bifurcation to limit cycle 3.3.1 Effect of noise on hysteresis (or bistability) of a subcritical Hopf bifurcation 3.3.2 Stochastic (or P) bifurcation 3.3.3 Triggering in thermoacoustic systems 3.4 References 4 Thermoacoustic Instability: Beyond Limit Cycle Oscillations 4.1 Bifurcation of thermoacoustic instability beyond the state of limit cycle 4.2 Other dynamical states of thermoacoustic instability 4.2.1 Strange nonchaos 4.2.2 Intermittency 4.3 Routes to chaos for thermoacoustic oscillations 4.3.1 Period-doubling route to chaos 4.3.2 Ruelle-Takens-Newhouse route to chaos 4.3.3 Intermittency route to chaos 4.4 Nonlinear nature of flame-acoustic interactions 4.5 References 5 Thermoacoustic Instability is Self-Organization in a Complex System 5.1 Examples of complex systems 5.2 Nonlinearity: The reductionist’s nightmare 5.3 Emergence 5.4 Pattern formation 5.5 Order emerging from chaos 5.6 Onset of thermoacoustic instability in turbulent combustors 5.7 Fractals and multifractals 5.8 Collective interaction in complex systems 5.9 Complex networks 5.10 Why should we use complex systems approach to study thermoacoustic instability in turbulent combustors? 5.11 Practical applications 5.12 References 6 Intermittency - A State Precedes Thermoacoustic Instability and Blowout in Turbulent Combustors 6.1 Classification of sound waves generated by turbulent flame in a combustor 6.2 What is combustion noise? 6.2.1 Phase space dynamics of acoustic pressure fluctuations during combustion noise 6.2.2 0-1 test for chaos 6.3 What is thermoacoustic instability? 6.4 Transition from combustion noise to thermoacoustic instability in turbulent combustors 6.4.1 Reformulating the onset of thermoacoustic instability as a loss of chaos 6.4.2 Intermittency route to thermoacoustic instability 6.4.3 Characteristics of the intermittency signal 6.4.4 Bifurcation analysis of intermittency route to thermoacoustic instability 6.5 Phase space and recurrence analysis of the intermittency route to thermoacoustic instability 6.6 Intermittency route to flame blowout 6.7 Type of intermittency en-route to thermoacoustic instability and its scaling laws 6.8 References 7 Spatiotemporal Dynamics of Flow, Flame, and Acoustic Fields during the Onset of Thermoacoustic Instability 7.1 Pattern formation 7.2 The emergence of patterns during the onset of thermoacoustic instability 7.3 Collective interaction of large-scale vortices during thermoacoustic instability 7.4 References 8 Synchronization of Self-excited Acoustics and Turbulent Reacting Flow Dynamics 8.1 Basics of synchronization of coupled oscillators 8.2 Mutual synchronization of the acoustic and turbulent reactive flow fields during the transition to thermoacoustic instability 8.2.1 Coupled behavior of the acoustic field and the heat release rate field in a turbulent combustor 8.2.2 Synchronization of the acoustic pressure and the global heat release rate signals during the onset of thermoacoustic instability 8.2.3 Spatiotemporal synchronization of the turbulent reacting flow field with the duct acoustics 8.3 Forced synchronization of limit cycle oscillations in thermoacoustic systems 8.3.1 Forced response of the self-excited acoustic field 8.3.2 Forced synchronization of limit cycle oscillations in a horizontal Rijke tube 8.3.3 Characteristics of the acoustic field and the heat release rate field during forced synchronization in a laminar combustor 8.3.4 Forced synchronization of multi-frequency (quasiperiodic and chaotic) thermoacoustic oscillations 8.3.5 Characteristics of forced synchronization of limit cycle oscillations in turbulent combustors 8.3.6 Forced synchronization of self-excited oscillations in the hydrodynamic field 8.4 References 9 Model for Intermittency Route to Thermoacoustic Instability 9.1 Governing equations for the one-dimensional fluid flow. 9.1.1 Continuity equation 9.1.2 Momentum equation 9.1.3 Energy equation 9.1.4 Linearized governing equations for the acoustic field 9.2 Model for intermittency route to thermoacoustic instability 9.3 References 10 Multifractal Analysis of a Turbulent Thermoacoustic System 10.1 Fractals 10.2 The Hurst exponent and fractal properties 10.3 Multifractals 10.4 Methods of multifractal analysis 10.4.1 Multifractal detrended fluctuation analysis (MFDFA) 10.4.2 Box-counting method 10.5 Combustion noise is multifractal and thermoacoustic instability is a loss of multifractality 10.6 Multifractal analysis during the transition to a flame blowout 10.7 Multifractal analysis of spatial flame structures during stable and unstable operation 10.8 References 11 Complex Network Approach to Thermoacoustic Systems 11.1 An introduction to complex networks 11.2 Measures of complex networks 11.3 Types of complex networks 11.3.1 Regular networks 11.3.2 Random network 11.3.3 Small-world networks 11.3.4 Scale-free networks 11.4 Complex network approach to study temporal dynamics of thermoacoustic systems 11.4.1 Combustion noise is scale-free 11.4.2 The onset of thermoacoustic instability as a transition from scale-free to regular networks 11.4.3 Small-world-like behavior of thermoacoustic instability using cycle network 11.4.4 Recurrence network topologies of different dynamical states of a thermoacoustic system 11.4.5 Directional dependence between the coupled acoustic pressure and heat release rate fluctuations using recurrence networks 11.5 Complex network approach to study spatial dynamics of thermoacoustic systems 11.5.1 Unweighted spatial networks of the time-averaged flow field using the Pearson coefficient 11.5.2 Weighted time-varying spatial networks obtained though acoustic power and vorticity fields 11.5.3 Weighted time-varying turbulence networks obtained though vorticity fields 11.6 References 12 Early Warning and Mitigation Strategies for Thermoacoustic Instability 12.1 Precursors for the onset of impending thermoacoustic instability . . . 418 12.2 Traditional approaches for passive and active controls of thermoacoustic instability 12.3 Control of thermoacoustic instability using methodologies from synchronization theory 12.3.1 Mitigation of thermoacoustic instability using amplitude death phenomenon 12.3.2 Open-loop control of thermoacoustic instability through asynchronous quenching 12.4 Identification of critical regions in the spatial reacting field 12.5 References 13 Oscillatory Instabilities in Other Fluid Systems 13.1 Aeroacoustic instabilities 13.2 Aeroelastic instabilities 13.3 References 14 Summary and Perspective 14.1 Temporal analysis 14.2 Spatiotemporal analysis 14.3 Mitigation Strategies 14.3.1 Evasion 14.3.2 Strategies based on the framework of synchronization theory 14.3.3 Smart passive control 14.4 Future issues 14.5 Final thoughts 14.6 References

    1 in stock

    £123.49

  • Lecture Notes on Acoustics and Noise Control

    Springer Nature Switzerland AG Lecture Notes on Acoustics and Noise Control

    1 in stock

    Book SynopsisThis textbook provides a guide to the fundamental principles of acoustics in a straightforward manner using a solid foundation in mathematics and physics. It is designed for those who are new to acoustics and noise control, and includes all the necessary material for a comprehensive understanding of the topic. It is written in lecture-note style and can be easily adapted to an acoustics-related one semester course at the senior undergraduate or graduate level. The book also serves as a ready reference for the practicing engineer new to the application of acoustic principles arising in product design and fabrication.Table of ContentsComplex Numbers for Harmonic Functions.- Solutions of Acoustic Wave Equation.- Derivation of Acoustic Wave Equation.- Acoustic Intensity and Specific Acoustic Impedance.- Solutions of Spherical Wave Equation.- Acoustic Waves from Spherical Sources.- Boundary Conditions and Mode Shapes.- Resonant Cavities and Acoustic Waveguides.- Power Transmission in Pipelines.- Filters and Resonators.- Sound Pressure Levels and Octave Bands.- Room Acoustics.

    1 in stock

    £61.74

  • Acoustic Emission: Fracture Detection in

    Springer International Publishing AG Acoustic Emission: Fracture Detection in

    1 in stock

    Book SynopsisThe book presents topical theoretical and experimental studies for developing advanced methods of detecting materials fracture and assessing their structural state using acoustic emission. It introduces new mathematical models characterizing the displacement fields arising from crack-like defects and establishes a new criterion for classifying different types of materials fracture based on specific parameters obtained from wavelet transforms of acoustic emission signals. The book applies this approach to experimental studies in three types of materials—fiber-reinforced composites, dental materials, and hydrogen-embrittled steels.Table of Contents1 Macrofracture of Structural Materials and Methods of Determining its Type................................................................................................... 1 1.1 Types of Structural Materials Fracture................................................................ 1 1.2 Application of the Acoustic Emission Method to Detect the Fracture of Structural Materials...................................................................... 8 1.3 Detection of Defects by Signals of Magnetoelastic Acoustic Emission ................................................................ 19 1.4 Methods of Spectral Analysis of AE Signals................................................... 21 1.5 Application of Wavelet Transform for Analysis of AE signals........................................................................................... 31 References............................................................................................................................... 43 2 Mathematical Models for Displacement Fields Caused by the Crack in an Elastic Half-Space............................................................................ 61 2.1 Basic Relations of Three-Dimensional Dynamic Problems of the Theory of Elasticity for Bodies with Cracks........................................... 62 2.2 Modeling of Wave Displacements Field on the Half-Space Surface due to Displacement of the Internal Crack Faces............................... 68 References............................................................................................................................ 102 3 Energy Criterion for Identification of the Types of Material Macrofracture............................................................................................. 105 3.1 Methods for Identifying the Types of Macrofracture................................... 105 3.2 Construction of the Energy Criterion.............................................................. 108 3.3 Continuous Wavelet Transform of the AE Signals Emitted under Fracture of Aluminum and its Alloy...................................................... 123 3.4 Specific Features of the Acoustic Emission Signals During Fracture of Aluminum Alloy Welded Joints under Quasi-Static Loading............................................................................................ 130 3.5 AE-identification of the Types of Fracture during Low-Temperature Creep Crack Growth........................................................... 135 3.6 Application of the Wavelet Transform to Study the Features of Non-Metallic Materials Fracture................................................... 140 References............................................................................................................................ 144 vii 4 Evaluation of the Types and Mechanisms of Fracture of Composite Materials According to Energy Criteria...................................... 151 4.1 Specific Features of Macrofracture of the Glass Fiber Reinforced Composites............................................................................ 152 4.2 AE-diagnostics of Fracture of the Aramid Fiber Reinforced Composites............................................................................ 159 References............................................................................................................................ 179 5 Ranking of Dental Materials and Orthopedic Constructions by their Tendency to Fracture.................................................................................. 185 5.1 State-of-the Art of Researches on Mechanical Properties of Dental Materials............................................................................................. 186 5.2 Determination of the Characteristics of Materials for Temporary Fixed Constructions of Dentures...................................................................... 187 5.3 Evaluation of the Types of Dental Polymer Fracture by the Energy Criterion........................................................................................... 199 5.4 Peculiarities of Some Tooth-Endocrown Systems Fracture under Quasi-Static Loading............................................... 205 References............................................................................................................................ 220 6 Rating of Hydrogen Damaging of Steels by Wavelet Transform of Magnetoelastic Acoustic Emission Signals................................. 227 6.1 Some Aspects of Operation the Technical Systems in Hydrogenous Medium................................................................................... 228 6.2 Method for Estimating the Hydrogen Damage of Structural Materials by Wavelet Transform of MAE Signals........................................ 232 6.3 Approbation of the Research Technigue on Specimens of Long-Term Operated Pipe Steels..................................................................... 244 References............................................................................................................................ 255

    1 in stock

    £132.99

  • Springer International Publishing AG Light and Waves: A Conceptual Exploration of

    Out of stock

    Book SynopsisThis book explores light and other types of waves, using this as a window into other aspects of physics. It emphasizes a conceptual understanding, using examples chosen from everyday life and the natural environment. For example, it explains how hummingbird feathers create shimmering colors, how musical instruments produce sound, and how atoms stick together to form molecules. It provides a unique perspective on physics by emphasizing commonalities among different types of waves, including string waves, water waves, sound waves, light waves, the matter waves of quantum mechanics, and the gravitational waves of general relativity. This book is targeted toward college non-science majors, advanced high school students, and adults who are curious about our physical world. It assumes familiarity with algebra but no further mathematics and is classroom-ready with many worked examples, exercises, exploratory puzzles, and appendices to support students from a variety of backgrounds.Trade Review“‘Light and Waves’ fills a need to educate non-science majors and laypeople on the joy of optics. This highly recommended book inspires questions, curiosity, excitement and interest in the natural universe. … this book special is the quality of the questions, the variety of worked problems with answers, the numerous exercises and crucial additional resources.” (Barry R. Masters, optica-opn.org, October 26, 2023)Table of ContentsContentsPreface1 Introduction1.1 Theories of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.1.1 Extramission theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.1.2 Particle theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.1.3 Wave theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.1.4 Particle-wave duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.1.5 Today . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.2 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Part I: Waves2 Properties of Waves 2.1 Introduction to waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1.1 Examples of waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1.2 Transverse, longitudinal, and surface waves . . . . . . . . . . . . . . . . . . . 182.1.3 Amplitude and wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Speed and velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.1 Speed and velocity of waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.2 Speed of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.3 Measuring the speed of light . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.4 Speed of light in a medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.5 Aside: High frequency stock market trading and the speed of light . . . . . . 232.3 Frequency and period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.1 Frequency and period of waves . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.2 Cars on a road analogy for waves . . . . . . . . . . . . . . . . . . . . . . . . . 262.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Superposition3.1 Superposition of waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.1 The superposition principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.2 Rogue waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.3 Constructive and destructive interference . . . . . . . . . . . . . . . . . . . . 313.1.4 Beating patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Standing waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.1 Reflection at boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.2 Standing waves from reflected waves and superposition . . . . . . . . . . . . . 333.2.3 Standing waves between two boundaries . . . . . . . . . . . . . . . . . . . . . 343.3 Thin film interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.1 Structural coloration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.4 Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.4.1 Diffraction through holes and around obstacles . . . . . . . . . . . . . . . . . 363.4.2 Huygen’s principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5 Diffraction and interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.5.1 Double-slit experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.5.2 Double-slit experiment analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 383.5.3 Diffraction gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.5.4 Single-slit experiment and analysis . . . . . . . . . . . . . . . . . . . . . . . . 403.5.5 The Arago-Poisson spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.5.6 Babinet’s principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.5.7 Atmospheric diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.7 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Wave Interactions 4.1 Resonance, coupling, and damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.1.1 Resonance and coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.1.2 Resonance with light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.1.3 Energy transfer at a constant frequency is reversible . . . . . . . . . . . . . . 484.1.4 Energy loss from damping is irreversible . . . . . . . . . . . . . . . . . . . . . 504.1.5 Aside: The Tacoma Narrows and Millennium Bridges . . . . . . . . . . . . . 514.2 Intensity spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2.1 Spectral graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2.2 Continuous and line spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.3 Transmission and absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.3.1 Transmission spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.3.2 Absorption spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.4 Doppler effect and red/blue shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.4.1 The Doppler effect for sound waves . . . . . . . . . . . . . . . . . . . . . . . . 594.4.2 Doppler effect for other types of waves . . . . . . . . . . . . . . . . . . . . . . 614.4.3 Supersonic motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Mechanical Waves 5.1 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.1.1 How waves work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.1.2 Speed of waves on a string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.1.3 Damped waves on a string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2.1 Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2.2 How sound waves work and speed of sound . . . . . . . . . . . . . . . . . . . 725.2.3 The sound spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.2.4 Sonar and Medical ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.3 The physics of music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.3.1 Physics terminology for music . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.3.2 Musical instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.3.3 The Western musical scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.4 Water waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.4.1 Forces and wave speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.4.2 Phase velocity and group velocity . . . . . . . . . . . . . . . . . . . . . . . . . 845.4.3 Water motion in waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.4.4 Long wavelength water waves: tsunamis, tides, and seiches . . . . . . . . . . 875.5 Seismic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.5.1 Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.5.2 Types of seismic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.5.3 Seismic wave speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925.5.4 The Earth’s structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Part II: Light 6 Electromagnetic waves 6.1 Light waves as electric and magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . 976.1.1 Scalars, vectors, and fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986.1.2 Static electric fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986.1.3 Static magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006.1.4 Dynamic electric and magnetic fields . . . . . . . . . . . . . . . . . . . . . . . 1026.1.5 Electromagnetic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.1.6 How light waves work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.1.7 Light in a medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046.2 The electromagnetic spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046.3 Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066.3.1 White objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066.3.2 Rayleigh scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.4 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086.4.1 Electromagnetic waves can be polarized . . . . . . . . . . . . . . . . . . . . . 1086.4.2 Polarized light from selective absorption . . . . . . . . . . . . . . . . . . . . . 1096.4.3 Other sources of polarized light . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.4.4 Birefringence and optical activity . . . . . . . . . . . . . . . . . . . . . . . . . 1106.4.5 Between crossed polarizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106.4.6 Circular polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137 Photons 7.1 Quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1157.1.1 Problems with classical mechanics . . . . . . . . . . . . . . . . . . . . . . . . 1157.1.2 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167.1.3 Quantum interpretation of the double-slit experiment . . . . . . . . . . . . . 1187.2 Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.2.1 Classical momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.2.2 Photon momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.2.3 Radiometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1207.2.4 Solar sails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1207.2.5 Laser tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1217.3 Matter waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1227.3.1 The de Broglie equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1227.3.2 Matter wave speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.3.3 Particle in a box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.3.4 The hydrogen atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1267.3.5 Atomic spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1287.4 Fluorescence, phosphorescence, and lasers . . . . . . . . . . . . . . . . . . . . . . . . 1297.4.1 Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297.4.2 Phosphorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1307.4.3 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1307.5 Quantum mechanics and information . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.5.1 Heisenberg uncertainty principle . . . . . . . . . . . . . . . . . . . . . . . . . 1317.5.2 Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1347.7 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1367.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1368 Blackbody radiation 8.1 Blackbody radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1398.1.1 Wien’s displacement law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1398.1.2 Stefan-Boltzmann Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1418.1.3 Radiation coupling for black and white objects . . . . . . . . . . . . . . . . . 1418.1.4 Two-way blackbody radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1428.2 The greenhouse effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1438.2.1 Greenhouse effects on Mars and Venus . . . . . . . . . . . . . . . . . . . . . . 1448.2.2 Global warming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1458.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1468.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1478.4.1 The Earth’s energy budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Part III: Rays 9 Shadows and Pinhole cameras 9.1 Shadows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1519.1.1 Umbra and penumbra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1519.2 Pinhole camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1539.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1539.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15410 Reflection 10.1 Reflection in general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15510.1.1 Requirements for reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15510.1.2 Law of reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15610.2 Flat reflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15710.2.1 One mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15710.2.2 Retroreflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15910.3 Concave reflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16010.3.1 Parabolic reflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16010.3.2 Concave spherical mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16110.4 Convex spherical mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16410.5 Mirrors, inversion, and symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16510.6 Fermat’s principle of least time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16610.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16710.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16811 Refraction11.1 Refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17111.2 Normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17111.3 Incidence at an angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17311.3.1 Snell’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17311.3.2 Snell’s Law in use, and total internal reflection . . . . . . . . . . . . . . . . . 17411.3.3 Examples of total internal reflection . . . . . . . . . . . . . . . . . . . . . . . 17511.4 Convex lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17511.5 Concave lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17711.6 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17711.7 Fermat’s principle of least time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17811.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17811.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17912 Vision 12.1 Color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18312.1.1 Color wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18312.1.2 Addition of light and the RGB color scheme . . . . . . . . . . . . . . . . . . . 18412.1.3 Light subtraction due to pigments and the CMYK color scheme . . . . . . . 18512.1.4 HSV color scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18712.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18812.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189Appendices A NumbersA.1 Scientific notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191A.1.1 Scientific notation on a calculator . . . . . . . . . . . . . . . . . . . . . . . . . 191A.2 More calculator advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192A.3 Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192B Units B.1 Units are your friends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195B.2 The metric system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195B.3 Unit math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197B.4 Unit conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197B.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199C Algebra C.1 Solving problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201C.2 Expressions and equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201C.2.1 Expersions and equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201C.2.2 Manipulating expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202C.2.3 Manipulating equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203C.3 Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204D Geometry D.1 Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205D.1.1 Similar triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205D.1.2 Right triangles and trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . 205D.2 Areas and volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

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