The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

While the history of musical instruments is nearly as old as civilisation itself, the science of acoustics is quite recent. By understanding the physical basis of how instruments are used to make music, one hopes ultimately to be able to give physical criteria to distinguish a fine instrument from a mediocre one. At that point science may be able to come to the aid of art in improving the design and performance of musical instruments. As yet, many of the subtleties in musical sounds of which instrument makers and musicians are aware remain beyond the reach of modern acoustic measurements. This book describes the results of such acoustical investigations - fascinating intellectual and practical exercises. Addressed to readers with a reasonable grasp of physics who are not put off by a little mathematics, this book discusses most of the traditional instruments currently in use in Western music. A guide for all who have an interest in music and how it is produced, as well as serving as a comprehensive reference for those undertaking research in the field.

The Stroh formalism is a powerful and elegant mathematical method developed for the analysis of the equations of anisotropic elasticity. The purpose of this exposition is to introduce the essence of this formalism and demonstrate its effectiveness in both static and dynamic elasticity. The equations of elasticity are complicated, because they constitute a system and, particularly for the anisotropic cases, inherit many parameters from the elasticity tensor. The Stroh formalism reveals simple structures hidden in the equations of anisotropic elasticity and provides a systematic approach to these equations.

This exposition is divided into three chapters. Chapter 1 gives a succinct introduction to the Stroh formalism so that the reader can grasp the essentials as quickly as possible. In Chapter 2 several important topics in static elasticity, which include fundamental solutions, piezoelectricity, and inverse boundary value problems, are studied on the basis of the Stroh formalism.

Chapter 3 is devoted to Rayleigh waves, for long a topic of utmost importance in nondestructive evaluation, seismology, and materials science. There we discuss existence, uniqueness, phase velocity, polarization, and perturbation of Rayleigh waves through the Stroh formalism.

This work will appeal to students and researchers in applied mathematics, mechanics, and engineering science.

Senior level/graduate level text/reference presenting state-of-the- art numerical techniques to solve the wave equation in heterogeneous fluid-solid media. Numerical models have become standard research tools in acoustic laboratories, and thus computational acoustics is becoming an increasingly important branch of ocean acoustic science. The first edition of this successful book, written by the recognized leaders of the field, was the first to present a comprehensive and modern introduction to computational ocean acoustics accessible to students. This revision, with 100 additional pages, completely updates the material in the first edition and includes new models based on current research. It includes problems and solutions in every chapter, making the book more useful in teaching (the first edition had a separate solutions manual). The book is intended for graduate and advanced undergraduate students of acoustics, geology and geophysics, applied mathematics, ocean engineering or as a reference in computational methods courses, as well as professionals in these fields, particularly those working in government (especially Navy) and industry labs engaged in the development or use of propagating models.

It goes without saying that atomic structure, including its dual wave-particle nature, cannot be demonstrated in the classroom. Thus, for most science teachers, especially those in physics and chemistry, the textbook is their key resource and their students core source of information. Science education historiography recognizes the role played by the history and philosophy of science in developing the content of our textbooks, and with this in mind, the authors analyze more than 120 general chemistry textbooks published in the USA, based on criteria derived from a historical reconstruction of wave-particle duality.

They come to some revealing conclusions, including the fact that very few textbooks discussed issues such as the suggestion, by both Einstein and de Broglie, and before conclusive experimental evidence was available, that wave-particle duality existed. Other large-scale omissions included de Broglie s prescription for observing this duality, and the importance of the Davisson-Germer experiments, as well as the struggle to interpret the experimental data they were collecting. Also untouched was the background to the role played by Schrodinger in developing de Broglie s ideas. The authors argue that rectifying these deficiencies will arouse students curiosity by giving them the opportunity to engage creatively with the content of science curricula. They also assert that it isn t just the experimental data in science that matters, but the theoretical insights and unwonted inspirations, too. In addition, the controversies and discrepancies in the theoretical and experimental record are key drivers in understanding the development of science as we know it today."

Physical Ultrasonics of Composites is a rigorous introduction to the characterization of composite materials by means of ultrasonic waves. Composites are treated here not simply as uniform media, but as inhomogeneous layered anisotropic media with internal structure characteristic of composite laminates. The objective here is to concentrate on exposing the singular behavior of ultrasonic waves as they interact with layered, anisotropic materials, materials which incorporate those structural elements typical of composite laminates.
This book provides a synergistic description of both modeling and experimental methods in addressing wave propagation phenomena and composite property measurements. After a brief review of basic composite mechanics, a thorough treatment of ultrasonics in anisotropic media is presented, along with composite characterization methods. The interaction of ultrasonic waves at interfaces of anisotropic materials is discussed, as are guided waves in composite plates and rods. Waves in layered media are developed from the standpoint of the "Stiffness Matrix," a major advance over the conventional, potentially unstable Transfer Matrix approach. Laminated plates are treated both with the stiffness matrix and using Floquet analysis. The important influence on the received electronic signals in ultrasonic materials characterization from transducer geometry and placement are carefully exposed in a dedicated chapter. Ultrasonic wave interactions are especially susceptible to such influences because ultrasonic transducers are seldom more than a dozen or so wavelengths in diameter. The book ends with a chapter devoted to the emerging field of air-coupled ultrasonics. This new technology has come of age with the development of purpose-built transducers and electronics and is finding ever wider applications, particularly in the characterization of composite laminates.

The dynamics of many nonlinear systems gravitate around a few common central themes: intermittency, order/coherence and disorder. These features affect scalings and lead to deviations from Gaussian behaviour. Intermittency may be the universal outcome of a large class of nonlinear systems; however the universality properties of specific nonlinear systems, that is the dependencies of the intermittent structure on initial and boundary conditions, remain open questions. This volume consists of articles by prominent figures who all participated in a workshop held at the Newton Institute in Cambridge. It reflects the aims of the workshop, namely to capture and summarise recent developments, encourage cross-fertilisation of ideas, lay out research directions for the future and provide an overview of our current understanding of the subject.

This book contains a complete and accurate mathematical treatment of the sounds of music with an emphasis on musical timbre. The book spans the range from tutorial introduction to advanced research and application to speculative assessment of its various techniques. All the contributors use a generalized additive sine wave model for describing musical timbre which gives a conceptual unity, but is of sufficient utility to be adapted to many different tasks.

Sound is integral to how we experience the world, in the form of noise as well as music. But what is sound? What is the physical basis of pitch and harmony? And how are sound waves exploited in musical instruments? In this Very Short Introduction Mike Goldsmith looks at the science of sound and explores sound in different contexts, covering the audible and inaudible, sound underground and underwater, accoustic and electric, and hearing in humans and animals. He also considers the problem of sound out of place - noise and its reduction. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

The extraordinary ability of dolphins to echolocate has fascinated scientists and the public since its discovery in the late 1950's. This is the first book to summarize modern research in this area, and presents a broad synthesis of this very interdisciplinary subject. The author is an internationally-recognized expert on dolphin sonar and is thus in a unique position to bring together research on the physiological, mathematical and engineering aspects of the subject. Of interest to auditory researchers, electrical engineers, acoustical physicists, and mammalian physiologists.

The ocean is transparent to sound where slight irregularities within the ocean cause sound fluctuations, and thus set limits on the many uses of sound in the ocean, similar to the limits imposed by the atmosphere on ground-based telescopes. This 1979 book attempts to connect the known structure of the ocean volume with experimental results in long-range sound transmission. Theories of wave propagation through irregular media, developed for optical and radio wave transmission are found to be inapplicable in many respects due to the complications of ocean structure, particularly the combination of anisotropy and 'sound channel'. The authors extend wave propagation theory to account for the ocean complications and introduces the path-integral approach to the solution of the strong-scattering regime that solves many long-standing problems. The book is written at the post-graduate level, but has been carefully organised to give experimenters a grasp of important results without undue mathematics.

In Moravian Soundscapes, Sarah Eyerly contends that the study of sound is integral to understanding the interactions between German Moravian missionaries and Native communities in early Pennsylvania. In the mid-18th century, when the frontier between settler and Native communities was a shifting spatial and cultural borderland, sound mattered. People listened carefully to each other and the world around them. In Moravian communities, cultures of hearing and listening encompassed and also superseded musical traditions such as song and hymnody. Complex biophonic, geophonic, and anthrophonic acoustic environments-or soundscapes-characterized daily life in Moravian settlements such as Bethlehem, Nain, Gnadenhutten, and Friedenshutten. Through detailed analyses and historically informed recreations of Moravian communal, environmental, and religious soundscapes and their attendant hymn traditions, Moravian Soundscapes explores how sounds-musical and nonmusical, human and nonhuman-shaped the Moravians' religious culture. Combined with access to an interactive website that immerses the reader in mid-18th century Pennsylvania, and framed with an autobiographical narrative, Moravian Soundscapes recovers the roles of sound and music in Moravian communities and provides a road map for similar studies of other places and religious traditions in the future.

The large number of text books on the theory of sound deal principally with periodic disturbances such as harmonic wave trains and standing waves and give scant attention to aperiodic disturbances with clearly defined fronts, conveniently called sound pulses. This monograph attempts to fill this gap by providing an up-to-date description of the theory of sound pulses and its developments. The treatment is based on the thoery of linear partial differential equations of hyperbolic type - a method which is frequently simpler and more effective than the commoner one of resolving the pulse into harmonic components by Fourier analysis; this is especially true of any treatment of pulse fronts as wave fronts in the sense of geometrical optics. The individual chapters deal with the equations of motion, wave fronts and characteristics, geometrical acoustics and their application to reflection problems and the diffraction of a pulse by a wedge, circular cylinder, sphere and other objects. The book will also be of interest to readers concerned with other aspects of wave propagation, such as electromagnetic waves.

This volume represents the findings of the first test cases considered by ERCOFTAC (European Research Consortium on Flow Turbulence and Combustion). The workshop, held in Lausanne, Switzerland, in 1990, studied five test cases: boundary layer in an S-shaped duct; periodic array of cylinders; transition in a boundary layer under the influence of free-stream turbulence; axisymmetric confined jet flows. These test cases represented the interests of both the academic and industrial groups in finding out the limits of various models and codes to predict real problems supported by experimental data. The articles summarise the work of each group and point to refinements and further study to perfect the models. As such there will be much of interest to all professionals and researchers concerned with the prediction of flows and turbulence.

Acoustics of Fluid-Structure Interactions addresses an increasingly important branch of fluid mechanics - the absorption of noise and vibration by fluid flow. This subject, which offers numerous challenges to conventional areas of acoustics, is of growing concern in places where the environment is adversely affected by sound. Howe presents useful background material on fluid mechanics and the elementary concepts of classical acoustics and structural vibrations. Using examples, many of which include complete worked solutions, he vividly illustrates the theoretical concepts involved. He provides the basis for all calculations necessary for the determination of sound generation by aircraft, ships, general ventilation and combustion systems, as well as musical instruments. Both a graduate textbook and a reference for researchers, Acoustics of Fluid-Structure Interactions is an important synthesis of information in this field. It will also aid engineers in the theory and practice of noise control.

This 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.

This highly informative and fascinating book brings together perspectives on sound by leading experts from a wide variety of disciplines. These include anthropology, physiology, zoology, physics, music, phonetics and film. Through crossing disciplinary boundaries, the volume hopes to inspire a richer and more creative approach to the acoustic world. Whilst aiming for a general audience and presented in an accessible style, several chapters also represent important contributions within their own disciplines or will serve as core texts for students. The sequence of nine chapters passes from cultural perspectives on silence, via the physics of sound, physiology of the ear, songs of birds, and sounds of human speech, to music. From the reconstruction of medieval music, via twentieth-century composition and the music of the Kaluli of Papua New Guinea, the volume concludes with the role of sound in film. Life will never sound the same again.

The study of vibration in physical systems is central to almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. The treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar, is then examined. Part II then concentrates on quantum systems, looking at the vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is well illustrated with many examples; and theory and experiment are compared. This is a useful introduction to the more advanced mathematical treatment of vibrations as it bridges the gap between the basic principles and more specialized concepts.

Noise pollution around airports, trains, and industries increasingly attracts environmental concern and regulation. Designers and researchers have intensified the use of large-eddy simulation (LES) for noise reduced industrial design and acoustical research. This book, written by 30 experts, presents the theoretical background of acoustics and of LES, followed by details about numerical methods, e.g. discretization schemes, boundary conditions, coupling aspects. Industrially relevant, hybrid RANS/LES techniques for acoustic source predictions are presented in detail. Many applications are featured ranging from simple geometries for mixing layers and jet flows to complex wing and car geometries. Selected applications include recent scientific investigations at industrial and university research institutions. Presently one can't offer perfect solution methodologies that address all relevant applications, however the book presents a state of the art collection of methods, tools and evaluation methodologies. The advantages and weaknesses of both the commercial and the research methodologies are carefully presented.

Reactive flows encompass a broad range of physical phenomena, interacting over many different time and space scales. Such flows occur in combustion, chemical lasers, the earth's oceans and atmosphere, and in stars. Because of a similarity in their descriptive equations, procedures for constructing numerical models of these systems are also similar, and these similarities can be exploited. Moreover, using the latest technology, what were once difficult and expensive computations can now be done on desktop computers. This new edition of a highly successful book presents algorithms useful for reactive flow simulations, describes trade-offs involved in their use, and gives guidance for building and using models of complex reactive flows. It takes account of the explosive growth in computer technology and the greatly increased capacity for solving complex reactive-flow problems that has occurred since the previous edition was published more than fifteen years ago. An indispensable guide on how to construct, use, and interpret numerical simulations of reactive flows, this book will be welcomed by advanced undergraduate and graduate students, and a wide range of researchers and practitioners in engineering, physics, and chemistry.

Acoustical imaging has become an indispensable tool in a variety of fields. Since its introduction, the applications have grown and cover a variety of techniques, producing significant results in fields as disparate as medicine and seismology. Cutting-edge trends continue to be discussed worldwide.

This book contains the proceedings of the 27th International Symposium on Acoustical Imaging (AI27), which took place in Saarbrucken, Germany, from March 24th to March 27th 2003. The Symposium belongs to a conference series in existence since 1968. AI27 comprised sessions on: Medical Imaging, Non-Destructive Testing, Seismic Imaging, Physics and Mathematics of Acoustical Imaging, Acoustic Microscopy.

During two well-attended workshops the applications of quantitative acoustical imaging in biology and medical applications, and in near-field imaging of materials, were discussed. Based on its cross-disciplinary aspects, the authors of the papers of AI27 present experiments, theory and construction of new instruments. "

As an acoustic engineer, Trevor Cox has spent his career eradicating unwanted noises - echoes in concert halls, clamour in classrooms. Until the day he heard something so astonishing that he had an epiphany: rather than quashing rare or bizarre sounds, we should be celebrating these sonic treasures. This is the story of his investigation into the mysteries of these Sonic Wonders of the World. In the Mojave Desert he finds sand dunes that sing. In France he discovers an echo that tells jokes. In California he drives down a musical road that plays the William Tell Overture. In Cathedrals across the world he learns how acoustics changed the history of the Church. Touching on physics, music, archaeology, neuroscience, biology, and design, Cox explains how sound is made and altered by the environment and how our body reacts to peculiar noises - from the exotic sonic wonders he encounters on his journey, or the equally unique and surprising sounds of our everyday environment. In a world dominated by the visual, Sonic Wonderland encourages us to become better listeners and to open our ears to the glorious cacophony around us. Listen to a selection of astonishing sounds here: https://soundcloud.com/sonicwonderland

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When and how did the universe begin? Why are we here? What is the nature of reality? Is the apparent "grand design" of our universe evidence of a benevolent creator who set things in motion--or does science offer another explanation? In this startling and lavishly illustrated book, Stephen Hawking and Leonard Mlodinow present the most recent scientific thinking about these and other abiding mysteries of the universe, in nontechnical language marked by brilliance and simplicity.
According to quantum theory, the cosmos does not have just a single existence or history. The authors explain that we ourselves are the product of quantum fluctuations in the early universe, and show how quantum theory predicts the "multiverse"--the idea that ours is just one of many universes that appeared spontaneously out of nothing, each with different laws of nature. They conclude with a riveting assessment of M-theory, an explanation of the laws governing our universe that is currently the "only" viable candidate for a "theory of everything" the unified theory that Einstein was looking for, which, if confirmed, would represent the ultimate triumph of human reason.