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Preface I have been asked on a number of occasions why the title of my professorship is 'engineering acoustics' and not 'acoustical engineering'. I reply that, although there is no clear dividing line, the distinction is announced by the qualifying adjectives. I under- stand 'engineering acoustics' to concern all acoustical and related vibrational aspects of engineering design, manufacture, products, systems and operations; and 'acoustical engineering' to mean the theory and practice of the manipulation and exploitation of sound to achieve useful ends. Engineering acoustics also involves the manipulation of sound; but the principal aim in this respect is to control it as an undesirable by-product that is potentially harmful to human health and well-being, and has adverse effects on the quality of human life, on the effectiveness of human activities, and on aesthetic sensibilities. Intense sound can also be responsible for the malfunction of engineering systems, such as space satellites, and for damage to mechanical structures, such as gas pipelines. Engineering acoustics embraces the broad field of modelling, analysis, design, development and testing of engineering systems with the aims of manufacturing, installing and operating systems which exhibit acceptable acoustical behaviour. It must not be assumed from the foregoing that this is a book about noise control. To be such it would need to cover the following: specification of noise control targets; regulatory aspects of noise, including statistical considerations; noise measurement systems and standardized noise measurement methods; derived indices; noise rating methods; noise source identification and quantification techniques; the noise generation characteristics of a wide range of machines and plant; noise control system design, materials, construction and performance; together with the many non-acoustic aspects of noise control systems such as fire resistance, integrity, reliability, weight, volume, hygiene, environmental survivability, maintenance and, of course, cost. These important aspects of acoustical technology are well covered elsewhere, and lie outside the scope of this textbook. The title of the book has been chosen to reflect its specific purpose, which is to assist readers to acquire an understanding of those concepts, principles, physical phenomena, theoretical models and mathematical representations that form the foundations of the practice of engineering acoustics. It is not essentially concerned with methodology, which would require another volume of similar size. Wherever possible, I have introduced a flavour of the practical relevance of the material presented. A list of specific references, together with a substantial bibliography, provide sources of background reading and information. This work has an essentially pedagogic function, based upon the author's 53 years' experience of teaching undergraduate, postgraduate and practising engineers. It is written principally for senior undergraduate and postgraduate students of engineering xiii xiv Preface who have previously followed no course in acoustics, and who wish to acquire a more than superficial knowledge and understanding of the subject. Its demands on mathema- tical knowledge and skill are modest: namely, an ability to handle complex numbers, basic differential and integral calculus, and second-order differential equations with constant coefficients. Its scale and scope considerably exceed that which can be accommodated within a single semester undergraduate unit. However, it would be suitable for serial presentation in the third and fourth years of an undergraduate engineering course, or in the first and second semesters of a Master's course. I shall not attempt to prescribe which sections are more or less challenging: that is up to the individual teacher. The book presents a comprehensive exposition of the fundamental elements of audio- frequency sound and vibration, with emphasis on those relating to noise generation by machinery, vehicles and industrial plant, and to the practice of noise control engineering. The specialist area of underwater acoustics si touched upon but not treated in detail. Lack of space precludes comparable coverage of the equally important topics of psycho- acoustics, auditorium acoustics, auditory function, subjective acoustics, the physiologi- cal and psychological effects of excessive sound, and audio-engineering, although reference si made to these where appropriate. For the same reason, I have had reluctantly to omit a survey of sound measurement equipment. For an overview of this extensive subject, readers are initially directed to Parts XVII and XVIII of the aidepolcycnE of Acoustics cited in the Bibliography (Crocker, 1997), and may consult the manuals of reputable instrument manufacturers for practical guidance on use. With its orientation towards practical aspects of acoustics, the book will also serve as a basic text for professional engineers who lack a formal training in acoustics and who wish to understand the fundamentals underlying the information provided by the handbooks, guides and software that support professional practice. However, it should be understood that it is not a reference book for the provision of guidance in the solution of practical problems, for which a selection of the literary resources can be found in the Bibliography. Great emphasis si placed on the qualitative description and explanation of the physical nature and characteristics of audio-frequency acoustical and vibrational phenomena. Each chapter begins with a brief survey of the practical importance of the area of acoustics that it treats. This si followed by a qualitative introduction to the physics of the quantities, processes and phenomena which form the subjects of the chapter, as a pedagogical prerequisite to the subsequent introduction of mathematical modelling and analysis. A distinguishing feature of this book si the complementation of the descriptive and mathematical treatment of acoustical phenomena by recommenda- tions and descriptions of procedures for their physical demonstration. Some are briefly mentioned at appropriate points in the text. Detailed prescriptions for the more elaborate demonstrations and laboratory exercises are presented in Appendix .7 This format provides teachers with tried and tested means of motivating the interest of the students, assisting them to understand the phenomena involved and to acquire an appreciation of the relevance, validity and limitations of associated theoretical models. As a result of consultation with a number of academic colleagues teaching acoustics to engineering students in many parts of the world, I am aware of a wish by some to find fully worked examples throughout the book. This presented me with three problems. First, I dislike a text that si fragmented by the regular appearance of worked examples, which interfere with its physical and expositional continuity. Second, as a result of many Preface xv years of teaching, it is my experience that it si all too easy for students to read (not work) through a worked example and to mislead themselves into believing that they have understood it; they can become competent at solving similar problems without actually gaining understanding. Third, the book was taking on mammoth proportions because of my emphasis on rather lengthy physical explanations, together with the inclusion of recommendations for physical demonstrations and formal laboratory exercises. I there- fore decided not to include fully worked examples, but instead to elaborate the answers to the questions posed at the end of each chapter by providing guidance, where appropriate. I believe that this format forces the student to consult the text in order to understand the basis of the question, while helping him or her to gain confidence in the exercise of analytical skill and numerical calculation by providing stepping stones on the personal journey toward a solution. I hope that this will not cause too much disaffection among academic colleagues. A no doubt contentious feature of the book si the consignment to an appendix of the analysis of free and forced vibration of the damped mass-spring oscillator (see Appendix .)5 The reasons for this relegation are as follows. First, sound experienced in everyday life is rarely purely tonal. I consequently wish the reader to get into the habit, at the outset, of thinking in terms of wavemotion of arbitrary time dependence, without being distracted by the lumped element, single-degree-of-freedom oscillator that involves no waves. Second, the oscillator si introduced in mechanics at high school, and subse- quently in the first year of most engineering courses, as a basic element of mechanics or applied mathematics. It si also introduced in Chapter 4 in terms of its impedance. Fourier analysis, together with a brief survey of practical aspects of frequency analysis, are similarly consigned to Appendix 2, because, in my opinion, its extensive treatment within the main body of an acoustics textbook interrupts the continuity of development of the principal subject of the book. It is, in fact, difficult to see where to place it logically within the main text. This follows Appendix ,1 which presents an explanation of the complex exponential representation of harmonic vibration and waves, which underpins almost every aspect of the analytical content of the book. Appendix 4 si a descriptive attempt to explain the distinction between 'coherence' and 'correlation'. Appendix 6 gives definitions of mean square and energetic quantities, defines the associated logarithmic measures and calculation procedures, and presents a very brief introduction to indices that are commonly used as a basis for relating physical sound levels to human response and potential risk to health. The fields of audiological science, sound perception and physiological effects, in which I have no specialist expertise, are vast and complex areas of knowledge, to which a brief section in this book could do no justice. They are best studied with the aid of specialized books and technical literature. Readers are directed to a good introduction to the current knowledge in these areas presented in Fundamentals of Noise and Vibration (Fahy and Walker, 1998), cited in the Bibliography. Perusal of the Contents List will reveal the structure of the presentation, and the scope of material covered by the book. I will therefore highlight here only those features that, to some extent, distinguish it from other books in the English language that serve to introduce the subject of technical acoustics to students studying it for the first time at university level. The introductory chapter makes a claim for acoustics as being one of the most interesting and rewarding areas of science and technology for students to pursue because of its ubiquitous role in everyday life, the vast spread of its practical applications and the xvi Preface interdisciplinary demands it places upon the professional acoustician. Acoustics is placed in the general context of modern engineering and society, the role of the engineering acoustician and the breadth of associated activities. As an antidote to the unavoidable emphasis on noise and vibration control that characterizes so many books on acoustics, and as an illustration of the ramifications of the subject, the chapter presents a selection of positive applications of sound and vibration in the fields of manufacturing industry, medicine, metrology and ecology, among others. Chapter 2 explains the physical nature of sound in fluids in qualitative terms and uses commonplace examples to illustrate a range of acoustic phenomena that feature in the subsequent analytical sections. During my lecturing career, I have become increasingly aware that the assumption of a continuum model of media, without some attempt to explain the nature of the molecular basis of continuum properties and behaviour, is unsatisfying to the more intellectually curious. Therefore, Chapter ,3 which ultimately leads to the development of the wave equation that governs sound propagation in fluids, opens with brief explanations of the reasons for the differences in the dynamic behaviour of solids, liquids and gases, together with the molecular basis of pressure and temperature. A considerable number of those colleagues in many countries whom I consulted in the initial stage of this work intimated that their students found difficulty in understanding and applying the concept of impedance. Chapter 4 represents an attempt to rationalize and explain the utility of a quantity that appears in diverse, and not always consistent, guises in the literature. The complexity of sound energy flux in fluids, resulting from wave interference, which si universally present in circumstances of practical concern to engineers, is not adequately signalled or explained in most introductory textbooks. The recent development and widespread application of sound intensity measurement justifies the inclusion of Chapter 5 as partial antidote to this lack. Sound sources are immensely diverse in mechanism, form and character. This presents a challenge for those who aspire to explain them in a manner that is at once rigorous and accessible to the less mathematically minded student. I attempt to overcome this problem by beginning Chapter 6 with a qualitative categorization of sources on the basis of their fundamental physical mechanism as an entr6e to mathematical representa- tion in terms of ideal, elementary archetypes. Although some may consider that the early introduction of the Dirac delta function and the free-space Green's function is premature in a book designed for undergraduate consumption, I consider that they are essential to the understanding of the basis of the integro-differential equation that relates sound fields to the boundary conditions satisfied by the fluid. This equation si implemented in the 'boundary element' software that graduates who aspire to pursue an acoustics-oriented career in industry or consultancy will be expected to apply. The absence of formal exposition of the theoretical bases of the finite and boundary element methods of acoustical modelling and analysis is partly justified by my belief that the variational approach to dynamics upon which they rest will be unfamiliar to most readers. The practical reason is one of lack of space in which formally to develop the underlying theory. The equivalence of forces applied to fluids and dipole sources is explained at some length: as si the duality of representation of fluid boundaries as either distributions of monopoles and dipoles, or as boundary conditions. The important subject of aerodynamic sound generation by non-linear mechanisms of turbulent fluid motion is not treated in any detail because its conceptual subtlety and mathematical complexity demand a level of understanding of unsteady fluid dynamics greater than Preface xvii that which I have assumed to be necessary for understanding the mathematical content of the book. It receives attention in qualitative terms and examples of jet noise characteristics are presented at the end of the chapter. Dissipation of sound energy into heat provides one of the principal means of controlling noise. Chapter 7 opens with an account of the molecular basis of fluid viscosity as a prelude to an introduction to the dynamic behaviour of fluids contained within the skeletons of porous solid materials. The collapse of acoustic impedance and attenuation data on the basis of a non-dimensional parameter akin to Reynolds number si explained in terms of the transition from low-frequency, viscosity-controlled fluid motion to inertia-controlled motion at high frequencies. Analysis of a number of mathematical models serves to emphasize the influence of installation geometry on the sound absorption performance of porous materials. Special emphasis si given to the crucial influence of the relation between radiation and internal resistances on the performance of resonant acoustic and vibrational absorbers, which appears to be largely neglected in other textbooks. In many systems of practical engineering importance, sound si channelled along ducts. Chapter 8 begins with a semi-quantitative description, in terms of multiple reflection of plane pulse wavefronts, of the generation of undamped and damped plane wave modes and resonances in uniform ducts terminated by reactive and resistive elements. Analysis of a simple model of fluid-structure interaction follows a conventional treatment of propagation and reactive attenuation of harmonic plane waves in uniform ducts. The formation of non-plane modes, together with the phenomenon of modal cut-off, si also initially demonstrated by the consideration of the propagation and reflection of plane pulse wavefronts. Mathematical analysis of propagation in ducts having both rigid and finite-impedance walls leads finally to a brief presentation of performance data for lined ducts and splitter attenuators. The behaviour of sound in enclosures si of interest in relation to auditoria, broad- casting and recording studios, vehicle compartments, petrochemical plant units and noise control covers, among others. Chapter 9 opens with an illustration of the temporal evolution of an impulsively excited sound field in a reverberant enclosure using an image model. A conventional wave model analysis demonstrates that the rapid increase of reflection arrivals with frequency that si revealed by the impulse model si complemented by a rapid increase with frequency of the density of natural frequencies, to a point where deterministic modal modelling si of little value, and response si unpredictable in detail. Alternative models in the forms of the diffuse field, and the balance between energy input and dissipation balance are introduced, together with the standard simple formulae for reverberation time and steady state sound pressure level. In particular, the nature of energy flow in quasi-diffuse reverberant fields si discussed. A simple model based upon the enclosed space Green's function reveals the factors that govern vibroacoustic coupling between structures and enclosed fluids. The chapter concludes with a brief introduction to the application of geometric (ray) models of sound propagation in auditoria and industrial workshops. Chapter 01 is devoted to structure-borne sound, which si the agent of transmission of audio-frequency disturbances in many systems of interest to engineers, principally in vehicles and buildings. The conventional analytical representation of structural vibra- tion in terms of damped normal modes, subject to various forms of force excitation, si eschewed for a travelling wave/energetic model which is of far greater use in the audio- frequency range. This model balances mechanical power inputs to subsystems against xviii Preface the local rate of dissipation of energy plus rate of transmission of energy to connected subsystems. The crucial problem of characterization of inputs in dynamic or kinematic form is explained. Expressions for propagation wavenumber, energy density and energy flux are developed for the structural wave types of principal interest in engineering acoustics. Derivation of the various forms of bending wave impedance of semi-infinite and infinite uniform beams illustrates that the parametric dependence of power input si quite different for dynamic and kinematic forms of excitation. A simple, but useful, model of high frequency vibration isolation si presented. The chapter concludes with an introduction to the two principal analytical models of sound radiation from vibrating surfaces: namely, the Convolution formulation in terms of the free-space Green's function and the spatial Fourier transform approach that underlies Nearfield Acoustical Holography. The influence of structural material properties and boundary conditions on sound energy radiation si explained and illustrated by examples. Chapter 11 on the transmission of airborne sound through single and double partitions si largely extracted from my earlier book, Sound and Structural Vibration (Fahy, 1987 - see Bibliography), with a more rigorous derivation of an expression for the transmission loss of a double panel containing a sound absorbent core and the addition of a simple model of a noise control enclosure. The mathematical techniques required to deal with problems of scattering and diffraction are generally more advanced than those assumed as prerequisites for achieving benefit from this book. Consequently, in the final chapter the reader si introduced to a graphical technique that broadly elucidates the origin and characteristics of diffraction by edges, together with some practical data relating to screens: but no diffraction theory si presented. The process of scattering by solid objects as equivalent to radiation by virtual sources si explained and illustrated by an analysis of scattering by a rigid sphere and a thin disc. The chapter continues with a simple example of the application of ray tracing analysis to refraction of sound by a linear gradient of sound speed and ends with a brief descriptive account of refraction by wind and temperature gradients near the surface of the Earth. The Appendices are intended to be essential reading and study: not as 'optional extras'. In fact, Appendices 1 to 6 could serve as a unit to be followed early in a course. I hope that Appendix 7 will not only provide teachers with a ready-made basis for illustrating acoustical phenomena and behaviour described in the text, but may also inspire them to develop improved versions and to introduce additions to the list. I look forward to receiving feedback for incorporation in a future edition. Note on terminology and notation The adjective 'harmonic' si used throughout the book to mean 'simple harmonic' or 'single frequency' in order to avoid a more lengthy adjectival phrase. The over-tilde si restricted to complex amplitudes of harmonically varying quantities. The rather unwieldy representation of the modulus of a complex amplitude (i.e. the real amplitude) si employed because students frequently make a factor of two error by confusing mean square quantities and the square of their amplitudes. In all the questions posed at the ends of the chapters the fluid si assumed to be air at a pressure of 501 Pa and a temperature of 20~ unless otherwise stated. Impedance ratios are referred to the characteristic impedance of air under these conditions, unless otherwise stated. stnemegdelwonkcA I am profoundly indebted to my dear wife Beryl for her love and support during the apparently never-ending gestation period of this book and for putting up with frequent disturbance at night by a partner who was either insomniac, or restlessly trying to solve insoluble mathematical problems in his dreams. I also wish to acknowledge with deep appreciation the thoughtful and efficient secretarial assistance provided by Sue Brindle. I was assisted in the proof-reading by Beryl, and by my youngest son Tom, who brought a suitably critical eye to the work, for the exercise of which he si much thanked. In addition to saving the reader from some of my more infelicitous expressions, Anne Trevillion, who copy-edited the manuscript, pointed out two major technical errors, for which I am eternally grateful. I would also like to acknowledge the contribution of the team of Academic Press editors and the typesetters and printers. I requested the assistance of my ISVR colleague Professor Chris Morfey, and my former colleague, Professor J. Stuart Bolton of Purdue University, with the task of reviewing the first drafts of Chapters 6 and ,7 respectively. These have greatly benefited from their conscientious attention, for which I am most grateful. However, any errors or other faults are entirely my responsibility. I also wish to acknowledge the beneficial influence of many lengthy conversations about some of the 'trickier' subjects of the book with my ISVR colleagues Dr Phil Joseph and Professor Phil Nelson. I was assisted with the acquisition of experimental data by Matthew Simpson, Rob Stansbridge, Anthony Wood and Dave Pitcaithley of ISVR, for which much thanks. Much of Chapter 5 and the major part of Chapter 11 are reproduced by kind permission of E & F N Spon and Academic Press, respectively. Figure 2.9 si reproduced by permission of Her Majesty's Stationery Office. I wish to acknowledge with thanks provision of the following graphical and photographic material. The photographs presented in Figs 5.11 and 5.13 were provided by Bruel & Kj~er of Naerum, Denmark. Photographs of the microstructure of sound-absorbent materials were supplied by Mr M. J. .B Shelton. The reverberation decay traces presented in Fig. 9.19 were supplied by Mr John Shelton of AcSoft Ltd. The photograph of a diffusor installation presented in Fig. 12.6 was supplied by Dr D'Antonio of RPG Diffusor Systems Inc. of Upper Marlboro, USA. Dr Matthew C. M. Wright of ISVR provided the computer output for Fig. 12.12. The wavefront pattern in Fig. 2.4 was specially commissioned from angler Michael Kemp Esq. Reference to the origins of all other material reproduced from other publications si provided at the point of presentation. xix 1 Sound Engineering 1.1 The importance of sound Sound is a ubiquitous component of our environment from which there is no escape. Even in the darkness of a deep underground cavern, the potholer hears the sound of the operation of his or her body. In the dark depths of the ocean, creatures communicate by sound, which is the only form of wave that propagates over long distances in water. Only in the reaches of cosmic space, and in high vacuums created on Earth, are atoms so isolated that the chance of interaction, and hence the existence of sound, is negligible. Sound is one of the principal media of communication between human beings, between higher animals, and between humans and domesticated animals. Sound informs us about our environment; as a result of evolution we find some sounds pleasant and some redolent of danger. The universal importance of music to human beings, and its emotional impact, remain mysterious phenomena that have yet to be satisfactorily explained. Unlike our eyes, our ears are sensitive to sound arriving from all directions; as such they constitute the sensors of our principal warning system, which is alert even when we are asleep. So, sound is vitally important to us as human beings. But, apart from audio engineers who capture and reproduce sound for a living, why should engineers practising in other fields have any professional interest in sound? The short answer has two parts. On the positive side, sound can be exploited for many purposes of concern to the engineer, as indicated later in this chapter. On the negative side, excessive sound has adverse psychological and physiological effects on human beings that engineers are employed to mitigate, preferably by helping to design inherently quiet machines, equipment and systems: but failing this, by developing and applying noise control measures. The adverse effects of excessive sound in causing hearing damage, raising stress levels, disturbing rest and sleep, reducing the efficiency of task performance, and interfering with verbal and musical communication, are widely experienced, recog- nized and recorded. In recent years, noise has become a major factor in influencing the marketability and competitiveness of industrial products such as cars and washing machines, as evidenced by advertising material. Many products are required to satisfy legal and regulatory requirements that limit the emission of noise into work places, homes and the general environment. Failure to meet these requirements has very serious commercial consequences. Aircraft are not certificated for commercial opera- tion unless they meet very stringent environmental noise limits. Road vehicles are not allowed on the road unless they satisfy legally enforced limits on roadside noise. Train noise is currently being subjected to the imposition of noise restrictions. 2 snoitadnuoF of gnireenignE Acoustics A less widely known adverse effect of excessive sound is its capacity to inflict serious fatigue damage on mechanical systems, such as the structures of aircraft, space rockets and gas pipelines, and to cause malfunction of sensitive components, such as the electronic circuits of Earth satellites. Sound is vitally important to the military, particularly with the advent of automated target recognition and ranging systems. Sound is a tell-tale. It gives warning that mechanical and physiological systems are not in good health. Sound generated by the pulmonary and cardiovascular systems provides evidence of abnormal state or operation, as foreseen by Robert Hooke over 300 years ago. The production of equipment for monitoring the state of machinery via acoustic and vibrational signals is a multimillion dollar business. The cost of monitoring is small compared with the cost of one day's outage of a 600 MW turbogenerator, which runs into more than one million dollars. Taken together, these different aspects of the impact of sound on human beings and engineering products provide convincing reasons why acoustics is a fascinating subject of study and practice for engineers. 1.2 Acoustics and the engineer Engineers conceive, model, analyse, design, construct, test, refine and manufacture devices and systems for the purpose of achieving practical ends: and, of course, to make money. This book deals with the concepts, principles, phenomena and theories that underlie the acoustical aspects of engineering. Not so long ago, the acoustics expert was only called in to the chief engineer's office when something acoustical had gone wrong; he or she was expected to act as a sonic firefighter. Today, major engineering companies involve acoustically knowledgeable staff in all the stages of their programmes of new product development, from concept to commissioning. The process of predicting the acoustical performance of a product or system at the 'paper' design stage is extremely challenging. The task is being progressively eased by the increasing availability of computer-based modelling and analysis software, particularly in the forms of finite element, boundary element and statistical energy analysis programs. However, the 'blind' application of these powerful routines brings with it the dangers of unjustified confidence in the resulting predictions. As in all theoretical analysis, it is vital that appropriate and valid models are constructed. The modeller must understand the physics of the problem tackled, particularly in respect of the relative influences on system behaviour of its geometric, material, construc- tional and operational parameters. Efficient design and development require engineers to identify those elements of a system that are likely to be critical in determining the sensitivity of system performance to design modifications. A major problem facing the acoustical designer is that details that are apparently of minor importance in respect of other aspects of performance and quality often have a major influence on acoustical performance. This is often not recognized by their 'non-acoustical' colleagues who may introduce small modifications in ignorance of their acoustical impact. Unfortunately, it is frequently impossible to predict this impact precisely in quantitative terms because the available models are not capable of such precision. One example in point concerns the design of seals for foot pedals in cars. The acoustical engineer is fully aware of the adverse effect on interior noise of even very small gaps around a seal, but the influence of gap geometry and material 1. Sound Engineering 3 properties of the seal on sound transmission is very difficult to predict. Another concerns damping, which has a major effect on the influence of structure-borne sound on noise level (see Chapter 10). But it is still not possible to model precisely the magnitude and distribution of damping caused by joint friction and the installation of trim components. 1.3 Sound the servant One might gain the impression from perusal of the titles and contents of many of the currently available books on acoustics that practitioners are almost exclusively concerned with noise and vibration control. This unfortunately suggests that acousti- cians spend most of their time preventing undesirable things from happening- or remedying the situation when they do. In fact, engineering for quietness is intellec- tually and technically challenging, and most beneficial to society. However, there is more to engineering acoustics than noise control, as I hope to convince you in the following paragraphs. Sound and vibration can be put to many positive uses apart from the obvious ones of sound recording and reproduction. Communication via sound waves is not confined to the air. Marine animals use it for long distance communication. Divers' helmets largely exclude water-borne sound, so they can use a system in which a microphone in the helmet drives a small loudspeaker that radiates sound into the water. A sensor in the receiver's helmet creates vibration in a bar held between the teeth, from where it is transmitted by bone conduction directly into the cochlea. Video pictures and data can be transmitted to base from autonomous underwater vehicles used to locate objects and to inspect and maintain offshore oil and gas rigs via acoustic waves. The vehicles can also be controlled using this form of communication. One of the most important practical benefits of waves is that they can be exploited to investigate regions of space remote from the operator. Passive reception of sound provides information about events occurring in the environment of the receiver. Underwater sound has a particular importance in this respect, because the range of visibility is always short, and negligible in the depths of the ocean. Sound is used to detect and monitor marine animals for census and ecological research purposes. It also signals suboceanic geological activity. Its use in sonar (sound navigation and ranging) systems in the marine military sphere is well known. In a recent development, the reflection from objects of naturally occurring underwater sound provides a means of detection that does not reveal the presence of the listener: this is called 'acoustic daylight'. Ultrasound cameras for underwater use are under development. Sound is increasingly used to locate and classify military vehicles on the field of battle. The vision system of most robots is based upon ultrasonic sensors. The chambers of nuclear reactors can be monitored for the onset of boiling by means of structure-borne sound transmitted from the fluid along solid waveguides. Passive sound reception and analysis has been used for centuries as a means of monitoring the activity and state of the internal organs of animals, as exemplified by the sound of turbulence generated by the narrowing of arteries. It is now used to indicate the activity and state of health of the fluid transport systems of trees and tomato plants. Optimal watering regimes are based upon this phenomenon. Machine condition-monitoring systems that utilize sound and vibration signals as one of a set

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Foundations of Engineering Acoustics takes the reader on a journey from a qualitative introduction to the physical nature of sound, explained in terms of common experience, to mathematical models and analytical results which underlie the techniques applied by the engineering industry to improve the
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