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Preface to the First and Second EditionsThis book introduces the physical principles of acoustics. The predominant objective is to develop those concepts and points of view that have proven most useful in traditional realms of application such as noise control, underwater acoustics, architectural acoustics, audio engineering, nondestructive testing, remote sensing, and medical ultrasonics. The book is suitable as a text or as supplementary reading for senior and first-year graduate students in engineering, physics, and mathematics.Preliminary versions of the book in the form of class notes have been used in a three-term (one academic year) introductory course in acoustics taken by graduate students in electrical engineering, aerospace engineering, mechanical engineering, engineering mechanics, and physics at the Georgia Institute of Technology. Portions of the presentation evolved from a graduate course on wave propagation previously taught at MIT to students from the departments of mechanical engineering, ocean engineering, and earth and planetary sciences. The mathematical developments and the assumptions concerning the prior academic experiences of the readers are such that no one with any of the backgrounds just mentioned should be precluded from taking a course in which this book is used as a text or as principal outside reading. The text, however, is intended to be at a level of mathematical sophistication and intellectual challenge comparable to distinguished graduate texts in the basic engineering sciences (such as fluid dynamics, solid mechanics, thermodynamics, and electromagnetic theory); a deep understanding of acoustical principles is not acquired by superficial efforts.Graduate courses rarely follow a text closely; the instructor is invariably deeply involved in research or in the applications of the subject and shapes the course content to conform with what appears timely, with the research programs at the institution, and with the common interests of the students. This book is intended to facilitate such flexibility. The common ground of introductory acoustics courses is covered thoroughly, so the student can fill in whatever gaps result because of the pace of the lectures. Since the text derives almost all of the equations frequently used in acoustics, the instructor can relegate to outside reading whatever derivations seem too time consuming for the lectures and can thereby concentrate on the physical xiii xiv Preface to the First and Second Editions

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An approximate wave equation is derived for sound propagation in an inhomogeneous fluid with ambient properties and flow that vary both with position and time. The derivation assumes that the characteristic length scale and characteristic time scale for the ambient medium are larger than the corresponding scales for the acoustic disturbance. For such a circumstance, it is argued that accumulative effects of inhomogeneities and the ambient unsteadiness are satisfactorily taken into account by a wave equation that is correct to first order in the derivatives of the ambient quantities. A derivation that consistently neglects second- and higher-order terms leads to a concise wave equation similar to the familiar ordinary wave equation of acoustics. The wide applicability of this equation is established by showing that it reduces to previously known wave equations for special cases and by showing, with the eikonal approximation, that it yields the geometrical acoustics equations for ray propagation in moving inhomogeneous media.

Formulas and procedures are described for the estimation of sound pressure amplitudes at locations partially shielded from the source by a barrier. The analytical development is based on the idealized models of a wave from a point or extended source incident on a rigid wedge or a three-sided semi-infinite barrier. Versions of the uniform asymptotic solution for the wedge problem which are convenient for numerical predictions are derived in terms of auxiliary Fresnel functions by means of complex variable techniques previously employed by Pauli from a generalization of the exact integral solution developed by Sommerfeld, MacDonald, Bromwich, and others and are interpreted within the spirit of Keller's geometrical theory of diffraction. The Kirchhoff approximation in terms of the Fresnel number is obtained in the limit of small angular deflections from shadow zone boundaries. An approximate and relatively simple expression for the double-edge diffraction by a thick three-sided barrier is given based on the single wedge diffraction solution and on concepts inherent to the geometrical theory of diffraction which reduces to finite and realistic limits when either source or listener are near the extended plane of the barrier's top. A simple approximation suggested by Maekawa based on the replacement of actual barriers by an equivalent thin screen with diffraction treated by the Kirchhoff approximation is discussed in terms of the present theory and it is concluded that in some instances this approximation may lead to sizeable errors. An alternate scheme is suggested whereby one approximates the actual barrier by a three-sided barrier wholly contained within the actual barrier.

A theory is presented that permits the extension of the method of normal modes to guided-wave propagation in a medium with properties varying slowly with horizontal coordinates in addition to varying with the vertical coordinate. The principal assumption is the neglect of coupling between normal modes. It is predicted that different frequencies in different modes follow different horizontal paths. A ray-tracing method is described for computing these paths. The theory is then applied to the study of the dispersion of waves from an explosive source in shallow water with slowly varying depth.

Fundamental issues relative to structural vibration and to scattering of sound from structures with imprecisely known internals are explored, with the master structure taken as a rectangular plate in a rigid baffle, which faces an unbounded fluid medium on the external side. On the internal side is a fuzzy structure, consisting of a random array of point-attached spring-mass systems. The theory predicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function rhp(fl) which gives a smoothed-out total mass, per unit plate area, of all those attached oscillators which have their natural frequencies less than a given value fl. The theory also predicts that the exact value of the damping in the fuzzy structure is of little importance, because the structure, even in the limit of zero damping, actually absorbs energy with an apparent frequency-dependent damping constant proportional to dfhp(u))/doi incorporated into the dynamical description of the master structure. A small finite value of damping within the internals will cause little appreciable change to this limiting value.

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