These two books, which arrived in the same mail, superficially seem not to be very similar to each other. Upon closer examination, however, one finds that they are both highly analytical, while at the same time both strongly emphasize applications. In fact, they tend to complement one another in an interesting way. Modern Methods in Analytical Acoustics was written in Great Britain and authored by Fellows and members of the Acoustical Society of America and others. John Ffowcs-Williams explains the genesis of the book in thePreface: "This book has grown out of lecture notes for a course ... [ presenting] the analytical techniques of selected topics relevant to modern sonar ... the course evolved... to cover notes and unsteady flow... the notes on which the lectures were based we now wish to put on a more permanent record." Each chapter of the book is a lecture written by one of the five authors; thus there is some stylistic variety from one chapter to the next. For example, one man's "Green's function" is another man's "Green function." The book is organized into three parts: The Classical Techniques of Wave Analysis; The Generation of Unsteady Fields; and Wave Modification.The name of the first part is interesting. The title of the book leads us to believe that we are supposed to be learning modern methods; the title of this part says that we are dealing with clas•sical techniques! There are ten chapters in this part: complex variable theory; generalized functions; Fourier transforms, random processes, digital sampling and wavelets; asymptotic evaluation of integrals; Wiener-Hopf technique; matched asymptotic expansions applied to acoustics; multiple scales; statistical energy analysis; mean energy and momentum effects in waves; and numerical methods•an appetizing menu for the mathematically inclined. The last, Chap. 10, Numerical Methods, chooses not to treat the currently available computer software packages.The second part, comprising seven chapters, is where the professional interests of the authors are revealed: noise source mechanisms; vortex sound; thermoacoustic sources and instabilities; effects of motion on acoustic sources (is Doppler supposed to be spelled with an umlaut?); propeller and helicopter noise; flow noise an surfaces; and fluid-loading interaction with vibrating surfaces. The penultimate chapter of this list, Chap. 16, Flow Noise on Surfaces, was paid for by the sonar community and does discuss such familiar items as sonar domes and line arrays. Thus, sonar has not been altogether lost in the development of the course over the years! The third part, consisting of nine chapters, is a bit puzzling. What does the term "wave modification" mean, exactly? The part seems to be intended to be a collection of advanced topics, and largely is. The list of topics is as follows: scattering and diffraction; inverse scattering; resonators; bubbles; reverberation; soiltons; nonlinear acoustics; chaotic dynamics and applica-tions in acoustics; and antisound. The first chapter on the list, Chap. 18, Scatter...

Reviewed by M. M. Sevik 1 Sound and Sources of Sound by A. P. Dowling and J. E. Ffowcs-Williams is based on a series of lectures given to undergi aduate engineering students at the University of Cambridge. The book is masterfully written and its use far transcends classroom instruction. In fact, it is recommended reading for all practicing engineers whose major concern is the control of sources of vibrations and sound that are induced by unsteady fluid flow. The book's major contribution to the literature of acoustics begins with Chapter 7. Here, sources of sound which are not due to the vibration of boundary surfaces are described. These include combustion noise, sound generated by the "creation of matter," by externally applied forces on a fluid, and by sound due to turbulent flow. Lighthill's equation is derived and its solution for the sound field is given. Lighthill's famous V s law for jet noise follows from dimensional analysis and its range of validity is discussed. Chapter 8 begins with the derivation of the reciprocal theorem. The ingenious application of this theorem leads to easy solutions of what would otherwise be very difficult problems. Examples are the sound scattered by a bubble entrained in a turbulent flow of water and the sound generated by turbulent quadrupoles near a sharp edge, such as the trailing edge of an airfoil. In many practical cases, sources of sound move relative to an observer. This class of problems is particularly significant in aeroacoustics, where Mach numbers are generally high. The sound field generated by moving sources is described in Chapter 9 in considerable detail. The Fourier decomposition of a wave field in Chapter 10 leads to useful clarifications of the physics of sound generation. It is demonstrated early in the chapter, for example, that "a sound field is generated by elements of the source with sonic phase velocity." In order to deal with the effects of turbulence, a discussion of the statistical analysis of random signals is provided. Cross correlation functions involving both separations in space and delays in time are defined and are used to establish some general characteristics of turbulent flows. The final chapter of the book deals with the response of structures to a spatially and temporally unsteady flow. Fluid loading-which is important in hydroacoustics-is clearly explained. The criteria for temporal or spatial instabilities of

Measurements with intensity meters have shown that energy vortices exist in certain sound fields. In these vortices, sound energy flows around closed paths, in the steady state. Vortices occur in some sound fields (e.g., that of a point source near a reflecting edge), but not in others (e.g., that of a plane rigid piston in a plane rigid baffle). It is shown that in a two-dimensional or axisymmetric sound field, a necessary and sufficient condition for a vortex to exist is the presence of an isolated maximum or minimum in the stream function. Two examples are given for a vortex in (a) a duct of square cross section, and (b) the field of two monopole sources, one of which just extinguishes the other. Some relations for the interaction between two monopole sources are also given.

The stability of boundary-layer flows that are formed on flexible surfaces is known to be affected by the surface response. A study of the manner in which energy is exchanged between the mean flow, the perturbation, and the vibrating surface has called for more knowledge of the way in which the Reynolds stress is influenced by wall vibration. The reason is that mean flow energy is transferred to the perturbation by the action of Reynolds stresses, so any change brought about in their level, as a result of surface motion, could influence the energy balance and consequently the stability of the system. An analysis of the Reynolds stresses near a vibrating surface is described and it is shown that they are increased by at least an order of magnitude whenever the surface is allowed to vibrate. [This research has been supported by the David Taylor Model Basin.]

The mechanics by which sound evolves from unsteady boundaries and flow can be represented in acoustic analogies which provide a formal structure for analyzing the process of sound creation. The acoustic analogy of Lighthill has been the firmest foundation for modeling the jet noise problem. Studies of that problem have gradually increased in sophistication and scope to a point where the analogy itself has been developed to display characteristics that are novel and a little startling. The early models regarded turbulence as prescribed and concentrated purely on the acoustical consequences of that turbulence. But the more advanced analogies recognize definite constraints on acoustically important elements of turbulence and point to the susceptibility of the noise generating elements of turbulence to external stimulus. Other long waves induced by turbulence can be similarly analyzed and correspondingly interesting deductions made on vibrational fields induced by turbulent flow. This paper will describe some of the developments leading to notions that turbulence can be influenced by well-chosen external stimuli and speculate a tittle on areas where these effects might have significant practical applications.