This book is a practical guide for researchers and advanced graduate students in biology and biophysics who need a quantitative understanding of acoustical systems such as hearing, sound production, and vibration detection in animals at the physiological level. It begins with an introduction to physical acoustics directed explicitly at their needs, covering the fundamental concepts and showing how they can be applied quantitatively to understand animals' auditory and sound-producing systems. Only after the relatively simple mechanical part of the system is explained does the author focus his attention on the underlying physiological processes.

This book is a practical guide for researchers and advanced graduate students in biology and biophysics who need a quantitative understanding of acoustical systems such as hearing, sound production, and vibration detection in animals at the physiological level. It begins with an introduction to physical acoustics, covering the fundamental concepts and showing how they can be applied quantitatively to understand auditory and sound-producing systems in animals. Only after the relatively simple mechanical part of the system is explained does the author focus his attention on the underlying physiological processes. The book is written on three levels. For those wanting a brief survey of the field, each chapter begins with a nonmathematical synopsis which summarizes the content and refers to the figures, all of which are designed to be understood apart from the main text. At the next level, the reader can follow the main text, but need not give close attention to anything but the general concepts and techniques involved. At the third level, the reader should follow the mathematical arguments in detail and attempt the discussion of questions at the end of each chapter. The author has provided detailed solutions which serve to expand the discussions of particular cases.

When we wrote the first edition of this book, we directed our presenta­ tion to the reader with a compelling interest in musical instruments who has "a reasonable grasp of physics and who is not frightened by a little mathematics." We are delighted to find how many such people there are. The opportunity afforded by the preparation of this second edition has allowed us to bring our discussion up to date by including those new insights that have arisen from the work of many dedicated researchers over the past decade. We have also taken the opportunity to revise our presentation of some aspects of the subject to make it more general and, we hope, more immediately accessible. We have, of course, corrected any errors that have come to our attention, and we express our thanks to those friends who pointed out such defects in the early printings of the first edition. We hope that this book will continue to serve as a guide, both to those undertaking research in the field and to those who simply have a deep interest in the subject. June 1991 N.H.F and T.D.R.

The first edition of this book presented the principles of vibration and sound with only a little discussion of applications of these principles. During the past eight years, our own experience, as well as that of other teachers who used it as a textbook, has indicated that students would benefit from more discussion of applications. In this edition we have revised some of the mate­ rial in the first nine chapters, but more importantly we have added four new chapters dealing with applications, including microphones, loudspeakers, and other transducers; acoustics of concert halls and studios; sound and noise outdoors; and underwater sound. Of course we could have selected many additional applications of vibration and sound, but that would have led to a book with too much material for the average acoustics course in physics and engineering departments. We think there is now ample material in the book so that instructors may select the applications of particular in­ terest and omit the others without loss of continuity. We have continued to stress concepts over detailed theory, as seems most appropriate for an in­ troductory course. We appreciate the comments we have received from users, students, and teachers alike, and we continue to welcome feedback. September 2003 Thomas D. Rossing Neville H. Fletcher Preface to the First Edition Some years ago we set out to write a detailed book about the basic physics of musical instruments.

When we wrote the first edition of this book, we directed our presenta­ tion to the reader with a compelling interest in musical instruments who has "a reasonable grasp of physics and who is not frightened by a little mathematics." We are delighted to find how many such people there are. The opportunity afforded by the preparation of this second edition has allowed us to bring our discussion up to date by including those new insights that have arisen from the work of many dedicated researchers over the past decade. We have also taken the opportunity to revise our presentation of some aspects of the subject to make it more general and, we hope, more immediately accessible. We have, of course, corrected any errors that have come to our attention, and we express our thanks to those friends who pointed out such defects in the early printings of the first edition. We hope that this book will continue to serve as a guide, both to those undertaking research in the field and to those who simply have a deep interest in the subject. June 1991 N.H.F and T.D.R.

The first edition of this book presented the principles of vibration and sound with only a little discussion of applications of these principles. During the past eight years, our own experience, as well as that of other teachers who used it as a textbook, has indicated that students would benefit from more discussion of applications. In this edition we have revised some of the mate­ rial in the first nine chapters, but more importantly we have added four new chapters dealing with applications, including microphones, loudspeakers, and other transducers; acoustics of concert halls and studios; sound and noise outdoors; and underwater sound. Of course we could have selected many additional applications of vibration and sound, but that would have led to a book with too much material for the average acoustics course in physics and engineering departments. We think there is now ample material in the book so that instructors may select the applications of particular in­ terest and omit the others without loss of continuity. We have continued to stress concepts over detailed theory, as seems most appropriate for an in­ troductory course. We appreciate the comments we have received from users, students, and teachers alike, and we continue to welcome feedback. September 2003 Thomas D. Rossing Neville H. Fletcher Preface to the First Edition Some years ago we set out to write a detailed book about the basic physics of musical instruments.

When we wrote the first edition of this book, we directed our presenta­ tion to the reader with a compelling interest in musical instruments who has "a reasonable grasp of physics and who is not frightened by a little mathematics." We are delighted to find how many such people there are. The opportunity afforded by the preparation of this second edition has allowed us to bring our discussion up to date by including those new insights that have arisen from the work of many dedicated researchers over the past decade. We have also taken the opportunity to revise our presentation of some aspects of the subject to make it more general and, we hope, more immediately accessible. We have, of course, corrected any errors that have come to our attention, and we express our thanks to those friends who pointed out such defects in the early printings of the first edition. We hope that this book will continue to serve as a guide, both to those undertaking research in the field and to those who simply have a deep interest in the subject. June 1991 N.H.F and T.D.R.

Some years ago we set out to write a detailed book about the basic physics of musical instruments. There have been many admirable books published about the history of the development of musical instruments, about their construction as a master craft, and about their employment in musical perfor­ mance; several excellent books have treated the acoustics of musical instru­ ments in a semiquantitative way; but none to our knowledge had then at­ tempted to assemble the hard acoustic information available in the research literature and to make it available to a wider readership. Our book The Physics of Musical Instruments, published by Springer-Verlag in 1991 and subsequently reprinted several times with only minor corrections, was the outcome of our labor. Because it was our aim to make our discussion of musical instruments as complete and rigorous as possible, our book began with a careful introduction to vibrating and radiating systems important in that field. We treated simple linear oscillators, both in isolation and coupled together, and extended that to a discussion of some aspects of driven and autonomous nonlinear oscilla­ tors. Because musical instruments are necessarily extended structures, we then went on to discuss the vibrations of strings, bars, membranes, plates, and shells, paying particular attention to the mode structures and characteristic frequencies, for it is these that are musically important.

The history of musical instruments is nearly as old as the history of civilization itself, and the aesthetic principles upon which judgments of musical quality are based are intimately connected with the whole culture within which the instruments have evolved. An educated modem Western player or listener can make critical judgments about particular instruments or particular per­ formances but, to be valid, those judgments must be made within the appro­ priate cultural context. The compass of our book is much less sweeping than the first paragraph might imply, and indeed our discussion is primarily confined to Western musical instruments in current use, but even here we must take account of centuries of tradition. A musical instrument is designed and built for the playing of music of a particular type and, conversely, music is written to be performed on particular instruments. There is no such thing as an "ideal" instrument, even in concept, and indeed the unbounded possibilities of modem digital sound-synthesis really require the composer or performer to define a whole set of instruments if the result is to have any musical coherence. Thus, for example, the sound and response of a violin are judged against a mental image of a perfect violin built up from experience of violins playing music written for them over the centuries. A new instrument may be richer in sound quality and superior in responsiveness, but if it does not fit that image then it is not a better violin.

The first edition of this book presented the principles of vibration and sound with only a little discussion of applications of these principles. During the past eight years, our own experience, as well as that of other teachers who used it as a textbook, has indicated that students would benefit from more discussion of applications. In this edition we have revised some of the mate­ rial in the first nine chapters, but more importantly we have added four new chapters dealing with applications, including microphones, loudspeakers, and other transducers; acoustics of concert halls and studios; sound and noise outdoors; and underwater sound. Of course we could have selected many additional applications of vibration and sound, but that would have led to a book with too much material for the average acoustics course in physics and engineering departments. We think there is now ample material in the book so that instructors may select the applications of particular in­ terest and omit the others without loss of continuity. We have continued to stress concepts over detailed theory, as seems most appropriate for an in­ troductory course. We appreciate the comments we have received from users, students, and teachers alike, and we continue to welcome feedback. September 2003 Thomas D. Rossing Neville H. Fletcher Preface to the First Edition Some years ago we set out to write a detailed book about the basic physics of musical instruments.

Some years ago we set out to write a detailed book about the basic physics of musical instruments. There have been many admirable books published about the history of the development of musical instruments, about their construction as a master craft, and about their employment in musical perfor­ mance; several excellent books have treated the acoustics of musical instru­ ments in a semiquantitative way; but none to our knowledge had then at­ tempted to assemble the hard acoustic information available in the research literature and to make it available to a wider readership. Our book The Physics of Musical Instruments, published by Springer-Verlag in 1991 and subsequently reprinted several times with only minor corrections, was the outcome of our labor. Because it was our aim to make our discussion of musical instruments as complete and rigorous as possible, our book began with a careful introduction to vibrating and radiating systems important in that field. We treated simple linear oscillators, both in isolation and coupled together, and extended that to a discussion of some aspects of driven and autonomous nonlinear oscilla­ tors. Because musical instruments are necessarily extended structures, we then went on to discuss the vibrations of strings, bars, membranes, plates, and shells, paying particular attention to the mode structures and characteristic frequencies, for it is these that are musically important.

This book is a practical guide for researchers and advanced graduate students in biology and biophysics who need a quantitative understanding of acoustical systems such as hearing, sound production, and vibration detection in animals at the physiological level. It begins with an introduction to physical acoustics directed explicitly at their needs, covering the fundamental concepts and showing how they can be applied quantitatively to understand animals' auditory and sound-producing systems. Only after the relatively simple mechanical part of the system is explained does the author focus his attention on the underlying physiological processes.

This book is a practical guide for researchers and advanced graduate students in biology and biophysics who need a quantitative understanding of acoustical systems such as hearing, sound production, and vibration detection in animals at the physiological level. It begins with an introduction to physical acoustics, covering the fundamental concepts and showing how they can be applied quantitatively to understand auditory and sound-producing systems in animals. Only after the relatively simple mechanical part of the system is explained does the author focus his attention on the underlying physiological processes. The book is written on three levels. For those wanting a brief survey of the field, each chapter begins with a nonmathematical synopsis which summarizes the content and refers to the figures, all of which are designed to be understood apart from the main text. At the next level, the reader can follow the main text, but need not give close attention to anything but the general concepts and techniques involved. At the third level, the reader should follow the mathematical arguments in detail and attempt the discussion of questions at the end of each chapter. The author has provided detailed solutions which serve to expand the discussions of particular cases.

When we wrote the first edition of this book, we directed our presenta­ tion to the reader with a compelling interest in musical instruments who has "a reasonable grasp of physics and who is not frightened by a little mathematics." We are delighted to find how many such people there are. The opportunity afforded by the preparation of this second edition has allowed us to bring our discussion up to date by including those new insights that have arisen from the work of many dedicated researchers over the past decade. We have also taken the opportunity to revise our presentation of some aspects of the subject to make it more general and, we hope, more immediately accessible. We have, of course, corrected any errors that have come to our attention, and we express our thanks to those friends who pointed out such defects in the early printings of the first edition. We hope that this book will continue to serve as a guide, both to those undertaking research in the field and to those who simply have a deep interest in the subject. June 1991 N.H.F and T.D.R.

The first edition of this book presented the principles of vibration and sound with only a little discussion of applications of these principles. During the past eight years, our own experience, as well as that of other teachers who used it as a textbook, has indicated that students would benefit from more discussion of applications. In this edition we have revised some of the mate­ rial in the first nine chapters, but more importantly we have added four new chapters dealing with applications, including microphones, loudspeakers, and other transducers; acoustics of concert halls and studios; sound and noise outdoors; and underwater sound. Of course we could have selected many additional applications of vibration and sound, but that would have led to a book with too much material for the average acoustics course in physics and engineering departments. We think there is now ample material in the book so that instructors may select the applications of particular in­ terest and omit the others without loss of continuity. We have continued to stress concepts over detailed theory, as seems most appropriate for an in­ troductory course. We appreciate the comments we have received from users, students, and teachers alike, and we continue to welcome feedback. September 2003 Thomas D. Rossing Neville H. Fletcher Preface to the First Edition Some years ago we set out to write a detailed book about the basic physics of musical instruments.

When we wrote the first edition of this book, we directed our presenta­ tion to the reader with a compelling interest in musical instruments who has "a reasonable grasp of physics and who is not frightened by a little mathematics." We are delighted to find how many such people there are. The opportunity afforded by the preparation of this second edition has allowed us to bring our discussion up to date by including those new insights that have arisen from the work of many dedicated researchers over the past decade. We have also taken the opportunity to revise our presentation of some aspects of the subject to make it more general and, we hope, more immediately accessible. We have, of course, corrected any errors that have come to our attention, and we express our thanks to those friends who pointed out such defects in the early printings of the first edition. We hope that this book will continue to serve as a guide, both to those undertaking research in the field and to those who simply have a deep interest in the subject. June 1991 N.H.F and T.D.R.

The first edition of this book presented the principles of vibration and sound with only a little discussion of applications of these principles. During the past eight years, our own experience, as well as that of other teachers who used it as a textbook, has indicated that students would benefit from more discussion of applications. In this edition we have revised some of the mate­ rial in the first nine chapters, but more importantly we have added four new chapters dealing with applications, including microphones, loudspeakers, and other transducers; acoustics of concert halls and studios; sound and noise outdoors; and underwater sound. Of course we could have selected many additional applications of vibration and sound, but that would have led to a book with too much material for the average acoustics course in physics and engineering departments. We think there is now ample material in the book so that instructors may select the applications of particular in­ terest and omit the others without loss of continuity. We have continued to stress concepts over detailed theory, as seems most appropriate for an in­ troductory course. We appreciate the comments we have received from users, students, and teachers alike, and we continue to welcome feedback. September 2003 Thomas D. Rossing Neville H. Fletcher Preface to the First Edition Some years ago we set out to write a detailed book about the basic physics of musical instruments.

When we wrote the first edition of this book, we directed our presenta­ tion to the reader with a compelling interest in musical instruments who has "a reasonable grasp of physics and who is not frightened by a little mathematics." We are delighted to find how many such people there are. The opportunity afforded by the preparation of this second edition has allowed us to bring our discussion up to date by including those new insights that have arisen from the work of many dedicated researchers over the past decade. We have also taken the opportunity to revise our presentation of some aspects of the subject to make it more general and, we hope, more immediately accessible. We have, of course, corrected any errors that have come to our attention, and we express our thanks to those friends who pointed out such defects in the early printings of the first edition. We hope that this book will continue to serve as a guide, both to those undertaking research in the field and to those who simply have a deep interest in the subject. June 1991 N.H.F and T.D.R.

Some years ago we set out to write a detailed book about the basic physics of musical instruments. There have been many admirable books published about the history of the development of musical instruments, about their construction as a master craft, and about their employment in musical perfor­ mance; several excellent books have treated the acoustics of musical instru­ ments in a semiquantitative way; but none to our knowledge had then at­ tempted to assemble the hard acoustic information available in the research literature and to make it available to a wider readership. Our book The Physics of Musical Instruments, published by Springer-Verlag in 1991 and subsequently reprinted several times with only minor corrections, was the outcome of our labor. Because it was our aim to make our discussion of musical instruments as complete and rigorous as possible, our book began with a careful introduction to vibrating and radiating systems important in that field. We treated simple linear oscillators, both in isolation and coupled together, and extended that to a discussion of some aspects of driven and autonomous nonlinear oscilla­ tors. Because musical instruments are necessarily extended structures, we then went on to discuss the vibrations of strings, bars, membranes, plates, and shells, paying particular attention to the mode structures and characteristic frequencies, for it is these that are musically important.

The history of musical instruments is nearly as old as the history of civilization itself, and the aesthetic principles upon which judgments of musical quality are based are intimately connected with the whole culture within which the instruments have evolved. An educated modem Western player or listener can make critical judgments about particular instruments or particular per­ formances but, to be valid, those judgments must be made within the appro­ priate cultural context. The compass of our book is much less sweeping than the first paragraph might imply, and indeed our discussion is primarily confined to Western musical instruments in current use, but even here we must take account of centuries of tradition. A musical instrument is designed and built for the playing of music of a particular type and, conversely, music is written to be performed on particular instruments. There is no such thing as an "ideal" instrument, even in concept, and indeed the unbounded possibilities of modem digital sound-synthesis really require the composer or performer to define a whole set of instruments if the result is to have any musical coherence. Thus, for example, the sound and response of a violin are judged against a mental image of a perfect violin built up from experience of violins playing music written for them over the centuries. A new instrument may be richer in sound quality and superior in responsiveness, but if it does not fit that image then it is not a better violin.

The first edition of this book presented the principles of vibration and sound with only a little discussion of applications of these principles. During the past eight years, our own experience, as well as that of other teachers who used it as a textbook, has indicated that students would benefit from more discussion of applications. In this edition we have revised some of the mate­ rial in the first nine chapters, but more importantly we have added four new chapters dealing with applications, including microphones, loudspeakers, and other transducers; acoustics of concert halls and studios; sound and noise outdoors; and underwater sound. Of course we could have selected many additional applications of vibration and sound, but that would have led to a book with too much material for the average acoustics course in physics and engineering departments. We think there is now ample material in the book so that instructors may select the applications of particular in­ terest and omit the others without loss of continuity. We have continued to stress concepts over detailed theory, as seems most appropriate for an in­ troductory course. We appreciate the comments we have received from users, students, and teachers alike, and we continue to welcome feedback. September 2003 Thomas D. Rossing Neville H. Fletcher Preface to the First Edition Some years ago we set out to write a detailed book about the basic physics of musical instruments.

Some years ago we set out to write a detailed book about the basic physics of musical instruments. There have been many admirable books published about the history of the development of musical instruments, about their construction as a master craft, and about their employment in musical perfor­ mance; several excellent books have treated the acoustics of musical instru­ ments in a semiquantitative way; but none to our knowledge had then at­ tempted to assemble the hard acoustic information available in the research literature and to make it available to a wider readership. Our book The Physics of Musical Instruments, published by Springer-Verlag in 1991 and subsequently reprinted several times with only minor corrections, was the outcome of our labor. Because it was our aim to make our discussion of musical instruments as complete and rigorous as possible, our book began with a careful introduction to vibrating and radiating systems important in that field. We treated simple linear oscillators, both in isolation and coupled together, and extended that to a discussion of some aspects of driven and autonomous nonlinear oscilla­ tors. Because musical instruments are necessarily extended structures, we then went on to discuss the vibrations of strings, bars, membranes, plates, and shells, paying particular attention to the mode structures and characteristic frequencies, for it is these that are musically important.