Preface

Waves are everywhere. Everything waves. There are familiar, everyday sorts of waves in water, ropes and springs. There are less visible but equally pervasive sound waves and electromagnetic waves. Even more important, though only touched on in this book, is the wave phenomenon of quantum mechanics, built into the fabric of our space and time. How can it make sense to use the same word — “wave” — for all these disparate phenomena? What is it that they all have in common? The superficial answer lies in the mathematics of wave phenomena. Periodic behavior of any kind, one might argue, leads to similar mathematics. Perhaps this is the unifying principle. In this book, I introduce you to a deeper, physical answer to the questions. The mathematics of waves is important, to be sure. Indeed, I devote much of the book to the mathematical formalism in which wave phenomena can be described most insightfully. But I use the mathematics only as a tool to formulate the underlying physical principles that tie together many different kinds of wave phenomena. There are three: linearity, translation invariance and local interactions. You will learn in detail what each of these means in the chapters to come. When all three are present, wave phenomena always occur. Furthermore, as you will see, these principles are a great practical help both in understanding particular wave phenomena and in solving problems. I hope to convert you to a way of thinking about waves that will permanently change the way you look at the world. The organization of the book is designed to illustrate how wave phenomena arise in any system of coupled linear oscillators with translation invariance and local interactions. We begin with the single harmonic oscillator and work our way through standing wave normal modes in more and more interesting systems. Traveling waves appear only after a thorough exploration of one-dimensional standing waves. I hope to emphasize that the physics of standing waves is the same. Only the boundary conditions are different. When we finally get to traveling waves, well into the book, we will be able to get to interesting properties very quickly. For similar reasons, the discussion of two- and three-dimensional waves occurs late in the book, after you have been exposed to all the tools required to deal with one-dimensional waves. This allows us at least to set up the problems of interference and diffraction in a xiii xiv PREFACE simple way, and to solve the problems in some simple cases. Waves move. Their motion is an integral part of their being. Illustrations on a printed page cannot do justice to this motion. For that reason, this book comes with moving illustrations, in the form of computer animations of various wave phenomena. These supplementary programs are an important part of the book. Looking at them and interacting with them, you will get a much more concrete understanding of wave phenomena than can be obtained from a book alone. I discuss the simple programs that produce the animations in more detail in Appendix A. Also in this appendix are instructions on the use of the supplementary program disk. The subsections that are illustrated with computer animations are clearly labeled in the text by and the number of the program. I hope you will read these parts of the book while sitting at your computer screens. The sections and problems marked with a * can be skipped by instructors who wish to keep the mathematical level as low as possible. Two other textbooks on the subject, Waves, by Crawford and Optics by Hecht, influenced me in writing this book. The strength of Crawford’s book is the home experiments. These experiments are very useful additions to any course on wave phenomena. Hecht’s book is an encyclopedic treatment of optics. In my own book, I try to steer a middle course between these two, with a better treatment of general wave phenomena than Hecht and a more appropriate mathematical level than Crawford. I believe that my text has many of the advantages of both books, but students may wish to use them as supplementary texts. While the examples of waves phenomena that we discuss in this book will be chosen (mostly) from familiar waves, we also will be developing the mathematics of waves in such a way that it can be directly applied to quantum mechanics. Thus, while learning about waves in ropes and air and electromagnetic fields, you will be preparing to apply the same techniques to the study of the quantum mechanical world. I am grateful to many people for their help in converting this material into a textbook. Adam Falk and David Griffiths made many detailed and invaluable suggestions for improvements in the presentation. Melissa Franklin, Geoff Georgi, Kevin Jones and Mark Heald, also had extremely useful suggestions. I am indebted to Nicholas Romanelli for copyediting and to Ray Henderson for orchestrating all of it. Finally, thanks go to the hundreds of students who took the waves course at Harvard in the last fifteen years. This book is as much the product of their hard work and enthusiasm, as my own.

Howard Georgi

Cambridge, MA