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VAN NOSTRAND MOMENTUM BOOK #4- R.A.WALDRON VAN NOSTRAND MOMENTUM BOOKS PUBLISHED FOR THE COMMISSION ON COLLEGE PHYSICS GENERAL EDITOR EDWARD U. CONDON, University of Colorado, Boulder EDITORIAL BOARD Melba Phillips, University of Chicago William T. Scott, University of Nevada Jeremy Bernstein, New York University NO. 1. ELEMENTARY PARTICLES David H. Frisch and Alan M. ThomdiKe NO. 2. RADIO EXPLORATION OF THE PLANETARY SYSTE
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  VAN NOSTRAND MOMENTUM BOOK #4- R.A.WALDRON  VAN NOSTRAND MOMENTUM BOOKS PUBLISHED FOR THECOMMISSION ON COLLEGE PHYSICS GENERAL EDITOR EDWARD U. CONDON, Universityof Colorado, Boulder EDITORIAL BOARD Melba Phillips, University of Chicago William T. Scott, University of Nevada Jeremy Bernstein, New York University NO. 1. ELEMENTARY PARTICLES David H. Frisch andAlan M.ThomdiKe NO. 2. RADIO EXPLORATION OF THE PLANETARY SYSTEM Alex G. Smithand Thomas D. Carr NO. 3. THE DISCOVERY OF THEELECTRON TheDevelopment of the AtomicConcept ofElectricity David L. Anderson NO. 4. WAVES AND OSCILLATIONS R.A. Waldron NO. 5. CRYSTALS AND LIGHT An Introduction to Optical Crystallography Elizabeth A. Wood '4 R. A. WALDRON The Marconi Com -y Limited WA Yk J ? OSCILLATIONS Published for The Commission on College PhysicsD. VAN NOSTRAND COMPANY, INC. Princeton, New Jersey Toronto London New York *> ^  D. VAN NOSTRAND COMPANY, INC. 120 Alexander St., Princeton, New Jersey(Principal Office) 24 West 40 Street, New York 18, New York D. Van Nostrand Company, Ltd. 358, Kensington High Street, London, W.14, England D. Van Nostrand Company (Canada) , Ltd. 2j Hollin^er Road, Toronto 16, Canada Copyright © 1964, byD. VAN NOSTRAXD COMPANY, INC. Published simultaneously in Canada by D. Van Nostrand Company (Canada) , Ltd. No reproduction i?i any for?n of this book, in whole or in part(except for brief quotation in critical articles or reviews), may be made with- outwritten authorization from the publishers PRINTED IN THE UNITED STATES OF AMERICA Preface As asmall child I used to play withwater waves in the bath. As I grew older I learned more about waves, and I am still learning. There is no end to the study, for there are so many kinds of waves, and there is so much to be learned about each of them. They still fascinate me The study of waves is essentially mathematical, and it has not been possibleto avoid using some mathematics in this book, al- though it has been kept as simple aspossible. Where it is necessary to use sophisticated concepts, mathematical detail and rigor have been cast overboard in favor of qualitative descriptions. It is hoped that, having learned in this book ofthe existenceofcertain mathe- maticaltechniques,readers will be sufficiently interested to look elsewhere for information about the techniques themselves. Waves can be studied at a highly sophisticated mathematical level, or wondered over when watching the sea from the top of a cliff, or when idly throwing stones into apond, or at a railway sta- tion when an engine bashes a line of cars. In this little book, I have triedto describe some ofthe facts about waves and the relationships between variouskinds of waves, particularly the latter, which have captured my imagination. It is not possible to do full justice to the subject in a book of this size, but in any case this is not what I wanted to do. Rather than present a cut-and-dried exposition, my aim has been to sketchvarious topics, and hint at others, and point out cross-connections, in the hope that at least some among my readers will be stimulated to enquire further, and experience for themselves thejoys and satisfactions which come as new facts are encountered and deeperunderstanding is achieved. R. A. Waldron in  Introduction This book, as its title indicates, is concerned with waves and oscil- lations, and the emphasis is on the waves, for oscillations of a resonator can beregarded as superpositions of waves.Before em- barking on our discussion, itis helpful to decide just what it is that we are going to discuss — in brief, what is a wave? In a sense, ofcourse, everybody knows what a wave is. The word, or its equivalents in otherlanguages, exists in the vocabulary of every child. As small children, we have all played withwater waves, and with waves on strings. In these cases, we can actually see thewaves, and in a concrete, down-to-earth, everyday sense we know very well what wemean by the word. However, when we get a little older, we learn that sound is conveyed to our ears by means of waves, and that our radios detect radiowaves. We cannot see radio waves and sound waves; we cannotbe aware of them, as waves, in the same way that we are aware of water waves and waves on strings. We also learn that lightconsists of waves, but there is no obviousconnection between waves and the sensation of vision. What is it, then, about the propagation of radio waves, of light, of sound, that leads us toreferto them as waves? Firstly, let us note that in no case are we directly aware of a wave. We do not, contrary to our first impression, see water waves. We see only water, with its surface arranged in a certain way. Takeaway the water, and the waves do not remain. Similarly, we can be aware of the motion of a string as waves travel on it, butnot of the waves themselves. Thus it doesnot seem so strange that we can- not be directly aware of light, sound, orradio waves. We recognize the existenceof water waves by observations that we make, not on the waves, but on thewater; we see the crests and troughs,regularly spaced, and thedistance between successive
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