|
|
|
Waves
|
(Buch) |
Dieser Artikel gilt, aufgrund seiner Grösse, beim Versand als 2 Artikel!
| Inhalt: |
|
WAVES A MATHEMATICAL ACCOUNT OF THE COMMON TYPES OF WAVE MOTION BY C. A. COULSON, M. A., Ph. D. LECTURER IN MATHEMATICS IN THE UNIVERSITY OF ST ANDREWS, FORMERLY FELLOW OF TRINITY COLLEGE, CAMBRIDGE With 29 Figures OLIVER AND BOYD EDINBURGH I TWEEDDALE COURT LONDON 98 GREAT RUSSELL STREET, W. C. 1941 PREFACE THE object of this book is to consider from an elementary standpoint as many different types of wave motion as possible. In almost every case the fundamental problem is the same, since it consists in solving the standard equation of wave motion the various applications differ chiefly in the conditions imposed upon these solutidn. jj For this reason it is desirable that the subject of waves should be treated as one whole, rather than in several distinct parts the present tendency is in this direction. It is presupposed that the reader is familiar with the elements of vector analysis, the simpler results of which are freely quoted. In a sense this present volume may be regarded as a sequel to Rutherfords Vector Methods, published in this series. In a volume of this size, it is not possible to deal thoroughly with any one branch of the subject nor indeed is this desirable in a book which is intended as an introduction to the more specialised and elaborate treatises necessary to the specialist. This book is intended for University students covering a general course of Applied Mathematics or Natural Philosophy in the final year of their honours degree. A few topics, such as elastic waves in continuous media, or at the common boundary of two media, and radiation from aerials, have unavoidably had to be omitted for lack of space. The reader is referred to any of the standard works onelasticity and wireless for a discussion of these problems, vii viii PREFACE This book would not be complete without a reference of gratitude to my friends Dr D. E. Rutherford and Dr G. S. Rushbrooke, who have read the proofs, checked most of the examples and contributed in no small way to the clarity of my arguments. My thanks are also offered to my wife for her share in the preparation of the manuscript. C. A. 0. January 1941. CONTENTS CHAPTER I THE EQUATION OF WAVE MOTION PAGE Introductory 1 General Form of Progressive Waves ..... 1 Harmonic Waves 2 Plane Waves 4 The Equation of Wave Motion 5 Principle of Superposition ....... 5 Special Types of Solution 6 List of Solutions ........ 13 Equation of Telegraphy 15 Exponential Form of Harmonic Waves . . . .16 A Solved Example 17 Examples 19 CHAPTER n WAVES ON STRINGS The Differential Equation 21 Kinetic and Potential Energies ...... 23 Inclusion of Initial Conditions ...... 25 Reflection at a Change of Density 25 Reflection at a Concentrated Load 28 Alternative Solutions 29 Strings of Finite Length, Normal Modes .... 30 String Plucked at its Mid-point, . . ., .31 The Energies of the Normal Modes 33 Normal Co-ordinates ....... 36 String with Load at its Mid-point . . . . .37 Damped Vibrations ........ 39 Method of Reduction to a Steady Wave .... 40 Examples 41 x CONTENTS CHAPTER III WAVES IN MEMBRANES PAGE The Differential Equation ....... 43 Solution for a Rectangular Membrane .... 44 Normal Co-ordinates for Rectangular Membrane ... 47 Circular Membrane ........ 48 Examples ......... 50 CHAPTER IV LONGITUDINAL WAVES IN BARS AND SPRINGS Differential Equation for Waves along a Bar . . .51 Free Vibrations of a Finite Bar ...... 53Vibrations of a Clamped Bar . . . . . .53 Normal Co-ordinates ........ 53 Case of a Bar in a state of Tension ..... 54 Vibrations of a Loaded Spring ...... 55 Examples . . . . . . . . .59 CHAPTER v WAVES IN LIQUIDS Summary of Hydrodynamical Formulae .... 60 Tidal Waves and Surface Waves ..... 62 Tidal Waves, General Conditions 63 Tidal Waves in a Straight Channel ..... 64 Tidal Waves on Lakes and Tanks 67 Tidal Waves on Rectangular and Circular Tanks ... 70 Paths of the Particles 70 Method of Reduction to a Steady Wave . . . .71 Surface Waves, the Velocity Potential . ... |
|
i.d.R. innert 7-14 Tagen versandfertig
Newsfeed | 
Facebook | 
Twitter
