Details

Vibrations and Waves


Vibrations and Waves


Manchester Physics Series 2. Aufl.

von: George C. King

39,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 22.06.2009
ISBN/EAN: 9780470746509
Sprache: englisch
Anzahl Seiten: 256

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Beschreibungen

This introductory text emphasises physical principles, rather than the mathematics. Each topic begins with a discussion of the physical characteristics of the motion or system. The mathematics is kept as clear as possible, and includes elegant mathematical descriptions where possible. Designed to provide a logical development of the subject, the book is divided into two sections, vibrations followed by waves. A particular feature is the inclusion of many examples, frequently drawn from everyday life, along with more cutting-edge ones. Each chapter includes problems ranging in difficulty from simple to challenging and includes hints for solving problems. Numerous worked examples included throughout the book.
<p>Editors' Preface to the Manchester Physics Series xi</p> <p>Author's Preface xiii</p> <p><b>1 SIMPLE HARMONIC MOTION 1</b></p> <p>1.1 Physical Characteristics of Simple Harmonic Oscillators 1</p> <p>1.2 A Mass on a Spring 2</p> <p>1.2.1 A mass on a horizontal spring 2</p> <p>1.2.2 A mass on a vertical spring 5</p> <p>1.2.3 Displacement, velocity and acceleration in simple harmonic motion 5</p> <p>1.2.4 General solutions for simple harmonic motion and the phase angle φ 7</p> <p>1.2.5 The energy of a simple harmonic oscillator 10</p> <p>1.2.6 The physics of small vibrations 12</p> <p>1.3 The Pendulum 17</p> <p>1.3.1 The simple pendulum 17</p> <p>1.3.2 The energy of a simple pendulum 19</p> <p>1.3.3 The physical pendulum 22</p> <p>1.3.4 Numerical solution of simple harmonic motion3 24</p> <p>1.4 Oscillations in Electrical Circuits: Similarities in Physics 27</p> <p>1.4.1 The LC circuit 27</p> <p>1.4.2 Similarities in physics 29</p> <p>PROBLEMS 1 29</p> <p><b>2 THE DAMPED HARMONIC OSCILLATOR 33</b></p> <p>2.1 Physical Characteristics of the Damped Harmonic Oscillator 33</p> <p>2.2 The Equation of Motion for a Damped Harmonic Oscillator 34</p> <p>2.2.1 Light damping 35</p> <p>2.2.2 Heavy damping 37</p> <p>2.2.3 Critical damping 38</p> <p>2.3 Rate of Energy Loss in a Damped Harmonic Oscillator 41</p> <p>2.3.1 The quality factor Q of a damped harmonic oscillator 43</p> <p>2.4 Damped Electrical Oscillations 46</p> <p>PROBLEMS 2 47</p> <p><b>3 FORCED OSCILLATIONS 49</b></p> <p>3.1 Physical Characteristics of Forced Harmonic Motion 50</p> <p>3.2 The Equation of Motion of a Forced Harmonic Oscillator 50</p> <p>3.2.1 Undamped forced oscillations 50</p> <p>3.2.2 Forced oscillations with damping 54</p> <p>3.3 Power Absorbed During Forced Oscillations 60</p> <p>3.4 Resonance in Electrical Circuits 64</p> <p>3.5 Transient Phenomena 66</p> <p>3.6 The Complex Representation of Oscillatory Motion 68</p> <p>3.6.1 Complex numbers 68</p> <p>3.6.2 The use of complex numbers to represent physical quantities 71</p> <p>3.6.3 Use of the complex representation for forced oscillations with damping 74</p> <p>PROBLEMS 3 74</p> <p><b>4 COUPLED OSCILLATORS 77</b></p> <p>4.1 Physical Characteristics of Coupled Oscillators 77</p> <p>4.2 Normal Modes of Oscillation 78</p> <p>4.3 Superposition of Normal Modes 81</p> <p>4.4 Oscillating Masses Coupled by Springs 87</p> <p>4.5 Forced Oscillations of Coupled Oscillators 93</p> <p>4.6 Transverse Oscillations 96</p> <p>PROBLEMS 4 99</p> <p><b>5 TRAVELLING WAVES 105</b></p> <p>5.1 Physical Characteristics of Waves 106</p> <p>5.2 Travelling Waves 106</p> <p>5.2.1 Travelling sinusoidal waves 109</p> <p>5.3 The Wave Equation 112</p> <p>5.4 The Equation of a Vibrating String 114</p> <p>5.5 The Energy in a Wave 116</p> <p>5.6 The Transport of Energy by a Wave 119</p> <p>5.7 Waves at Discontinuities 121</p> <p>5.8 Waves in Two and Three Dimensions 126</p> <p>5.8.1 Waves of circular or spherical symmetry 130</p> <p>PROBLEMS 5 133</p> <p><b>6 STANDING WAVES 137</b></p> <p>6.1 Standing Waves on a String 137</p> <p>6.2 Standing Waves as the Superposition of Two Travelling Waves 144</p> <p>6.3 The Energy in a Standing Wave 147</p> <p>6.4 Standing Waves as Normal Modes of a Vibrating String 149</p> <p>6.4.1 The superposition principle 149</p> <p>6.4.2 The superposition of normal modes 150</p> <p>6.4.3 The amplitudes of normal modes and Fourier analysis 153</p> <p>6.4.4 The energy of vibration of a string 156</p> <p>PROBLEMS 6 158</p> <p><b>7 INTERFERENCE AND DIFFRACTION OF WAVES 161</b></p> <p>7.1 Interference and Huygen’s Principle 161</p> <p>7.1.1 Young’s double-slit experiment 163</p> <p>7.1.2 Michelson spectral interferometer 170</p> <p>7.2 Diffraction 172</p> <p>7.2.1 Diffraction at a single slit 172</p> <p>7.2.2 Circular apertures and angular resolving power 177</p> <p>7.2.3 Double slits of finite width 179</p> <p>PROBLEMS 7 181</p> <p><b>8 THE DISPERSION OF WAVES 183</b></p> <p>8.1 The Superposition of Waves in Non-Dispersive Media 183</p> <p>8.1.1 Beats 184</p> <p>8.1.2 Amplitude modulation of a radio wave 186</p> <p>8.2 The Dispersion of Waves 187</p> <p>8.2.1 Phase and group velocities 188</p> <p>8.3 The Dispersion Relation 192</p> <p>8.4 Wave Packets 195</p> <p>8.4.1 Formation of a wave packet 197</p> <p>PROBLEMS 8 201</p> <p>APPENDIX: SOLUTIONS TO PROBLEMS 205</p> <p>Index 223</p>
"Each chapter is accompanied by a set of problems that form an important part of the book. The book could be used by undergraduate students taking a course in oscillation or wave physics." (<i>Zentralblatt MATH,</i> 2010)<br /> <br /> <p>"The text concisely describes vibrations and waves through mathematical equations with an emphasis on their physical meaning." (<i>Outrider</i>, January 2010)</p>
<b>Professor George C. King</b>, Department of Physics & Astronomy, University of Manchester, Manchester, UK.
<b>The Manchester Physics Series<br /></b>General Editors: F.K. Loebinger; F. Mandl; D.J. Sandiford, School of Physics and Astronomy, The University of Manchester <p><i>Properties of Matter: </i>B.H. Flowers and E Mendoza</p> <p><i>Statistical Physics</i>, Second Edition: F. Mandl</p> <p><i>Electromagnetism</i>, Second Edition: I.S. Grant and W.R.Phillips</p> <p><i>Statistics</i>, R.J. Barlow</p> <p><i>Solid State Physics</i>, Second Edition: J.R. Hook and H.E. Hall</p> <p><i>Quantum Mechanics</i>, F. Mandl</p> <p><i>Computing for Scientists</i>, R.J. Barlow and A.R. Barnett</p> <p><i>The Physics of Stars</i>, Second Edition, A.C. Phillips</p> <p><i>Nuclear Physics</i>, J.S. Lilley</p> <p><i>Introduction to Quantum Mechanics</i>, A.C. Phillips</p> <p><i>Particle Physics</i>, Third Edition: B.R. Martin and G. Shaw</p> <p><i>Dynamics and Relativity</i>, J.R. Forshaw and A.G. Smith</p> <p><i>Vibrations and Waves</i>, G.C. King</p> <p><i>Vibrations and Waves</i> is based on an introductory course given regularly by the author. The text provides the student with a thorough grounding in the theory of vibrations and waves.</p> <p>Throughout the book, the fundamental principles of vibrations and waves are emphasised so that these principles can be applied to a wide range of oscillating systems and to different kinds of waves.</p> <p>The text, which is divided into two sections, <i>vibrations</i> followed by <i>waves</i>, follows a logical progression from the simple harmonic oscillator to waves in continuous media.</p> <p><i>Vibrations</i> and <i>Waves</i> includes:</p> <ul> <li>Vibrations and waves beautifully and concisely described in terms of the mathematical equations used throughout the book</li> <li>Worked examples throughout</li> <li>Problems ranging in difficulty from simple to challenging</li> </ul> <p>Solutions and hints to the problems at the end of the book</p>

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