Vibrations and Waves
Description
Emphasizing physical principles rather than mathematics, Vibrations and Waves, 2nd edition delivers a comprehensive and logical overview of the subject. 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 appropriate.
This book features many worked examples, frequently drawn from everyday life (e.g., why microwave ovens typically have rotating turntables), along with more cutting-edge ones. Each chapter includes problems ranging in difficulty from simple to challenging and provides hints for solving problems. This new edition has been updated with even more worked examples, exercises, and relations to everyday problems.
Vibrations and Waves discusses sample topics including:
Simple harmonic motion, covering displacement, velocity, acceleration, and the physics of small vibrations
The damped harmonic oscillator, covering light, leavy, and critical damping in its equation of motion
Traveling waves, covering the transport of energy by a wave, waves at discontinuities, and waves in two and three dimensions
The dispersion of waves, covering phase and group velocities and the superposition of waves in non-dispersive media
Interference and diffraction of waves, covering Young's double-slit experiment and the Michelonson spectral interferometer
Vibrations and Waves is an essential textbook for all readers learning about waves and vibrations for the first time, either on their own or through an undergraduate or advanced undergraduate course.
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Content
Editors' Preface to the Manchester Physics Series ix
Preface to First Edition xi
Preface to Second Edition xiii
1 Simple Harmonic Motion 1
1.1 Physical Characteristics of Simple Harmonic Oscillators 1
1.2 A Mass on a Spring 2
1.2.1 A Mass on a Horizontal Spring 2
1.2.2 A Mass on a Vertical Spring 4
1.2.3 Displacement, Velocity and Acceleration in SHM 5
1.2.4 General Solutions for SHM and the Phase Angle ¿ 7
1.2.5 The Energy of a Simple Harmonic Oscillator 9
1.2.6 The Physics of Small Vibrations 11
1.3 The Pendulum 16
1.3.1 The Simple Pendulum 16
1.3.2 The Energy of a Simple Pendulum 18
1.3.3 The Physical Pendulum 21
1.3.4 Numerical Solution of SHM 23
1.4 Oscillations in Electrical Circuits: Similarities in Physics 26
1.4.1 The LC Circuit 26
1.4.2 Similarities in Physics 27
Problems 1 29
2 The Damped Harmonic Oscillator 35
2.1 Physical Characteristics of Damped Harmonic Oscillators 35
2.2 The Equation of Motion for a Damped Harmonic Oscillator 36
2.2.1 Light Damping 37
2.2.2 Heavy Damping 40
2.2.3 Critical Damping 40
2.3 Rate of Energy Loss in a Damped Harmonic Oscillator 43
2.3.1 The Quality Factor Q of a Damped Harmonic Oscillator 44
2.4 Damped Electrical Oscillations 47
Problems 2 49
3 Forced Oscillations 53
3.1 Physical Characteristics of Forced Harmonic Motion 54
3.2 The Equation of Motion of a Forced Harmonic Oscillator 54
3.2.1 Undamped Forced Oscillations 54
3.2.2 Forced Oscillations with Damping 57
3.3 Power Absorbed During Forced Oscillations 63
3.4 Resonance in Electrical Circuits 68
3.5 Transient Phenomena 70
3.6 The Complex Representation of Oscillatory Motion 72
3.6.1 Complex Numbers 72
3.6.2 The Use of Complex Numbers to Represent Physical Quantities 75
3.6.3 Use of the Complex Representation for Forced Oscillations with Damping 76
Problems 3 78
4 Coupled Oscillators 85
4.1 Physical Characteristics of Coupled Oscillators 85
4.2 Normal Modes of Oscillation 86
4.3 Superposition of Normal Modes 89
4.4 Oscillating Masses Coupled by Springs 93
4.5 Forced Oscillations of Coupled Oscillators 101
4.6 Transverse Oscillations 104
Problems 4 108
5 Travelling Waves 115
5.1 Physical Characteristics ofWaves 116
5.2 TravellingWaves 116
5.2.1 Travelling SinusoidalWaves 119
5.3 TheWave Equation 122
5.4 The Equation of a Vibrating String 124
5.5 The Energy in aWave 126
5.6 The Transport of Energy by aWave 129
5.7 Waves at Discontinuities 130
5.8 Waves in Two and Three Dimensions 134
5.8.1 Waves of Circular or Spherical Symmetry 138
Problems 5 141
6 StandingWaves147
6.1 StandingWaves on a String 147
6.2 StandingWaves as the Superposition of Two TravellingWaves 153
6.3 The Energy in a StandingWave 155
6.4 StandingWaves as Normal Modes of a Vibrating String 157
6.4.1 The Superposition Principle 157
6.4.2 The Superposition of Normal Modes 158
6.4.3 The Amplitudes of Normal Modes and Fourier Analysis 161
6.4.4 The Energy of Vibration of a String 163
Problems 6 165
7 Interference and Diffraction of Waves 169
7.1 Interference and Huygens' Principle 169
7.1.1 Young's Double-Slit Experiment 172
7.1.2 Michelson Spectral Interferometer 178
7.2 Diffraction 180
7.2.1 Diffraction at a Single Slit 181
7.2.2 Circular Apertures and Angular Resolving Power 185
7.2.3 Double Slits of Finite Width 187
Problems 7 188
8 The Dispersion of Waves 193
8.1 The Superposition ofWaves in Non-Dispersive Media 193
8.1.1 Beats 194
8.1.2 Amplitude Modulation of a RadioWave 196
8.2 The Dispersion ofWaves 197
8.2.1 Phase and Group Velocities 197
8.3 The Dispersion Relation 201
8.4 Wave Packets 204
8.4.1 Formation of aWave Packet 205
Problems 8 209
Index 215