Vibrations and Waves (Manchester Physics Series)

Vibrations and Waves......Page 4
Contents......Page 9
Editors’ Preface to the Manchester Physics Series......Page 13
Author’s Preface......Page 15
1.1 Physical Characteristics of Simple Harmonic Oscillators......Page 18
1.2.1 A mass on a horizontal spring......Page 19
1.2.3 Displacement, velocity and acceleration in simple harmonic motion......Page 22
1.2.4 General solutions for simple harmonic motion and the \nphase angle φ......Page 24
1.2.5 The energy of a simple harmonic oscillator......Page 27
1.2.6 The physics of small vibrations......Page 29
1.3.1 The simple pendulum......Page 34
1.3.2 The energy of a simple pendulum......Page 36
1.3.3 The physical pendulum......Page 39
1.3.4 Numerical solution of simple harmonic motion3......Page 41
1.4.1 The LC circuit......Page 44
PROBLEMS 1......Page 46
2.1 Physical Characteristics of the Damped Harmonic Oscillator......Page 50
2.2 The Equation of Motion for a Damped Harmonic Oscillator......Page 51
2.2.1 Light damping......Page 52
2.2.2 Heavy damping......Page 54
2.2.3 Critical damping......Page 55
2.3 Rate of Energy Loss in a Damped Harmonic Oscillator......Page 58
2.3.1 The quality factor Q of a damped harmonic oscillator......Page 60
2.4 Damped Electrical Oscillations......Page 63
PROBLEMS 2......Page 64
3 FORCED OSCILLATIONS......Page 66
3.2.1 Undamped forced oscillations......Page 67
3.2.2 Forced oscillations with damping......Page 71
3.3 Power Absorbed During Forced Oscillations......Page 77
3.4 Resonance in Electrical Circuits......Page 81
3.5 Transient Phenomena......Page 83
3.6.1 Complex numbers......Page 85
3.6.2 The use of complex numbers to represent physical quantities......Page 88
PROBLEMS 3......Page 91
4.1 Physical Characteristics of Coupled Oscillators......Page 94
4.2 Normal Modes of Oscillation......Page 95
4.3 Superposition of Normal Modes......Page 98
4.4 Oscillating Masses Coupled by Springs......Page 104
4.5 Forced Oscillations of Coupled Oscillators......Page 110
4.6 Transverse Oscillations......Page 113
PROBLEMS 4......Page 116
5 TRAVELLING WAVES......Page 122
5.2 Travelling Waves......Page 123
5.2.1 Travelling sinusoidal waves......Page 126
5.3 The Wave Equation......Page 129
5.4 The Equation of a Vibrating String......Page 131
5.5 The Energy in a Wave......Page 133
5.6 The Transport of Energy by a Wave......Page 136
5.7 Waves at Discontinuities......Page 138
5.8 Waves in Two and Three Dimensions......Page 143
5.8.1 Waves of circular or spherical symmetry......Page 147
PROBLEMS 5......Page 150
6.1 Standing Waves on a String......Page 154
6.2 Standing Waves as the Superposition of Two Travelling Waves......Page 161
6.3 The Energy in a Standing Wave......Page 164
6.4.1 The superposition principle......Page 166
6.4.2 The superposition of normal modes......Page 167
6.4.3 The amplitudes of normal modes and Fourier analysis......Page 170
6.4.4 The energy of vibration of a string......Page 173
PROBLEMS 6......Page 175
7.1 Interference and Huygen’s Principle......Page 178
7.1.1 Young’s double-slit experiment......Page 180
7.1.2 Michelson spectral interferometer......Page 187
7.2.1 Diffraction at a single slit......Page 189
7.2.2 Circular apertures and angular resolving power......Page 194
7.2.3 Double slits of finite width......Page 196
PROBLEMS 7......Page 198
8.1 The Superposition of Waves in Non-Dispersive Media......Page 200
8.1.1 Beats......Page 201
8.1.2 Amplitude modulation of a radio wave......Page 203
8.2 The Dispersion of Waves......Page 204
8.2.1 Phase and group velocities......Page 205
8.3 The Dispersion Relation......Page 209
8.4 Wave Packets......Page 212
8.4.1 Formation of a wave packet......Page 214
PROBLEMS 8......Page 218
APPENDIX: SOLUTIONS TO PROBLEMS......Page 222
Index......Page 240