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Mechanical and Electromagnetic Vibrations and Waves

by: Bé; cherrawy, Tamer

Mechanical and Electromagnetic Vibrations and Waves

by: Bé; cherrawy, Tamer

ISBN 13:
9781848212831
ISBN 10:
1848212836
Edition: 1st
Format: Hardcover
Copyright: 01/17/2012
Publisher: Wiley-ISTE

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Summary

This text deals with vibrations and waves. Its aim is to understand the basic principles and methods of analysing various physical phenomena. After a detailed study of mechanical and electromagnetic vibrations, their superposition and Fourier analysis, the wave part includes the general properties of propagation, a detailed study of mechanical (elastic and acoustic) and electromagnetic waves, propagation, attenuation, dispersion, reflection, interference and diffraction of waves. Included also are chapters on the effect of motion of sources and observers (both classical and relativistic), emission of electromagnetic waves, standing and guided waves. A final chapter on de Broglie waves constitutes an introduction to quantum mechanics.

Preface	p. xi
Free Oscillations	p. 1
Oscillations and waves, period and frequency	p. 1
Simple harmonic vibrations: differential equation and linearity	p. 2
Complex representation and phasor representation	p. 5
Point mass subject to a force-Kx	p. 9
Angular oscillations	p. 12
Damped oscillations	p. 15
Dissipation of the energy of a damped oscillator	p. 19
Oscillating LCR circuits	p. 20
Small oscillations of a system with one degree of freedom	p. 22
Nonlinear oscillators	p. 25
Systems with two degrees of freedom	p. 25
Generalization to systems with n degrees of freedom	p. 29
Normal variables for systems with n degrees of freedom*	p. 32
Summary	p. 35
Problem solving suggestions	p. 38
Conceptual questions	p. 39
Problems	p. 40
Superposition of Harmonic Oscillations, Fourier Analysis	p. 51
Superposition of two scalar and isochronous simple harmonic oscillations	p. 51
Superposition of two perpendicular and isochronous vector oscillations, polarization	p. 53
Superposition of two perpendicular and non-isochronous oscillations	p. 57
Superposition of scalar non-synchronous harmonic oscillations, beats	p. 58
Fourier analysis of a periodic function	p. 60
Fourier analysis of a non-periodic function	p. 65
Fourier analysis of a signal, uncertainty relation	p. 67
Dirac delta-function	p. 69
Summary	p. 71
Problem solving suggestions	p. 74
Conceptual questions	p. 75
Problems	p. 76
Forced Oscillations	p. 83
Transient regime and steady regime	p. 83
Case of a simple harmonic excitation force	p. 85
Resonance	p. 87
Impedance and energy of a forced oscillator in the steady regime	p. 88
Complex impedance	p. 92
Sustained electromagnetic oscillations	p. 94
Excitation from a state of equilibrium*	p. 96
Response to an arbitrary force, nonlinear systems*	p. 97
Excitation of a system of coupled oscillators*	p. 99
Generalization of the concepts of external force and impedance*	p. 103
Some applications	p. 104
Summary	p. 105
Problem solving suggestions	p. 106
Conceptual questions	p. 107
Problems	p. 108
Propagation in Infinite Media	p. 115
Propagation of one-dimensional waves	p. 115
Propagation of two- and three-dimensional waves	p. 117
Propagation of a vector wave	p. 121
Polarization of a transverse vector wave	p. 123
Monochromatic wave, wave vector and wavelength	p. 125
Dispersion	p. 127
Group velocity	p. 129
Fourier analysis for waves*	p. 130
Modulation*	p. 133
Energy of waves	p. 135
Other unattenuated wave equations, conserved quantities*	p. 137
Impedance of a medium*	p. 139
Attenuated waves	p. 140
Sources and observers in motion, the Doppler effect and shock waves	p. 143
Summary	p. 148
Problem solving suggestions	p. 150
Conceptual questions	p. 152
Problems	p. 153
Mechanical Waves	p. 159
Transverse waves on a taut string	p. 159
Strain and stress in elastic solids	p. 162
Elastic waves in massive springs and rods	p. 166
Propagation of sound in a pipe	p. 168
Transverse waves on elastic membranes	p. 172
Mechanical waves in three dimensions	p. 174
Energy of mechanical waves	p. 176
Progressive waves, impedance and intensity	p. 179
Elements of physiological acoustics	p. 183
Infrasounds and ultrasounds	p. 185
Surface waves*	p. 186
Summary	p. 191
Problem solving suggestions	p. 194
Conceptual questions	p. 194
Problems	p. 195
Electromagnetic Waves	p. 201
Principal results of the electromagnetic theory	p. 201
The propagation equations of the fields in vacuum and infinite dielectrics	p. 204
Electromagnetic simple harmonic plane waves	p. 205
Energy density and the Poynting vector	p. 206
Polarization of electromagnetic waves	p. 207
Momentum density and angular momentum density, radiation pressure*	p. 209
Electromagnetic waves in plasmas*	p. 212
Electromagnetic waves in Ohmic conductors*	p. 214
Quantization of electromagnetic radiation	p. 218
Electromagnetic spectrum	p. 219
Emission of electromagnetic radiations	p. 221
Spontaneous emission and stimulated emission	p. 223
Summary	p. 226
Problem solving suggestions	p. 229
Conceptual questions	p. 229
Problems	p. 231
Reflection and Refraction of Waves	p. 237
Reflection of an elastic wave on two joined strings	p. 237
Reflection and transmission of a one-dimensional acoustic wave	p. 240
General laws of reflection and transmission of three-dimensional waves	p. 243
Reflection and refraction of a three-dimensional acoustic wave	p. 246
Reflection and refraction of an electromagnetic wave at the interface of dielectrics	p. 248
Case of linear polarization in the plane of incidence	p. 249
Case of linear polarization perpendicular to the plane of incidence	p. 250
Conservation of energy	p. 252
Brewster's law	p. 253
Case of attenuated waves in the second medium*	p. 255
Summary	p. 258
Problem solving suggestions	p. 260
Conceptual questions	p. 261
Problems	p. 262
Interference and Diffraction	p. 269
Order and fringes of interference of two waves	p. 269
Intensity and contrast	p. 271
Interference of light waves, Young's experiment	p. 273
Multiwave interference, conditions for interference	p. 277
Holography	p. 281
Thin film interference	p. 282
The Huygens-Fresnel principle and diffraction by an aperture	p. 285
Diffraction grating	p. 290
Diffraction of X-rays	p. 295
Summary	p. 297
Problem solving suggestions	p. 299
Conceptual questions	p. 300
Problems	p. 301
Standing Waves and Guided Waves	p. 307
One-dimensional standing waves	p. 308
Standing waves on a membrane and in a rectangular cavity	p. 313
Fourier analysis of standing waves*	p. 316
Resonance and standing waves	p. 319
Sound wave guided by two parallel plates	p. 320
Guided sound waves in a rectangular pipe	p. 322
Transmission lines	p. 324
Electromagnetic waveguides*	p. 326
Waveguides formed by two plane and parallel plates*	p. 328
Guided electromagnetic waves in a hollow conductor*	p. 331
Applications of waveguides	p. 335
Summary	p. 337
Problem solving suggestions	p. 340
Conceptual questions	p. 341
Problems	p. 342
Answers to the Problems	p. 349
Appendices	p. 371
Mathematical Review	p. 373
Expansion formulas	p. 373
Logarithmic, exponential and hyperbolic functions	p. 374
Trigonometric functions	p. 374
Integrals	p. 375
Complex numbers	p. 378
Vector analysis in Cartesian coordinates	p. 380
Vector analysis in curvilinear coordinates	p. 382
Units in Physics	p. 387
Multiples and submultiples of units	p. 387
Fundamental and derived SI units	p. 387
Mechanical units	p. 388
Electromagnetic units	p. 389
Some Physical Constants	p. 391
Mechanical and thermodynamic constants	p. 391
Electromagnetic and atomic constants	p. 392
Further Reading	p. 393
Index	p. 395
Table of Contents provided by Ingram. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Mechanical and Electromagnetic Vibrations and Waves

Mechanical and Electromagnetic Vibrations and Waves

9781848212831

1848212836

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