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Mechanical and Electromagnetic Vibrations and Waves

Book Description

Dealing with vibrations and waves, this text aims to provide understanding of the basic principles and methods of analysing various physical phenomena.

The content 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.

It features chapters on the effect of motion of sources and observers (both classical and relativistic), emission of electromagnetic waves, standing and guided waves and a final chapter on de Broglie waves constitutes an introduction to quantum mechanics.

Table of Contents

  1. Coverpage
  2. Titlepage
  3. Copyright
  4. Table of Contents
  5. Preface
  6. Chapter 1. Free Oscillations
    1. 1.1. Oscillations and waves, period and frequency
    2. 1.2. Simple harmonic vibrations: differential equation and linearity
    3. 1.3. Complex representation and phasor representation
    4. 1.4. Point mass subject to a force–Kx
    5. 1.5. Angular oscillations
    6. 1.6. Damped oscillations
    7. 1.7. Dissipation of the energy of a damped oscillator
    8. 1.8. Oscillating LCR circuits
    9. 1.9. Small oscillations of a system with one degree of freedom
    10. 1.10. Nonlinear oscillators
    11. 1.11. Systems with two degrees of freedom
    12. 1.12. Generalization to systems with n degrees of freedom
    13. 1.13. Normal variables for systems with n degrees of freedom*
    14. 1.14. Summary
    15. 1.15. Problem solving suggestions
    16. 1.16. Conceptual questions
    17. 1.17. Problems
  7. Chapter 2. Superposition of Harmonic Oscillations, Fourier Analysis
    1. 2.1. Superposition of two scalar and isochronous simple harmonic oscillations
    2. 2.2. Superposition of two perpendicular and isochronous vector oscillations, polarization
    3. 2.3. Superposition of two perpendicular and non-isochronous oscillations
    4. 2.4. Superposition of scalar non-synchronous harmonic oscillations, beats
    5. 2.5. Fourier analysis of a periodic function
    6. 2.6. Fourier analysis of a non-periodic function
    7. 2.7. Fourier analysis of a signal, uncertainty relation
    8. 2.8. Dirac delta-function
    9. 2.9. Summary
    10. 2.10. Problem solving suggestions
    11. 2.11. Conceptual questions
    12. 2.12. Problems
  8. Chapter 3. Forced Oscillations
    1. 3.1. Transient regime and steady regime
    2. 3.2. Case of a simple harmonic excitation force
    3. 3.3. Resonance
    4. 3.4. Impedance and energy of a forced oscillator in the steady regime
    5. 3.5. Complex impedance
    6. 3.6. Sustained electromagnetic oscillations
    7. 3.7. Excitation from a state of equilibrium*
    8. 3.8. Response to an arbitrary force, nonlinear systems*
    9. 3.9. Excitation of a system of coupled oscillators*
    10. 3.10. Generalization of the concepts of external force and impedance*
    11. 3.11. Some applications
    12. 3.12. Summary
    13. 3.13. Problem solving suggestions
    14. 3.14. Conceptual questions
    15. 3.15. Problems
  9. Chapter 4. Propagation in Infinite Media
    1. 4.1. Propagation of one-dimensional waves
    2. 4.2. Propagation of two- and three-dimensional waves
    3. 4.3. Propagation of a vector wave
    4. 4.4. Polarization of a transverse vector wave
    5. 4.5. Monochromatic wave, wave vector and wavelength
    6. 4.6. Dispersion
    7. 4.7. Group velocity
    8. 4.8. Fourier analysis for waves*
    9. 4.9. Modulation*
    10. 4.10. Energy of waves
    11. 4.11. Other unattenuated wave equations, conserved quantities*
    12. 4.12. Impedance of a medium*
    13. 4.13. Attenuated waves
    14. 4.14. Sources and observers in motion, the Doppler effect and shock waves
    15. 4.15. Summary
    16. 4.16. Problem solving suggestions
    17. 4.17. Conceptual questions
    18. 4.18. Problems
  10. Chapter 5. Mechanical Waves
    1. 5.1. Transverse waves on a taut string
    2. 5.2. Strain and stress in elastic solids
    3. 5.3. Elastic waves in massive springs and rods
    4. 5.4. Propagation of sound in a pipe
    5. 5.5. Transverse waves on elastic membranes
    6. 5.6. Mechanical waves in three dimensions
    7. 5.7. Energy of mechanical waves
    8. 5.8. Progressive waves, impedance and intensity
    9. 5.9. Elements of physiological acoustics
    10. 5.10. Infrasounds and ultrasounds
    11. 5.11. Surface waves*
    12. 5.12. Summary
    13. 5.13. Problem solving suggestions
    14. 5.14. Conceptual questions
    15. 5.15. Problems
  11. Chapter 6. Electromagnetic Waves
    1. 6.1. Principal results of the electromagnetic theory
    2. 6.2. The propagation equations of the fields in vacuum and infinite dielectrics
    3. 6.3. Electromagnetic simple harmonic plane waves
    4. 6.4. Energy density and the Poynting vector
    5. 6.5. Polarization of electromagnetic waves
    6. 6.6. Momentum density and angular momentum density, radiation pressure*
    7. 6.7. Electromagnetic waves in plasmas*
    8. 6.8. Electromagnetic waves in Ohmic conductors*
    9. 6.9. Quantization of electromagnetic radiation
    10. 6.10. Electromagnetic spectrum
    11. 6.11. Emission of electromagnetic radiations
    12. 6.12. Spontaneous emission and stimulated emission
    13. 6.13. Summary
    14. 6.14. Problem solving suggestions
    15. 6.15. Conceptual questions
    16. 6.16. Problems
  12. Chapter 7. Reflection and Refraction of Waves
    1. 7.1. Reflection of an elastic wave on two joined strings
    2. 7.2. Reflection and transmission of a one-dimensional acoustic wave
    3. 7.3. General laws of reflection and transmission of three-dimensional waves
    4. 7.4. Reflection and refraction of a three-dimensional acoustic wave
    5. 7.5. Reflection and refraction of an electromagnetic wave at the interface of dielectrics
      1. 7.5.1. Case of linear polarization in the plane of incidence
      2. 7.5.2. Case of linear polarization perpendicular to the plane of incidence
      3. 7.5.3. Conservation of energy
      4. 7.5.4. Brewster’s law
    6. 7.6. Case of attenuated waves in the second medium*
    7. 7.7. Summary
    8. 7.8. Problem solving suggestions
    9. 7.9. Conceptual questions
    10. 7.10. Problems
  13. Chapter 8. Interference and Diffraction
    1. 8.1. Order and fringes of interference of two waves
    2. 8.2. Intensity and contrast
    3. 8.3. Interference of light waves, Young’s experiment
    4. 8.4. Multiwave interference, conditions for interference
    5. 8.5. Holography
    6. 8.6. Thin film interference
    7. 8.7. The Huygens-Fresnel principle and diffraction by an aperture
    8. 8.8. Diffraction grating
    9. 8.9. Diffraction of X-rays
    10. 8.10. Summary
    11. 8.11. Problem solving suggestions
    12. 8.12. Conceptual questions
    13. 8.13. Problems
  14. Chapter 9. Standing Waves and Guided Waves
    1. 9.1. One-dimensional standing waves
    2. 9.2. Standing waves on a membrane and in a rectangular cavity
    3. 9.3. Fourier analysis of standing waves*
    4. 9.4. Resonance and standing waves
    5. 9.5. Sound wave guided by two parallel plates
    6. 9.6. Guided sound waves in a rectangular pipe
    7. 9.7. Transmission lines
    8. 9.8. Electromagnetic waveguides*
    9. 9.9. Waveguides formed by two plane and parallel plates*
    10. 9.10. Guided electromagnetic waves in a hollow conductor*
    11. 9.11. Applications of waveguides
    12. 9.12. Summary
    13. 9.13. Problem solving suggestions
    14. 9.14. Conceptual questions
    15. 9.15. Problems
  15. Answers to the Problems
  16. Appendices
    1. Appendix A. Mathematical Review
      1. A.1. Expansion formulas
      2. A.2. Logarithmic, exponential and hyperbolic functions
      3. A.3. Trigonometric functions
      4. A.4. Integrals
      5. A.5. Complex numbers
      6. A.6. Vector analysis in Cartesian coordinates
      7. A.7. Vector analysis in curvilinear coordinates
    2. Appendix B. Units in Physics
      1. B.1. Multiples and submultiples of units
      2. B.2. Fundamental and derived SI units
      3. B.3. Mechanical units
      4. B.4. Electromagnetic units
    3. Appendix C. Some Physical Constants
      1. C.1. Mechanical and thermodynamic constants
      2. C.2. Electromagnetic and atomic constants
  17. Further Reading
  18. Index