Physics of Waves
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Beschreibung:
Because of the increasing demands and complexity of undergraduate physics courses (atomic, quantum, solid state, nuclear, etc.), it is often impossible to devote separate courses to the classic wave phenomena of optics, acoustics, and electromagnetic radiation. This brief comprehensive text helps alleviate the problem with a unique overview of classical wave theory in one volume.
By examining a sequence of concrete and specific examples (emphasizing the physics of wave motion), the authors unify the study of waves, developing abstract and general features common to all wave motion. The fundamental ideas of wave motion are set forth in the first chapter, using the stretched string as a particular model. In Chapter Two, the two-dimensional membrane is used to introduce Bessel functions and the characteristic features of waveguides. In Chapters Three and Four, elementary elasticity theory is developed and applied to find the various classes of waves that can be supported by a rigid rod. The impedance concept is also introduced at this point. Chapter Five discusses acoustic waves in fluids.
The remainder of the book offers concise coverage of hydrodynamic waves at a liquid surface, general waves in isotropic elastic solids, electromagnetic waves, the phenomenon of wave diffraction, and other important topics. A special feature of this book is the inclusion of additional material designed to encourage the serious student to investigate topics often not covered in lectures. Throughout, the mathematics is kept relatively simple (mostly differential equations) and is accessible to advanced undergraduates with a year of calculus. In addition, carefully selected problems at the end of each section extend the coverage of the text by asking the student to supply mathematical details for calculations outlined in the section, or to develop the theory for related cases.
Impressively broad in scope, Physics of Waves offers a novel approach to the study of classical wave theory — a wide-ranging but thorough survey of an important discipline that pervades much of contemporary physics. The simplicity, breadth, and brevity of the book make it ideal as a classroom text or as a vehicle for self-study.
1 Transverse Waves on a String
1.1 The wave equation for an ideal stretched string
1.2 A general solution of the one-dimensional wave equation
1.3 Harmonic or sinusoidal waves
1.4 Standing sinusoidal waves
1.5 Solving the wave equation by the method of separation of variables
1.6 The general motion of a finite string segment
1.7 Fourier series
1.8 Energy carried by waves on a string
1.9 The reflection and transmission of waves at a discontinuity
*1.10 Another derivation of the wave equation for strings
*1.11 Momentum carried by a wave
2 Waves on a Membrane
2.1 The wave equation for a stretched membrane
2.2 Standing waves on a rectangular membrane
2.3 Standing waves on a circular membrane
2.4 Interference phenomena with plane traveling waves
3 Introduction to the Theory of Elasticity
3.1 The elongation of a rod
3.2 Volume changes in an elastic medium
3.3 Shear distortion in a plane
3.4 The torsion of round tubes and rods
3.5 The statics of a simple beam
3.6 The bending of a simple beam
3.7 Helical springs
4 One-dimensional Elastic Waves
4.1 Longitudinal waves on a slender rod
(a) The wave equation
(b) Standing waves
(c) Energy and power
(d) Momentum transport
4.2 The impedance concept
4.3 Rods with varying cross-sectional area
4.4 The effect of small perturbations on normal-mode frequencies
4.5 Torsional waves on a round rod
4.6 Transverse waves on a slender rod
(a) The wave equation
(b) Solution of the wave equation
(c) Traveling waves
(d) Normal-mode vibrations
4.7 Phase and group velocity
4.8 Waves on a helical spring
*4.9 Perturbation calculations
5 Acoustic Waves in Fluids
5.1 The wave equation for fluids
*5.2 The velocity of sound in gases
5.3 Plane acoustic waves
(a) Traveling sinusoidal waves
(b) Standing waves of sound
5.4 The cavity (Helmholtz) resonator
5.5 Spherical acoustic waves
5.6 Reflection and refraction at a plane interface
5.7 Standing waves in a rectangular box
5.8 The Doppler effect
*5.9 The velocity potential
*5.10 Shock Waves
*6 Waves on a Liquid Surface
6.1 Basic hydrodynamics
(a) Kinematical equations
(b) The equation of continuity
(c) The Bernoulli equation
6.2 Gravity waves
6.3 Effect of surface tension
6.4 Tidal waves and the tides
(a) Tidal waves
(b) Tide-generating forces
(c) Equilibrium theory of tides
(d) The dynamical theory of tides
6.5 Energy and power relations
*7 Elastic Waves in Solids
7.1 Tensors and dyadics
7.2 Strain as a dyadic
7.3 Stress as a dyadic
7.4 Hooke's law
7.5 Waves in an isotropic medium
(a) Irrotational waves
(b) Solenoidal waves
7.6 Energy relations
*7.7 Momentum transport by a shear wave
*8 Electromagnetic Waves
8.1 Two-conductor transmission line
(a) Circuit equations
(b) Wave equation
(c) Characteristic impedance
(d) Reflection from terminal impedance
(e) Impedance measurement
8.2 Maxwell's equations
8.3 Plane waves
8.4 Electromagnetic energy and momentum
8.5 Waves in a conducting medium
8.6 Reflection and refraction at a plane interface
(a) Boundary conditions
(b) Normal incidence on a conductor
(c) Oblique incidence on a nonconductor
8.7 Waveguides
(a) The vector wave equation
(b) General solution for waveguides
(c) Rectangular cross section
*(d) Circular cross section
8.8 Propagation in ionized gases
8.9 Spherical waves
9 Wave Propagation in Inhomogeneous and Obstructed Media
9.1 The WKB approximation
9.2 Geometrical optics
9.3 The Huygens-Fresnel principle
9.4 Kirchhoff diffraction theory
(a) Green's theorem
(b) The Helmholtz-Kirchhoff theorem
(c) Kirchoff boundary conditions
9.5 Diffraction of transverse waves
*9.6 Young's formulation of diffraction
10 Fraunhofer Diffraction
10.1 The paraxial approximation
10.2 The Fraunhofer limit
10.3 The rectangular aperture
10.4 The single slit
10.5 The circular aperture
10.6 The double slit
10.7 Multiple slits
*10.8 Practical diffraction gratings for spectral analysis
(a) Gratings of arbitrary periodic structure
(b) The grating equation
(c) Dispersion
(d) Resolving power
*10.9 Two-dimensional gratings
*10.10 Three-dimensional gratings
11 Fresnel Diffraction
11.1 Fresnel zones
(a) Circular zones
(b) Off-axis diffraction
(c) Linear zones
11.2 The rectangular aperture
(a) Geometry and notation
(b) The Cornu spiral
11.3 The linear slit
11.4 The straight edge
12 Spectrum Analysis of Waveforms
12.1 Nonsinusoidal periodic waves
12.2 Nonrecurrent waves
12.3 Amplitude-modulated waves
12.4 Phase-modulated waves
12.5 The motion of a wave packet in a dispersive medium
12.6 The Fourier transform method
12.7 Properties of transfer functions
12.8 Partial coherence in a wavefield
Appendixes
A. Vector calculus
B. The Smith calculator
C. Proof of the uncertainty relation
Index