Fundamentals of Wave Phenomena
2: University of Iowa, Iowa City, IA, USA
This textbook is written for use in any university course related to the physics of waves, wave theory, and electromagnetic waves in departments such as Physics, Electrical Engineering, Mechanical Engineering, Civil Engineering, and Mathematics. The only prerequisite knowledge is a course in calculus. This textbook provides a unified treatment of waves that either occur naturally or can be excited and propagated in various media. This includes both longitudinal and transverse waves. The book covers both mechanical and electrical waves, which are normally covered separately due to their differences in physical phenomena. This text focuses more on the similarities of all waves, mechanical orelectromagnetic, and therefore allows the reader to formulate a unified understanding of wave phenomena in its totality. This second edition contains extensive updates and advances in the understanding of wave phenomena since the publication of the first edition (1985). Numerous additional problems are now present and several chapters have been rewritten and combined. This is the first book in the Mario Boella Series on Electromagnetism in Information and Communication. Key features include: A unified treatment of wave phenomena; Numerical techniques using MATLAB; Both mechanical and electrical waves are described; Necessary mathematics required to understand the material summarized within; Only prerequisite is an introductory course in calculus.
Other keywords: shock wave; massspring transmission line; Fresnel diffraction; wave differential equation; plane electromagnetic wave; partial differentiation; Fraunhofer diffraction; standing wave reflection; nonuniform spherical wave; synchrotron radiation; electromagnetic wave radiation; Fourier analysis; spherical mirror aberration; sound wave; wave motion; mechanical oscillation system; chaos; geometrical optics; Dopplershifted frequency; nonlinear oscillation; Young experiment; wave momentum; Taylor series expansion; wave equation; complex number; Einstein photon theory; cyclotron radiation; Laplace transform; soliton; nonlinear wave equation
 Book DOI: 10.1049/SBEW044E
 Chapter DOI: 10.1049/SBEW044E
 ISBN: 9781891121920
 eISBN: 9781613531112
 Page count: 402
 Format: PDF

Front Matter
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1 Review of Oscillations
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In this chapter, we review oscillation phenomena, both mechanical and electromagnetic, since oscillations and waves have many common properties, hence understanding oscillations can greatly help us understand wave phenomena. More importantly, harmonic (or sinusoidal) waves that we frequently encounter in daily life are created by physical objects undergoing oscillatory motions.

2 Wave Motion
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The article discusses the creation of waves on a string, sinusoidal (harmonic) waves, wave differential equation partial differentiation, nonsinusoidal waves, phase and group velocities dispersion and two wave superposition.

3 Some Mathematics
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4 Fundamentals of Mechanical Waves
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In this chapter, general aspects of mechanical waves are discussed. One important requirement for a medium to accommodate mechanical waves is that the medium be elastic. If it is compressed or expanded by a force, it should be able to restore its original shape when the force is removed. Sound waves can propagate in hard soil but not in soft clay. Waves can be created on a rope under a tension but not on a rope without tension.

5 SoundWaves in Solids, Liquids, and Gases
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Longitudinal waves in an elastic body (or medium) are generally called sound waves. The most familiar sound waves are those that propagate in air. However, sound waves can propagate even in solids or liquids. Sound waves are associated with the compressional and rarefactional motion of molecules in the direction that the wave propagates. This is similar to the longitudinal waves that propagate along a massspring transmission line that was discussed in the previous chapter. Earthquakes generally produce both longitudinal waves and transverse waves, the latter propagating slower than the former. When we are hit by an earthquake, we first feel a horizontal motion arising from the longitudinal waves, and some time later, a tumbling vertical movement from the transverse waves. In this chapter, we study the properties of the longitudinal sound waves in solids, liquids, and gases.

6 Wave Reflection and Standing Waves
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When a ball hits a hard wall, it is reflected by the wall. This reflection phenomenon can alternatively be interpreted in terms of the reflection of energy and momentum associated with the ball. If the wall is soft, the collision is inelastic and the wall completely absorbs the energy and momentum of the ball. No reflection occurs in this case. As we have seen, waves carry energy and momentum and whenever waves encounter an obstacle, they are reflected by the obstacle. Echoes are caused by the reflection of sound waves. Radars use the reflection of electromagnetic waves (microwaves) from metal objects such as airplanes. Wave reflection gives rise to an important wave phenomenon called standing waves, which play essential roles in most musical instruments. As the name indicates, standing waves do not propagate and therefore are not associated with energy and momentum transfer. They essentially behave as spatially distributed oscillators that only store energy. They can create waves in a surrounding medium by radiation. For example, the strings in a piano oscillate with distinct frequencies that are determined by the length, tension, and mass of each string. Each string can create sound waves in air with a particular frequency.

7 Spherical Waves, Waves in a Nonuniform Media, and Multidimensional Waves
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We have frequently used the following representative waveform equation in order to describe several kinds of waves (waves on a string, sound waves in gases and solids, etc.) where 0 is the amplitude of the sinusoidal displacement wave. The amplitude 0 is a constant that is specified by the source of the waves which may be a speaker for sound waves in air. For a wave equation, we observe the same amplitude 0 everywhere along the wave that is propagating in a lossless media. Such waves are called onedimensional or plane waves. The terminology of a plane wave results from the fact that all points transverse to the direction of propagation reside in a plane.

8 Doppler Effect of Sound Waves and Shock Waves
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The tone or frequency of a siren from a police car or fire engine seems to change from higher to lower value when the vehicle passes an observer even though the actual siren frequency is a constant. The driver of the vehicle, however, always hears the same frequency as if it were stationary. The apparent change in the frequency caused by the motion of the source of the wave (the siren in this case) relative to an observer is called the Doppler effect. C. J. Doppler (18031853) was an Austrian physicist who discovered the effect in light waves. Earlier in the seventeenth century, Danish astronomer Ole Roemer estimated the velocity of light from the apparent change in the revolution time of one of the moons of Jupiter. His estimate was c = 2 x 108 m/s, which is amazingly close to the modern value of 3.0 x 108 m/s considering the quality of the data available at the time. It turns out that the method used by Roemer was based on the same principle as the Doppler effect. For the sound waves that are propagating in air, we have three separate entities to consider: the source that emits the waves with a certain frequency, the observer that detects the waves, and the medium in which the wave propagates. All of these entities can be moving with respect to any of the others.

9 Electromagnetic Waves
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In this chapter we derive the wave equation for electromagnetic waves using basic knowledge. In fact, all we need is Kirchhoff's voltage and current laws. Then we generalize the primitive method using macroscopic Maxwell's equations (namely, Faraday's induction law and Maxwell's displacement current). Finally, you will be introduced to the differential (or microscopic) form of Maxwell's equations, which govern all electromagnetic phenomena.

10 Radiation of Electromagnetic Waves
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This chapter describes the physical mechanisms behind the radiation of electromagnetic waves. In summary, we have seen that if charged particles are subject to acceleration, radiation of electromagnetic waves will occur. Radiation from antennas is due to the acceleration of conduction electrons. Radiation carries energy away. Therefore to maintain a steady state, there must be a source of energy that is fed into the radiation system.

11 Interference and Diffraction
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This chapter covers the following topics: Interference Between Two Harmonic Waves; Young's Experiment; Multislit Structure; Optical Interference in Thin Films; Diffraction I (Fraunhofer Diffraction); Resolution of Optical Devices and Diffraction II (Fresnel Diffraction).

12 Geometrical Optics
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This chapter following topics: reflection and refraction; Total Reflection; Spherical Surfaces; Spherical Aberration of Mirrors; Lenses; Chromatic Aberration; Optical Instruments; Physical Meaning of Focusing and Matrix Method in Geometrical Optics.

13 Particle Nature of Light
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This chapter covers the following topics: Photoelectric Effect and Einstein's Photon Theory; Hydrogen Atom and deBroglieWave.

14 Fourier Analyses and Laplace Transformation
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The chapter discusses the sinusoidal functions, Fourier series, Fourier spectrum operator method, Laplace transform. We have studied many kinds of waves (mechanical and electromagnetic) in terms of sinusoidal waves.

15 Nonlinear Waves, Solitons, Shocks, and Chaos
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The chapter discusses nonlinear oscillations, nonlinear wave equation, Fermi, Pasta, and Ulam recurrence phenomena, KdV soliton properties, shocks and chaos.

Appendix A: Constants and Units
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Appendix B: Trigonometric Identities, Calculus, and Laplace Transforms
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Appendix C: References
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Appendix D: Answers to Selected Problems
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Back Matter
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Supplementary material

Instructor Resources for "Fundamentals of Wave Phenomena, 2nd edition"

An Instructor Pack is available for instructors who have adopted the book for a course. To request an Instructor Pack, please email [email protected], including details of your institution and the course you are teaching.

An Instructor Pack is available for instructors who have adopted the book for a course. To request an Instructor Pack, please email [email protected], including details of your institution and the course you are teaching.