Introduction to Waves

The collective motions of large numbers of particles often have properties which are only loosely related to the particles themselves, and which are better described using 

FIGURE 3.5 Sound waves in air are waves of gas pressure. The positions of the maxima and minima change with time. The waves travel at a characteristic speed s = kv determined by properties of the air molecules and independent of wavelength or frequency. 

The threshold of hearing corresponds to a pressure variation of about 2 x 10 10 atm. Such a wave has a power density of 10-20 W m-2. The typical human ear responds comfortably to pressures up to a factor of 106 greater than this threshold at that point, pain is usually felt. The sound waves most young adults can hear have frequencies 

The lowest frequency is called the fundamental, all of the other frequencies are multiples of the fundamental and are called harmonics. Doubling the frequency corresponds to raising a note by one octave. When a piano and a flute play middle-A, they both produce a distribution of sound waves with a fundamental frequency of 440 Hertz, but they sound different because the amplitudes of the different harmonics depend on the instrument. 

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Pei Chi Chou, Introduction to Wave Propagation in Composite Materials, in Can-posite Materials Workshop, S. W. Tsai, J. C. Halpin, and Nicholas H. Pagano (Editors), St. Louis, Missouri, 13-21 July 1967, Technomic, Westport Connecticut 1968, pp. 193-216. 

It was an exciting place to be for the new, 26-year-old assistant professor of theoretical chemistry, Linus Pauling. He was thrilled to have his first official office (a corner of the X-ray laboratory), his first graduate student (a Texan, J. Holmes Sturdivant, who quickly became a lifelong friend), and his first class to teach ( An Introduction to Wave Mechanics with Applications to Chemistry ). He was... 

An introduction to wave mechanics The wave-nature of electrons... 

Scott S K 1994 Oscillations, Waves and Chaos in Chemical Kinetics (Oxford Oxford University Press) A short, final-year undergraduate level introduction to the subject. 

Epstein I R and Pojnian J A 1998 An Introduction to Nonlinear Chemical Dynamics Oscillations, Waves, Patterns and Chaos (Oxford Oxford University Press)... 

Field R J and Burger M (eds) 1984 Oscillations and Travelling Waves in Chemical Systems (New York Wiley) Multi-author survey of nonlinear kinetics field to 1984, still a valuable introduction to researchers in this area. 

This is an introduction to the techniques used for the calculation of electronic excited states of molecules (sometimes called eximers). Specifically, these are methods for obtaining wave functions for the excited states of a molecule from which energies and other molecular properties can be calculated. These calculations are an important tool for the analysis of spectroscopy, reaction mechanisms, and other excited-state phenomena. 

The ideas developed in this chapter are descriptive of shock waves in fluids. Solids have many significant features that distinguish them from liquids and gases, such as shear strength, polymorphic phase transformations, heterogeneous structure, anisotropy, and viscoplastic behavior. The influences of these special properties of solids on shock compression are the topics of several of the other chapters, and for the most part are ignored in this introduction to the basic principles of shock compression. 

I. C. Skidmore, An Introduction to Shock Waves in Solids, Appl. Mater. Res. 4, 131... 

Wave propagation in an inhomogeneous anisotropic material such as a fiber-reinforced composite material is a very complex subject. However, its study is motivated by many important applications such as the use of fiber-reinforced composites in reentry vehicle nosetips, heatshields, and other protective systems. Chou [6-56] gives an introduction to analysis of wave propagation in composite materials. Others have applied wave propagation theory to shell stress problems. 

Abstract This is an introduction to gravitational wave astronomy. The physical bases of gravitation and the generation and detection of gravitational waves are recalled and then kilometric detectors under construction are described. 

In this section we state the postulates of quantum mechanics in terms of the properties of linear operators. By way of an introduction to quantum theory, the basic principles have already been presented in Chapters 1 and 2. The purpose of that introduction is to provide a rationale for the quantum concepts by showing how the particle-wave duality leads to the postulate of a wave function based on the properties of a wave packet. Although this approach, based in part on historical development, helps to explain why certain quantum concepts were proposed, the basic principles of quantum mechanics cannot be obtained by any process of deduction. They must be stated as postulates to be accepted because the conclusions drawn from them agree with experiment without exception. 

The first two chapters serve as an introduction to quantum theory. It is assumed that the student has already been exposed to elementary quantum mechanics and to the historical events that led to its development in an undergraduate physical chemistry course or in a course on atomic physics. Accordingly, the historical development of quantum theory is not covered. To serve as a rationale for the postulates of quantum theory, Chapter 1 discusses wave motion and wave packets and then relates particle motion to wave motion. In Chapter 2 the time-dependent and time-independent Schrodinger equations are introduced along with a discussion of wave functions for particles in a potential field. Some instructors may wish to omit the first or both of these chapters or to present abbreviated versions. 

H.M. Kingston and L.B. Jassie (eds), Introduction to Micro-wave Sample Preparation, ACS Professional Reference Book, American Chemical Society, Washington, DC (1988). 

Figure 3.3 (a) The potential energy function assumed in the particle-in-a-one-dimensional-box model, (b) A wave function satisfying the boundary conditions, (c) An unacceptable wave function. (Reproduced with permission from P. A. Cox, Introduction to Quantum Theory and Atomic Structure, 1996, Oxford University Press, Oxford, Figure 2.6.)... 

In this chapter, I will try to present an introduction to these various techniques with emphasis on EXAFS and X-ray standing waves and their application to the study of electrochemical interfaces. Each technique will be treated from theoretical and experimental points of view, and selected examples from the literature will be employed to illustrate their application to the study of electrochemical interfaces. 

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