Vibrations electromagnetics

Syllabus (1957-1958) pp 137-38 (Frank-Kamenetskii formulation) 151-62 [Session 13, entitled "Hetergeneity of the Initiation Process , includes initiation of solid expls by impact, friction, thermal effect, elastic waves by ultrasonic vibrations, electromagnetic energy and chemical influence. 

The harmonic oscillator is a model which has several important applications in both classical and quantum mechanics. It serves as a prototype in the mathematical treatment of such diverse phenomena as elasticity, acoustics, AC circuits, molecular and crystal vibrations, electromagnetic fields and optical properties of matter. 

The enterprise defines the utilization environments for each of the operational scenarios. All environmental factors, natural or induced, which may affect system performance, should be identified and defined. Factors, which ensure that the system minimizes the potential for human or machine errors or failures that cause injurious accidents or death, and impart minimal risk of death, injury, or acute chronic illness, disability, and/or reduced job performance of the humans who support the system life cycle, are identified. Specifically, weather conditions (e.g., rain, snow, sun, wind, ice, dust, and fog), temperature ranges, topologies (e.g., ocean, mountains, deserts, plains, and vegetation), biological (e.g., animal, insects, birds, and fungi), time (e.g., day, night, and dusk), induced (e.g., vibration, electromagnetic, acoustic, and chemical), or other envi-... 

In this work, a microwave interferometric method and apparatus for vibration measurements is described. The principle of operation is based on measurement of the phase of reflected electromagnetic wave changing due to vibration. The most important features of the method are as follows simultaneous measurement of tlie magnitude and frequency of the rotating object high measurement accuracy weak influence of the roll diameter, shape and distance to the object under test. Besides, tlie reflecting surface can be either metallic or non-metallic. Some technical characteristics are given. 

Both infrared and Raman spectroscopy provide infonnation on the vibrational motion of molecules. The teclmiques employed differ, but the underlying molecular motion is the same. A qualitative description of IR and Raman spectroscopies is first presented. Then a slightly more rigorous development will be described. For both IR and Raman spectroscopy, the fiindamental interaction is between a dipole moment and an electromagnetic field. Ultimately, the two... 

Figure Bl.2.1. Schematic representation of the dependence of the dipole moment on the vibrational coordinate for a heteronuclear diatomic molecule. It can couple with electromagnetic radiation of the same frequency as the vibration, but at other frequencies the interaction will average to zero.

Raman scattering has been discussed by many authors. As in the case of IR vibrational spectroscopy, the interaction is between the electromagnetic field and a dipole moment, however in this case the dipole moment is induced by the field itself The induced dipole is pj j = a E, where a is the polarizability. It can be expressed in a Taylor series expansion in coordinate isplacement... 

Electronic structure theory describes the motions of the electrons and produces energy surfaces and wavefiinctions. The shapes and geometries of molecules, their electronic, vibrational and rotational energy levels, as well as the interactions of these states with electromagnetic fields lie within the realm of quantum stnicture theory. 

To get the frequency v in centimeters-, the nonstandard notation favored by spectioscopists, one divides the frequency in hertz by the speed of light in a vacuum, c = 2.998 x lO " cm s-, to obtain a reciprocal wavelength, in this case, 4120 cm-. This relationship arises because the speed of any running wave is its frequency times its wavelength, c = vX in the case of electromagnetic radiation. The Raman spectral line for the fundamental vibration of H2 is 4162 cm-. .., not a bad comparison for a simple model. 

Gaseous H CI has a strong absorption band centered at about X = 3.40 X 10 m in the infrared portion of the electromagnetic radiation spec-tmm. On the assumption that D bonds to Cl with the same str ength that H does, predict the frequency of vibration in Hz and rad of D CI. 

The hydrogen atom attached to an alkane molecule vibrates along the bond axis at a frequency of about 3000 cm. What wavelength of electromagnetic radiation is resonant with this vibration What is the frequency in hertz What is the force constant of the C II bond if the alkane is taken to be a stationary mass because of its size and the H atom is assumed to execute simple harmonic motion ... 

The interaction of a molecular species with electromagnetic fields can cause transitions to occur among the available molecular energy levels (electronic, vibrational, rotational, and nuclear spin). Collisions among molecular species likewise can cause transitions to occur. Time-dependent perturbation theory and the methods of molecular dynamics can be employed to treat such transitions. 

Section 13 20 IR spectroscopy probes molecular structure by examining transitions between vibrational energy levels using electromagnetic radiation m the 625-4000 cm range The presence or absence of a peak at a charac tenstic frequency tells us whether a certain functional group is present Table 13 4 lists IR absorption frequencies for common structural units... 

In absorption spectroscopy a beam of electromagnetic radiation passes through a sample. Much of the radiation is transmitted without a loss in intensity. At selected frequencies, however, the radiation s intensity is attenuated. This process of attenuation is called absorption. Two general requirements must be met if an analyte is to absorb electromagnetic radiation. The first requirement is that there must be a mechanism by which the radiation s electric field or magnetic field interacts with the analyte. For ultraviolet and visible radiation, this interaction involves the electronic energy of valence electrons. A chemical bond s vibrational energy is altered by the absorbance of infrared radiation. A more detailed treatment of this interaction, and its importance in deter-... 

In the process of absorption or emission of infrared radiation involving transitions between two vibrational states the interaction is usually between the molecule and the electric, rather than the magnetic, component of the electromagnetic radiation (see Section 2.1). For this... 

Electromagnetic flow meters ate avadable with various liner and electrode materials. Liner and electrode selection is governed by the corrosion characteristics of the Hquid. Eor corrosive chemicals, fluoropolymer or ceramic liners and noble metal electrodes are commonly used polyurethane or mbber and stainless steel electrodes are often used for abrasive slurries. Some fluids tend to form an insulating coating on the electrodes introducing errors or loss of signal. To overcome this problem, specially shaped electrodes are avadable that extend into the flow stream and tend to self-clean. In another approach, the electrodes are periodically vibrated at ultrasonic frequencies. 

Foxboro s Model 823 transmitter uses a taut wire stretched between a measuring diaphragm and a restraining element. The differential process pressure across the measuring diaphragm increases the tension on the wire, thus changing the wire s natural frequency when it is excited by an electromagnet. This vibration (1800—3000 H2) is picked up inductively in an oscillator circuit which feeds a frequency-to-current converter to get a 4—20 m A d-c output. 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

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