Chapter 24: Symbolic Representation Of General Alternating Waves
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Theory and Calculation of Alternating Current Phenomena |
| Year | 1900 |
| Section ID | theory-calculation-alternating-current-phenomena-1900-chapter-24 |
| Location | lines 22449-23642 |
| Status | candidate |
| Word Count | 3142 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER XXIV. SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES. 253. The vector representation, A = a1 +y<zu = a (cos a -\-j sin d) of the alternating wave, A — a0 cos (<£ — a) applies to the sine wave only. The general alternating wave, however, contains an in- finite series of terms, of odd frequencies, A = Al cos (<£ — #1) 4- Az cos (3 <£ — #3) + A& cos (5 <£ — #5) -f thus cannot be directly represented by one complex vector quantity. The replacement of the general wave by its equivalent sine wave, as before discussed, that is a sine wave of equal effective intensity and equal power, while sufficiently accu- rate in many cases, completely fails in other cases, espe- cially in circuits containing capacity, or in circuits containingSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Waves / transmission lines
Section titled “Waves / transmission lines”CHAPTER XXIV. SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES. 253. The vector representation, A = a1 +y<zu = a (cos a -\-j sin d) of the alternating wave, A — a0 cos (<£ — a) applies to the sine wave only. The general alternating wave, however, contains an in- finite series of terms, of odd frequencies, A = Al cos (<£ — #1) ...Dielectricity / capacity
Section titled “Dielectricity / capacity”... antity. The replacement of the general wave by its equivalent sine wave, as before discussed, that is a sine wave of equal effective intensity and equal power, while sufficiently accu- rate in many cases, completely fails in other cases, espe- cially in circuits containing capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction ma- chines, synchronous induction motors, oversaturated mag- netic circuits, etc.). Since, however, the individual harmonics of the gen ...Impedance / reactance
Section titled “Impedance / reactance”... ine wave of equal effective intensity and equal power, while sufficiently accu- rate in many cases, completely fails in other cases, espe- cially in circuits containing capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction ma- chines, synchronous induction motors, oversaturated mag- netic circuits, etc.). Since, however, the individual harmonics of the general alternating wave are independent of each other, that is, all products of different harmonics vanish, e ...Radiation / light
Section titled “Radiation / light”... p- resent different frequencies, and thus cannot be combined. The general wave of E.M.F. is thus represented by, the general wave of current by, if, is the impedance of the fundamental harmonic, where xm is that part of the reactance which is proportional to the frequency (inductance, etc.). x0 is that part of the reactance which is independent of the frequency (mutual induction, synchronous motion, etc.). xc is that part of the reactance which is inversely pro- portional to the frequency (capacity, etc.). The impedance for the nth harmo ...Chapter-Local Concept Hits
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| Frequency | 14 | seeded |
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| Light | 2 | seeded |
Chapter-Local Glossary Hits
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| ether | 2 | seeded |
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Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Waves / transmission lines: Map Steinmetz’s wave and line language onto modern distributed constants, propagation velocity, standing waves, and reflections.
- Dielectricity / capacity: Check whether the passage treats capacity, condensers, displacement, or dielectric stress as field storage rather than only circuit algebra.
- Impedance / reactance: Translate historical opposition terms into modern impedance, admittance, conductance, susceptance, and complex-plane notation.
- Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Waves / transmission lines: Standing/traveling wave passages may support richer field interpretations; the page keeps those readings separate from verified Steinmetz wording.
- Dielectricity / capacity: A Wheeler-style reading may emphasize dielectric compression, field stress, and stored potential, but this page treats that as interpretation unless Steinmetz explicitly says it.
- Radiation / light: Radiation and wave language can invite ether-field comparison, but source wording, modern radiation theory, and speculative synthesis must stay separated.
Promotion Checklist
Section titled “Promotion Checklist”- Open the full source text and the scan or raw PDF.
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