Chapter 27: 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 | 1916 |
| Section ID | theory-calculation-alternating-current-phenomena-chapter-27 |
| Location | lines 33011-34776 |
| Status | candidate |
| Word Count | 3340 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 1 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER XXVII SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series of terms, of odd frequencies, A = Aicos( 0- ^i) + ^3 cos (3 (^ - 63) + As cos (5 <^ - ^5) + 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 accurate in many cases, completely fails in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (andSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Waves / transmission lines
Section titled “Waves / transmission lines”CHAPTER XXVII SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series of terms, of odd frequencies, A = Aicos( 0- ^i ...Dielectricity / capacity
Section titled “Dielectricity / capacity”... uantity. 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 accurate in many cases, completely fails in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction machines, synchronous induction motors, oversaturated magnetic circuits, etc.). Since, however, the individual harmonics of the general ...Impedance / reactance
Section titled “Impedance / reactance”... a sine wave of equal effective intensity and equal power, while sufficiently accurate in many cases, completely fails in other cases, especially in circuits con- taining capacity, or in circuits containing periodically (and in synchronism with the wave) varying resistance or reactance (as alternating arcs, reaction machines, synchronous induction motors, oversaturated magnetic circuits, etc.). Since, however, the individual harmonics of the general alter- nating wave are independent of each other, that is, all products of different harmonics vanish, eac ...Complex quantities
Section titled “Complex quantities”CHAPTER XXVII SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series of t ...Chapter-Local Concept Hits
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| Frequency | 16 | seeded |
| Light | 2 | seeded |
| Ether | 1 | seeded |
Chapter-Local Glossary Hits
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| counter e.m.f. | 2 | source-located candidate |
| ether | 1 | seeded |
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Figure Candidates
Section titled “Figure Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
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theory-calculation-alternating-current-phenomena-fig-191 | 0 Fig. 191. of the harmonic, and the winding of the motor primary. Thus, | line 34764 |
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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.
- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
- Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
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.
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