Chapter 3: Standing Waves
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Theory and Calculation of Transient Electric Phenomena and Oscillations |
| Year | 1909 |
| Section ID | theory-calculation-transient-electric-phenomena-oscillations-chapter-52 |
| Location | lines 29316-30243 |
| Status | candidate |
| Word Count | 2711 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER III. STANDING WAVES. 14. If the propagation constant of the wave vanishes, h = 0, the wave becomes a stationary or standing wave, and the equa- tions of the standing wave are thus derived from the general equations (50) to (61), by substituting therein h = 0, which gives R2 = V(k2 - LCm2)2; (97) hence, if k2 > LCm2, R2 = tf- LCm2; and if /c2 < LCm2, R2 = LCm2'- tf. Therefore, two different cases exist, depending upon the rela- tive values of Ar* and LCm2, and in addition thereto the inter- mediary or critical case, in which k2 = LCm2. These three cases require separate consideration. is a circuit constant, while k is the wave length constant, that is, the higher k the shorter the wave length. A. Short waves, k2Source-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Waves / transmission lines
Section titled “Waves / transmission lines”CHAPTER III. STANDING WAVES. 14. If the propagation constant of the wave vanishes, h = 0, the wave becomes a stationary or standing wave, and the equa- tions of the standing wave are thus derived from the general equations (50) to (61), by substituting therein h = 0, which gives R2 = V(k2 - LCm ...Radiation / light
Section titled “Radiation / light”... Cm2'- tf. Therefore, two different cases exist, depending upon the rela- tive values of Ar* and LCm2, and in addition thereto the inter- mediary or critical case, in which k2 = LCm2. These three cases require separate consideration. is a circuit constant, while k is the wave length constant, that is, the higher k the shorter the wave length. A. Short waves, k2 > LCm2, (99) hence, R2 = k2 - LCm2 (100) and q = V ^ - ™\ 442 STANDING WAVES 443 or approximately, for very large k, Herefrom then follows and VLC °l= k c' mL c ...Transients / damping
Section titled “Transients / damping”... cos (qt-kl)-(mB, + qB,'} sin (qt-kl)] + [(mB2'-qB3) cos (qt + Jd)-(mB2 + qBJ) sin (qt + kl)]}. (106) Equations (105) and (106) represent a stationary electrical oscil- lation or standing wave on the circuit. B. Long waves, k2 < LCm2] (107) 444 hence, and TRANSIENT PHENOMENA R22 = LCm2 - k2, s = (108) (109) or approximately, for very small values of &, 1 r herefrom then follows (HO) ci = c2 = 0, and (m + s) L ~T~ (m — s) L (111) Substituting now h = Oand (109), (111) into (50) and (51), the two wa ...Dielectricity / capacity
Section titled “Dielectricity / capacity”... = 0, (126) or - = §J (127) that is, the ratio of the energy coefficients is equal to the ratio of the reactive coefficients of the circuit. The standing wave can never be oscillatory, but is always exponential, or gradually dying out, if either the inductance L or the capacity 0 vanishes ; that is, the circuit contains no capacity or contains no inductance. In all other cases the standing wave is oscillatory for waves shorter than the critical value L = -— , where 0 V - 9 V §} > (128) and is exponential or gradual for standing waves longer ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
|---|---|---|
| Wave length | 33 | seeded |
| Frequency | 9 | seeded |
| Light | 3 | seeded |
| Magnetic permeability | 2 | seeded |
| Dielectric constant | 1 | seeded |
| Ether | 1 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
|---|---|---|
| wave length | 33 | seeded |
| ether | 1 | 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.
- Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
- Transients / damping: Separate the temporary term from the final steady-state term and compare with differential-equation response language.
- 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.
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.
- Radiation / light: Radiation and wave language can invite ether-field comparison, but source wording, modern radiation theory, and speculative synthesis must stay separated.
- Transients / damping: Transient collapse, impulse, and surge behavior can be compared with alternative field language, but only as a clearly marked reading.
- 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.
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