phenomenon 28.45 The harmonic series of a stretched string
open in the book ·
parts/03-classical-mechanics/11-oscillations-waves.tex:1577
· p. 963
- phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt
Rests on
- depends_on equation 28.46 eq:osc-wave-eq ¶
-
depends_on
theorem 9.57
Orthogonality of Sturm–Liouville eigenfunctions
¶
- depends_on equation 9.55 eq:slt-eigenproblem ¶
-
depends_on
lemma 9.56
Lagrange identity
¶
- depends_on definition 9.54 Sturm–Liouville differential operator ¶
- proves proof ch:07-odes-sturm-liouville@proof-28 ¶
- proves proof ch:07-odes-sturm-liouville@proof-29 ¶
- proves proof ch:11-oscillations-waves@proof-24 ¶
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Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites |
→ | Discorsi e dimostrazioni matematiche intorno a due nuove scienze | derived | parts/03-classical-mechanics/11-oscillations-waves.tex:1589 |
cites |
→ | Harmonie universelle, contenant la théorie et la pratique de la musique | derived | parts/03-classical-mechanics/11-oscillations-waves.tex:1589 |
depends_on |
→ | eq:osc-wave-eq | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:1593 |
depends_on |
→ | Orthogonality of Sturm–Liouville eigenfunctions | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:1593 |
proves |
← | ch:11-oscillations-waves@proof-24 | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:1596 |