equation 35.9 eq:expwa-plate-dispersion
open in the book ·
parts/03-classical-mechanics/18-exp-waves-acoustics.tex:452
- part of a statement or proof
Rests on
- step_from equation 35.8 eq:expwa-plate-eigenvalue ¶
Supports
- assumes experiment Chladni: the nodal figures of a vibrating plate ¶
-
step_from
equation 35.12
eq:expwa-chladni-law
¶
- tests experiment Chladni: the nodal figures of a vibrating plate ¶ ↺
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
step_from |
→ | eq:expwa-plate-eigenvalue | declared — taking $\nabla^{4}$ of a plane wave, which multiplies it by $k^{4}$, and solving for $\omega$ | parts/03-classical-mechanics/18-exp-waves-acoustics.tex:455 |
assumes |
← | Chladni: the nodal figures of a vibrating plate | declared | parts/03-classical-mechanics/18-exp-waves-acoustics.tex:378 |
step_from |
← | eq:expwa-chladni-law | declared — substituting $k\approx\pi(m+2n)/2a$ into the dispersion relation | parts/03-classical-mechanics/18-exp-waves-acoustics.tex:500 |