Abstract
In most of the motions of a plate (as also in those of a bell and of a taut membrane), the changes in shape cannot be expressed by linear curves, as in the transverse vibrations of other sounding bodies, but by curved surfaces, differently in different directions; and the nodes are not the motionless points but motionless lines, which one can call nodal lines.
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Notes
- 1.
The substance of Euler’s statement, rendered in modern terms, is that the only vibrational patterns of two-dimensional plates susceptible to mathematical analysis are those that are mathematically equivalent to a one-dimensional rod or “thread” vibrating in a single plane. Viewing the figures referred to by Chladni in the preceding paragraph may help clarify this for the reader.—JPC
- 2.
Chladni correctly observed that the frequencies for modes 3∣0, 4∣0, and 5∣0 are roughly 9, 16, and 25 times the frequency of mode 2∣0. The second part of Chladni’s observation is also correct. More accurate values for these ratios are 8.4, 15.0, and 23.9.—JPC
- 3.
Lord Rayleigh refers to this formula as “Chladni’s Law.” In fact, we have found that it holds up quite well for other structures with circular symmetry such as church bells.—TDR
- 4.
Jean-Joseph-Marie Amiot (1718–1793). French Jesuit missionary sent to China.—MAB
- 5.
I have been told that the inequalities on the outside of the gongong or tamtam appear to be produced by impressions of the pumice that was used in the mold. Some experiments have shown that the pieces of a similar instrument are not malleable.—EFF Chladni
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Chladni, E.F.F. (2015). Section 7: Vibrations of Plates. In: Treatise on Acoustics. Springer, Cham. https://doi.org/10.1007/978-3-319-20361-4_10
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DOI: https://doi.org/10.1007/978-3-319-20361-4_10
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