page_title: Ernst Chladni
section_title: Chladni figures
hierarchical_section_title: Ernst Chladni / Chladni figures
caption_attribution_description: Português: Clavicilindro, instrumento musical de fricção Deutsch: Clavicylinder
context_page_description: Ernst Florens Friedrich Chladni was a German physicist and musician. His most important work, for which he is sometimes labeled the father of acoustics, included research on vibrating plates and the calculation of the speed of sound for different gases. He also undertook pioneering work in the study of meteorites and is regarded by some as the father of meteoritics.
context_section_description: One of Chladni's best-known achievements was inventing a technique to show the various modes of vibration on a rigid surface, known as Chladni figures due to the various shapes or patterns created by various modes. When resonating, a plate or membrane is divided into regions that vibrate in opposite directions, bounded by lines where no vibration occurs (nodal lines). Chladni repeated the pioneering experiments of Robert Hooke who, on July 8, 1680, had observed the nodal patterns associated with the vibrations of glass plates. Hooke ran a violin bow along the edge of a plate covered with flour and saw the nodal patterns emerge.
  Chladni's technique, first published in 1787 in his book Entdeckungen über die Theorie des Klanges ("Discoveries in the Theory of Sound"), consisted of drawing a bow over a piece of metal whose surface was lightly covered with sand. The plate was bowed until it reached resonance, when the vibration causes the sand to move and concentrate along the nodal lines where the surface is still, outlining the nodal lines. The patterns formed by these lines are what are now called Chladni figures. Similar nodal patterns can also be found by assembling microscale materials on Faraday waves.
  Chladni had visited the Paris Academy in 1808 and had demonstrated the vibration patterns before an audience that included not only the leading French scientists but Napoleon himself; Napoleon set a prize for the best mathematical explanation. Sophie Germain's answer, although rejected due to flaws, was the only entry with the correct approach.
  Variations of this technique are still commonly used in the design and construction of acoustic instruments such as violins, guitars, and cellos.  Since the 20th century, it has become more common to place a loudspeaker driven by an electronic signal generator over or under the plate to achieve a more accurate adjustable frequency.
  In quantum mechanics, Chladni figures ("nodal patterns") are known to be related to the solutions of the Schrödinger equation for one-electron atoms, and the mathematics describing them was used by Erwin Schrödinger to arrive at the understanding of electron orbitals.
caption: Clavicylinder
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