Die Akustik.

Leipzig: Breitkopf & Härtel, 1802.

First edition of the foundation work of the modern science of acoustics. “Chladni (1756-1827), professor of physics in Breslau, was the first to reduce the general association between vibration and pitch to a tabular basis, and thus to lay the foundation of the modern science of acoustics. His first results were first reported in New Discoveries in the Theory of Sound, 1787, and were greatly enlarged upon in Acoustics, 1802. He spread sand on plates made of metal and glass, which were fixed in clamps. He then applied a violin bow to the edge of each plate and recorded the patterns produced thereby in the sand. These figures are still known by Chladni’s name” (PMM). “By his own account, Chladni found inspiration in the work of Georg Christoph Lichtenberg, who scattered powders over the surface of electrified resin cakes to produce the patterns known today as Lichtenberg figures. Figuring he could do the same thing with sound, Chladni began scattering sand on his rods and plates. He had a musician’s ear and could discern slight changes in frequency, so he noticed that different frequencies produced different distinct patterns, and he recorded them assiduously. Also, he developed a formula that predicted the sand patterns for vibrating circular plates. He published the results in his 1787 treatise Entdeckungen über die Theorie des Klanges. But his most seminal treatise was 1802’s Die Akustik, a systematic description of the vibrations of elastic bodies that earned him the moniker ‘father of acoustics’” (APS).

Leonardo da Vinci noted the unusual patterns formed by particles in response to vibrations. So did Galileo, who noticed that bits of bristle on the sounding board of an instrument would move in some areas but not in others. But these so-called "Chladni figures" bear the name of the man who conducted the first in-depth investigations of the phenomenon: a German physicist and musician named Ernst Florens Friedrich Chladni.

“Chladni was born in Wittenberg in 1756, to a long line of academics. His father was a law professor and dean of law at the University of Wittenberg. Both his mother and his sister died when he was still quite young. Chladni was mostly educated at home by his father, a strict disciplinarian. The boy was often confined to his room to study by day, and discouraged from fostering friendships, but he loved studying the stars and maps, yearned to travel, and began reading about science at age seven. As a teenager he was sent to boarding school near Leipzig, rooming with one of his teachers rather than with the other students. His father nixed his desire to study medicine and insisted he earn a law degree instead.

“Chladni went on to earn degrees in law and philosophy from the University of Leipzig, but his father died just as he completed his studies, leaving Chladni to provide for his stepmother. But it also freed him to finally pursue his scientific interests. He eked out a nomadic living giving lectures, initially on law, but eventually on geometry, geography, and the field to which he would go on to contribute so much as a researcher: acoustics.

“Chladni first began conducting experiments in his flat, moving beyond the usual studies of vibrations in string and wind instruments to focus on transverse vibrations of rods – inspired by earlier work by Leonhard Euler and Daniel Bernoulli – before turning to vibrations of plates, then largely an unknown field. Chladni might not have known it at the time – there is no specific mention in his surviving writings – but a century earlier, on July 8, 1680, Robert Hooke sprinkled sand over a solid metal plate, ran a violin bow along the edge to make the plate vibrate, and noted the unique patterns that formed as the sand grains rearranged themselves along the vibrational nodes” (APS).

“During the eighteenth century, scientists had undertaken experimental and theoretical work on the vibration of strings and had made attempts to study the vibration of rods and membranes. The vibrations of solid plates had not been treated, and Chladni, in his first report, emphasized that although the vibration of strings was understood, the production of sound by solid plates was not.

“By spreading sand over plates and running a violin bow over their edges, Chladni was able to observe the structure of the resulting vibrations, because the sand collected along the nodal curves where there was no motion. Patterns formed in this way were symmetrical and often spectacular, the lines of sand forming circles, stars, and other geometric patterns. Chladni first used circular and rectangular plates of glass and copper, three to six inches in diameter. Later he extended his observations to ellipses, semicircles, triangles, and six-sided polygons. He generally fixed the plates at one internal point, which became a node, and left the sides free. In a few cases a stationary point or line occurred on the edge of the plate.

“Chladni analyzed the sand patterns by classifying them according to geometrical shape and noting for each the corresponding pitch. Thus he was able to emphasize that the patterns and sounds of a vibrating plate are analogous to the shapes and tones of the modes in the harmonic series of a string.

“In addition to his analysis of surface vibrations, Chladni studied the vibrations of cylindrical and prismatic rods. For the latter, he again used the sand figure method. He deduced the velocity of sound in solids from the pitch that a long rod of a given material produces when made to vibrate longitudinally. He measured the velocity of sound in gases other than air in a similar way: he compared the pitch of a wind instrument filled with the gas being studied with the normal pitch of the instrument under standard atmospheric conditions.

“The visible demonstration of surface vibration received much attention in the 1820’s and 1830’s. In Germany, Friedrich Strehlke continued experimental investigations; Wilhelm and Ernst Weber dedicated their treatise on wave motion to Chladni, since they believed that the acoustical figures had stimulated the contemporary interest in the subject; and in the middle of the century Gustav Kirchoff worked on the mathematical theory of vibration. Thomas Young in England had been interested in the experiments as early as 1800, and Charles Wheatstone later analyzed them by a geometrical superposition principle. Michael Faraday knew about the phenomenon and experimented with the figures, considering especially the surrounding air currents.

“French scientists showed even more interest in Chladni’s work. Félix Savart, who was truly Chladni’s professional successor, carried on experimental investigations. Jean Baptiste Biot and Siméon Denis Poisson collaborated on a study of the sound vibrations of gases and gave much attention to Chladni’s relevant experiments. The most organized activity was in the study of the theory of the vibration of surfaces. 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. The physicists at the Academy responded by announcing a prize competition for the best mathematical study of elastic vibrations. They noted a similarity between Chladni’s demonstration of the nodal curves in vibrating surfaces and Joseph Sauveur’s demonstrations of the nodal points in vibrating strings a century earlier. Since Sauveur’s efforts had led to fruitful mathematical work, it was expected that the sand figures would have as beneficial an effect on theory. Sophie Germain was an early contributor to the large body of work on the mathematical theory of vibration, which, until the middle of the nineteenth century, is associated principally with Louis Navier, Poisson, and Augustin Cauchy” (DSB).

“Because the vibrational patterns showed exactly where modes of vibrations fell in the back plates of musical instruments, Chladni’s technique soon became a vital tool for violin makers and other instrument makers. It is still widely used today. Chladni himself invented two musical instruments: the euphony, inspired by Benjamin Franklin’s glass armonica, and the clavicylinder, an improvement of Hooke’s earlier musical cylinder, or ‘string phone.’

“And his research continues to inspire other scientists. Last year, a Physical Review Letters paper described how physicists at the University of Grenoble in France performed their own version of Chladni’s pioneering experiment. Rather than scattering sand on metal plates, they suspended polystyrene microbeads in water, injected the suspension into a microfluidic device, and stretched a membrane of polysilicone across a circular opening at the base to create a drum that vibrated. Then they recorded the positions of the microbeads with a camera attached to a microscope. When the plate vibrated, the beads arranged themselves at the antinodes, forming inverse Chladni figures the result of acoustic streaming in the fluid. The ability to form such patterns in a microfluidic device opens the door to using sound waves to organize objects into specific patterns for various technological applications, such as grouping cells into colonies and then using changing frequencies to shift their size and distribution, thereby affecting their development.

“Chladni died in April 1827 while on a lecture tour in Breslau, having never held a formal academic position. He never married, nor did he have children, and the site of his grave has been forgotten. But his patterns continue to inspire scientists and artists alike. While the great German author Johann Wolfgang von Goethe was mildly dismissive of Chladni when he first met him in Weimar in 1803, by the time of the latter’s death he had changed his tune. ‘Who will criticize our Chladni, the proud of the nation?’ Goethe wrote. ‘The world owes him gratitude, since he made the sound visible’” (APS).

PMM 233(b); Poggendorf I, 439; Honeyman 688; DSB III, 258; Roberts & Trent, p. 70; Sparrow, Milestones of Science 38. ‘July 8, 1680: The First Experiments that Inspired 18th Century ‘Chladni Figures’,’ APS News, July 2017 (https://www.aps.org/publications/apsnews/201707/history.cfm).



4to (232 x 202 mm), pp. [ii], xxxii, 304, [2], 305-310, engraved vignette portrait by J.W. Bollinger on title page, 11 folding plates. Contemporary half-sheep and marbled boards (spine ends worn, joints cracked, boards a bit rubbed). Custom half leather clam shell box with gilt spine lettering.

Item #5508

Price: $8,500.00