Treatise on Acoustics

Treatise on Acoustics
E.F.F. Chladni
Springer-Cham Heidelberg, New York/Dordrecht/London, (2015)
227 pp., hardbound, 129 USD,
ISBN: 978-3-319-20360-7
eBook, 99.00 USD

This book is the first English translation of Ernst Florens Friedrich Chladni’s (1756–1827) famous book Die Akustik, originally published in 1802 in German and in 1809 in French. This translation has been provided by Robert T. Beyer (1920–2008), former professor of physics at Brown University, based on the French edition.

Chladni (pronounced “clutnee” in English, like the u in “clutch”) is mainly known to the acoustics community for the generation and illustration of modal patterns of beams and plates with different boundary conditions (in German called “Chladnische Klangfiguren,” in English: “Chladni’s tone/clang figures”). With plates, he investigated a variety of different shapes: not only rectangular and circular plates, but also triangular and hexagonal plates, plus ellipses and semicircular plates, always using a violin bow for excitation. These kinds of modal patterns can be found—more or less—in any basic textbook on acoustics and in any language around the world. Ernst Florens Friedrich Chladni was born in Wittenberg, the native place of the Protestant Reformation initiated by Martin Luther. Chladni’s father was professor of law at Wittenberg University. His ancestors, being protestants, fled a century earlier from central Slovakia (at that time part of the Hungarian Kingdom) for religious reasons. It is no wonder that Ernst Florens was also supposed to study law, or that he finalized his studies with a PhD degree in 1782. Due to the strict regime of his father, Ernst Florens was not allowed to learn a musical instrument until the age of 19. Soon after his father’s death, he became interested in experimental acoustics and also studied the works of Leonhard Euler und Daniel Bernoulli. In an earlier book, Entdeckungen über die Theorie des Klanges, already published in 1787, Chladni described geometrical eigenfunctions and characteristic frequencies (as we would call them now) not only for transversal waves but also for longitudinal waves of strings and beams.

Without doing any harm to others working in the new field of acoustics at that time, we can definitely call Chladni the first experimental acoustician, though Euler and Bernoulli studied transversal and longitudinal vibrations earlier, but only theoretically. Chladni’s book, Treatise on Acoustics, can, therefore, be seen as a kind of review on his own work covering more than 25 years of physical studies of wave phenomena.

The book is split into four parts (with a number of sections in each thereof):

  1. Numerical Ratios of Vibrations (2),
  2. Characteristic Vibrations of Sounding Bodies (10),
  3. On Transmitted Vibrations, or the Propagation of Sound (2), and
  4. On the Sensation of Sound: On the Hearing of Men and Animals (2).

Each part has numerous chapters, albeit some are very short. The book’s appendix shows Chladni’s figures also being an annex in the original book. At the end of several sections, annotations made by Chladni are inserted in grey text boxes providing further explanation to literature from that time and other details. A preface written by Robert T. Beyer gives an account on the state of acoustics in 1800.

In part 1, starting with musical instruments and their harmonic ratios of tones, Chladni develops consonant and dissonant intervals and chords, ending up in a table providing numerical ratios of tone intervals and corresponding string lengths. In the second section, he addresses the concept of temperament applied to real musical instruments.

Part 2 addresses “sounding bodies” and so leads the path to a kind of acoustics, not just looking at musical instruments, by introducing also the direction of vibration: transverse, longitudinal, or even torsional by establishing reference to corresponding figures in the appendix. Subsequently, he treats vibrations of strings, stretched membranes, airflow in wind instruments, rods and strips, and even bended rods (like tuning forks and rings), always assuming constant thickness. But, Chladni, being aware of the fact that rods and strips with an uneven size and thickness show a different behavior, writes that those object types “could be the subject of much research.” In this part in chapter 95 on “Distortions of the Figures,” he addresses—for example—the effect of distortions of the nodal lines at a plate caused by touching and/or holding the plate at different locations along the perimeter. With some goodwill, one could see these experiments as a kind of first insight into damping effects at plates. Further he discusses modal patterns of plates (made of glass or a “sonorous” metal sheet, i.e., with low damping) depending on boundary conditions (two ends free, one fixed, two fixed). Chladni also develops some basic ideas on the behavior of three-dimensional bended surfaces, such as bells and vessels, by studying low-order modes by pouring water covered by some organic, plant-based powder into a bucket with the bell inside and observing the water being driven outward by the bell’s vibrating modes. This reveals that Chladni was a clever experimenter, knowing how to set up a proper experiment and also to impress others. For this reason, he was invited to Europe’s courts and palaces of that time to present his experiments. He gave a lot of public lectures, and also increased his income as a part-time lecturer at Wittenberg University through entrance fees. He was so well trained with his devices that he was able to reproduce any kind of experiment and its result at any location and upon request by the audience.

In the book’s third part, he addresses sound propagation through the air and other gases. From his writing it is clear to him that the sound propagation in air is based on longitudinal waves, while rigid bodies may have different kind of wave types. He assumed clearly that propagation is based on local fluctuations of “sound rays” not causing any transport effect of the air volume being involved. He discusses the speed of sound in the atmosphere (as already measured by Cassini and others) and the speed deviations due to local wind speed fluctuations and effects we nowadays call “diffraction in the atmosphere.” Further, he discusses megaphones, ear trumpets (used as hearing aids), speaking chambers, also called whispering galleries, and echo effects. Finally, he ends in a chapter “on the construction of halls that are favorable to sound” paving the way to room acoustics, and he discusses sound propagation in water by experiments. The final part addresses the hearing of men and animals. Besides the description of outer and inner parts of the ear, he lists some speculative ideas about the transmission, sensation, and impression of sound by the auditory system. At that time, it was not clear whether the ear itself is causing sensation and impression or whether the cortex is involved and to what extent.

On the whole, the book gives a good and detailed insight into the times of prenumerical acoustics around 1800. Robert T. Beyer’s book can be recommended to those willing to study in detail what the thoughts of a leading experimental physicist were—despite the fact that they were all called “philosophers” at that time.

Heinrich Metzen
DataKustik Greifenberg