Helmholtz Resonator

   The research of Herman L. F. von Helmholtz (1821-1894) straddled the interfaces between physics and physiology and psychology. His book, On the Sensations of Tone, published in 1862, at first appears to be on music and its perception, but on a deeper examination, is also a classic textbook on the subject of vibrations. Helmholtz and Koenig were at the University of Königsberg in East Prussia at the same time about 1850 and undoubtedly knew each other.

   The book describes the form of resonator that he developed for picking out particular frequencies from a complex sound. This consists of a body to contain a volume of air, a hole or neck in which a slug of air can vibrate back and forth, and a slender nipple that can be held in the ear canal (or, today, connected to a sound level meter). The enclosed volume of air acts as a spring connected to the mass of the slug of air, and vibrates in an adiabatic fashion at a frequency dependent on the density and volume of the air, its molecular composition, and the mass of the slug of air in the neck. The system is just the same as that used to find the ratio of the specific heats of gases using Rüchardt's method.
   Koenig made both cylindrical and spherical Helmholtz resonators. Until 1860 Helmholtz had been using as resonators whatever glass cylinders and tubes were at hand; about that year he asked Koenig to make metal resonators of both shapes to specific measurements for more careful work. 

   A set of spherical resonators at the University of Toronto is shown at the right. The 1889 Koenig catalogue does not list a set of five resonators, but these, on their original base, must be part of the collection of acoustic apparatus that Toronto bought from Koenig after the 1876 Centennial Exposition in Philadelphia. 

  This very large set of twenty two Helmholtz resonators is in the Garland Collection of Classic Physics Apparatus at Vanderbilt University. These were bought by Chancellor Garland to outfit the Vanderbilt physics department for the opening of the university in 1875. Garland had previously gone to visit Koenig in Paris to discuss his order. in 1889 a set of nineteen resonators cost 170 francs.
   Father John A. Zahm, Professor of Physics at Notre Dame in Indiana, visited Koenig, and wrote a book on acoustics based on Koenig's apparatus. He often bought two sets of apparatus, one for Notre Dame and one for St. Mary's College for Women just to the west. The nuns took good care of their apparatus, and this set of seven Helmholtz resonators is one of the many survivors at St. Mary's. 
  The resonant frequency of a Helmholtz resonator depends on its volume, and a cylindrical resonator permits the volume of the resonator to be changed by sliding the tubes in and out. The notes (and hence the resonant frequencies) are engraved on the side of the apparatus. This is one of a number of tunable Helmholtz resonators at the University of Vermont. 

   Quite similar resonators were made and sold by the firm of  Max Kohl of Chemnitz in Germany.


   This Helmholtz resonator, excited by an electrically-driven tuning fork, is part of a large device for Fourier synthesis at St. Mary's College in Notre Dame, Indiana. 

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