Invented by Herman von Helmholtz (1821-1894) these instruments were used to analyze the composition of musical and speech sounds by means of 'resonances'. Later improved by Rudolph Koenig (1832-1901), they were an essential tool for the 19th century acoustician.
Resonance can be observed in the following situation. When two adjacent guitar strings are tuned to the same note and one string is plucked the air vibrations caused by the first string will make the second string vibrate 'in sympathy': if you stop the first string the second will continue to sound. Resonance can also be used to amplify vibrations. Imagine pushing a child on a swing, for example. When you first push, the movements are small, but as you continue to give small regular pushes, each time just as the swing begins its motion away from you, the amplitude of the movement becomes larger and larger - the swing is resonating with your regular pushing motion. Further, you may have noticed that a playground swing will only move back and forth at a particular frequency - its natural frequency - and if you try and push the swing at the wrong moment (i.e., with a different frequency) the amplitude will be decreased.
Helmholtz resonance occurs whenever a volume of air in a cavity is caused to vibrate at its natural frequency, just like when you produce a note by blowing over the mouth of a wine bottle. In this case, the mass of air in the neck of the bottle is pushed away from equilibrium compressing the air inside the body of the bottle, which in turn acts like a spring, pushing the air in the neck and then pulling it back once it travels beyond its starting point. Blowing over the mouth of the bottle tends to reinforce the oscillation of the air at its natural frequency, which is determined by the dimensions of the bottle and the local atmospheric pressure.
Helmholtz theorized that musical and speech vowel sounds are composed of numerous different frequencies, referred to as harmonics or partials, and that the tonal quality or timbre of the sound was determined by the relative intensity of these partials. Using the amplifying effect of sympathetic resonance, Helmholtz designed and used these resonators to identify and estimate the relative strengths of the partials present in these sounds. The resonators were designed to have a very precise natural frequency and in general, the larger the resonator the lower the frequency. Each resonator, like a wine bottle, has a mouth, a neck and a main cavity, but they also have a thin 'nipple' opening at the back. By inserting the resonator's nipple into his ear, Helmholtz was able to detect when sounds of the specific frequency of his resonator were present.
Helmholtz resonators were used in a multitude of different apparatus, including Helmholtz's apparatus for the synthesis of sound and Koenig's apparatus for the analysis of sound. In modern times Helmholtz resonances are used to amplify bass frequencies in hi-fi speakers and headphones.
Torben Rees & Jonah Lipton
Torben Rees & Jonah Lipton, 'Helmholtz resonators: tools for the analysis of sound', Explore Whipple Collections, Whipple Museum of the History of Science, University of Cambridge, 2009 [http://www.hps.cam.ac.uk/whipple/explore/acoustics/hermanvonhelmholtz/helmholtzresonators/, accessed 27 February 2017]