In Search of the Missing Fundamental: by Richard K. Jones
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Fleisher & Fastl

Between 2005 and 2008, Helmut Fleischer and Hugo Fastl (Institut für Mechanik, Universität der Bundeswehr München) contributed to their ongoing series Beiträge zur Vibro- und Psychoakustik by conducting three studies on timpani. The trilogy Vibroakustische Untersuchungen an PaukenfellenFell, Kessel und Gestell der Orchesterpauke, and Physikalische und gehörbezogene Analyse von Paukenklängen confirmed the findings of the earlier studies done on timpani acoustics plus added much new and intriguing data to the field. The following is an English translation of the summary from each study.

Vibroakustische Untersuchungen an Paukenfellen *


Calculations and experiments are described towards better understanding the generation and radiation of sound by the kettledrum (timpani). The vibrational behavior of the heads of various kettledrums is studied using various approaches.

After a short review of the theory of the ideal membrane, the classical Chladni method is used to visualize nodal lines. Thereafter, acoustic experiments on kettledrums are depicted. Measuring the directional characteristics in the far field gives hints on the number of nodal diameters. The sound pressure or velocity in the near field can be exploited to reconstruct the radial distribution of the velocity of the head vibration and thus to identify nodal circles. The driving point impedance or admittance give insight into the vibration willingness of the head at a specific location. Non-contact approaches (Laser triangulation and Laser velocimetry) yield the bases for the Modal Analysis of kettledrum heads. Comprehensive experimental data are compiled by means of a Laser Scanning Vibrometer. Operating deflection shapes as well as eigenmodes of various heads in different tunings are presented.

The majority of the results is displayed as red-green colour maps in the appendix. These investigations are to assemble a multitude of experimental data to create an idea of the head’s vibrational characteristics. The aim is to improve modeling of the head with respect to the function of the kettledrum as a musical instrument.

Fig. 3o

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