Peter L. Hoekje Colby A. Payne David N. Kjar
Dept. of Phys., Univ. of Northern Iowa, Cedar Falls, IA 50614-0150
The vibrations of brass instrument bodies are important to musicians. Three proposed mechanisms by which players might detect these vibrations are radiation, mechanical coupling to hands and mouth, and alteration of the acoustic response of the instrument bore as felt by the lips. The first mechanism has been demonstrated by other researchers [e.g., B. Lawson and W. Lawson, J. Acoust. Soc. Am. 77, 1913--1916 (1985)]. The mechanical coupling is strong, but this mechanism has minimal musical significance. For the third mechanism, the coupling between the instrument shell vibrational modes and the cross-sectional modes of the air in the bore is dependent on their relative symmetries. In the narrow main bore only plane waves propagate; in theory these should couple only to cylindrically symmetric shell modes. Trombone bell vibrational mode patterns, identified by holographic interferometry, exhibit symmetries similar to those in church bells, with nodal circles and nodal meridians. However, they may be indexed by the single number m of the nodal meridian planes. For m>0, the frequencies f[sub m] are approximately described by a simplified Chladni's law of the form f[sub m]=C(m)[sup p]. For a typical trombone bell, C=209 Hz and p=1.1, while f[sub 0]=277 Hz.