New lattices of sound tubes with harmonically related eigenfrequencies

Jean-Pierre Dalmont (1) , G Le Vey (2, 3)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
3 Mines Nantes - Mines Nantes

In 1994, the first author of the present paper and J. Kergomard published in acta acustica a paper entitled : Latticies of sound tubes with harmonically related eigenfrequencies. These lattices are made of a succession of truncated cones with equal length that have to respect certain rules. When looking at the eigenmodes with closed-open boundary conditions (i.e. reed wind instruments case), the solution were found to be stepped cone, that is cones made with a succession of cylinders whith cross sections following the law a n = a 1 n(n + 1)/2. At the end of the paper, the authors wrote : Finally, it remains to be demonstrated rigorously that no other shapes of horn lattices have harmonically related eigenfrequencies. In the present paper we show instead that other stepped horns have this property.

Domaines: Acoustique [physics.class-ph]

Jean-Pierre Dalmont, G Le Vey. New lattices of sound tubes with harmonically related eigenfrequencies. International Symposium on Musical Acoustics, François GAUTIER (LAUM, Université du Maine) Joël GILBERT (LAUM, CNRS, Université du Maine), Jul 2014, Le Mans, France. ⟨hal-01312879⟩