Modelling of Shell Trumpet Overtones and Acoustics of Helicoidal Geometries

In this work, the propagation of acoustic waves in shell trumpets is explored, and the overtones generated by them are studied. We consider different shell geometries, for which their particular morphology is taken into account. This impacts the fundamental frequencies as well as the overtones. An analytical model based on differential equations is developed to predict these overtones and compared with real recordings of some shell trumpets belonging to several collections in Mexico (experimental results). As a consequence, the notes of archaeological shells that cannot be played due to their physical damage are estimated.