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Dependence of the internal geometry for the calculation of the Helmholtz frequency in an axisymmetrical acoustic resonator.

The well-known formula of Helmholtz is well established and perfectly suited to predict the resonance frequency of cylindrical resonators when using neck length corrections. The potteries celled in the walls of medieval buildings are the object of archaeological studies where the knowledge of their volume is the starting point to deduce their origin. The frequency measurement and Helmholtz's formula is a clever way to get the volume without touching the building in situ. However, the internal corrections which suppose an interior abrupt connection condition are less effective because this assumption is not realistic for the complex shape of potteries. This study investigates internal corrections for two types of often observed geometries of potteries with conical or parabolic transitions between the neck and the volume. Correction formulas are proposed according to both an experimental and a numerical study.