In a toroidal bend in a cylindrical wind instrument, with the same cross section as the cylindrical part, the inertance for longitudinal waves is reduced. This induces a change in the resonance frequency. The magnitude of this change depends on the length and the sharpness of the bend and on its position in the sound field. A transition to a cylinder gives an additional inertance correction. The present study compares known results from literature and adds new facts, employing analytical and numerical methods. Possible causes of the discrepancies between measurements and theory as reported in the literature are considered. The theory was verified by measurements on some toroidal bends in between cylindrical tube pieces. Corrections were applied for diameter differences between the torus and the rest of the pipe system. Within experimental uncertainty, a satisfactory correspondence with theory was found. The results obtained in the present study determine which diameter reduction in the bend can compensate...
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