ON THE INERTIAL END CORRECTION OF RESONATORS

Abstract

Inertial end correction is very important in the design of thin-necked resonators, perforated facings and speaker enclosures. A linear acoustic model of a piston-driven axially infinite tube is adopted to analyse the mass end correction of apertures in a tube finite in its transverse dimensions. Regular geometries such as rectangular and circular apertures and-tube sections are the object of the study. All the geometrical factors and wave actions are included in the mathematical formulations with some idealisations. As a result, generalised equations are obtained for the mass end correction due to the self-action of the aperture itself as well as the interaction between two apertures in a tube. Parametric studies are made for various geometric and frequency variables to investigate their effects. In addition to the axially infinite tube, a generalised formula for an axially finite tube is also derived. Using the end correction formula for the axially finite tubes, the transmission losses of Helmholtz resonators are predicted and compared with those from the plane wave theory as an application example.