A theoretical study of the interaction between finite-amplitude sound and a single Helmholtz resonator is hereby presented. The flows in the entrance region, orifice and cavity have been considered in detail with the aid of the appropriate conservation equations. To account for the non-linearities of the problem, the differential equations describing first-as well as second-order effects have been solved. The results of this study indicate that the experimentally observed losses can be attributed to the following two mechanisms: (i) viscous damping and (ii) energy loss which is associated with the dissipation of the kinetic energy of the jets which are periodically formed at both ends of the orifice; the latter is amplitude dependent. Plots of the theoretically predicted resistance (which includes both viscous and “jet” losses) as functions of velocity amplitude are in good agreement with available experimental data. Typical plots of resonator resistance and admittance are presented.
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