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Helmholtz resonator (HR) is widely used in various fields, but the classic HR usually should satisfy the acoustically compact condition, which limits the application range of the classic HR. This paper investigates analytically and numerically the acoustic performance of a HR in which the length of the neck is not limited under the acoustically compact conditions. An analytical model is developed for accurately and quickly predicting resonant frequencies and transmission loss of the Helmholtz resonator with an extended neck (HREN), and numerical simulations have been performed to validate the developed analytical model. Both the analytical and numerical studies reveal that the HREN has multiple resonant frequencies, and a method is developed for approximate and fast calculation of the multiple resonant frequencies. [ABSTRACT FROM AUTHOR]