This paper presents a theoretical study of the dispersion characteristics of sound wave propagation in a periodic ducted Helmholtz resonator (HR) system. The predicted result fits well with a numerical simulation using a finite element method. This study indicates that for the same system, no matter how many HRs are connected or what the periodic distance is, the area under average transmission loss T L¯ curves is always the same. The broader the noise attenuation band, the lower the peak attenuation amplitude. A noise control zone compromising the attenuation bandwidth or peak amplitude is proposed for noise control optimization.