Suppression of noise is vital to many branches of science and engineering, and various active and passive methods are reported in the literature and realised in practice for this purpose. Due to better reliability, stability and efficiency, Passive Noise Control (PNC) systems are preferred over Active Noise Control (ANC) systems. Absorption performance of traditional PNC system depends on its thickness, and maximum absorption occurs when this thickness is a quarter wavelength. To overcome this limit, acoustic metamaterials have been proposed with thickness in subwavelength range. This work discusses a bandwidth-limited passive noise control system enabled by an acoustic superscatterer, a type of metamaterial, to suppress the far-field sound radiated from a vibrating cylindrical rod. Superscatterers are known to expand the rigid boundary of an object, thereby enhancing the scattering cross-section of the object. The design of the acoustic superscatterer is based on the partially-resonant system in which a coating, i.e., double-negative metamaterial complementary to the host medium, is provided around a rigid object. When the source lies within the enhanced boundary of the complementary medium, the interaction between this boundary and the radiated wavefront suppresses the total forward radiated sound at the far-field. An analytical framework of this phenomenon is discussed, along with numerical cross-verification examples. In addition, the applicable bandwidth of superscattering and sound suppression thereof are also discussed with the help of integrated extinction theory, thus drawing conclusions vital for practical applications.