A study was conducted to demonstrate difference problem of noise suppression and other problems of active control of single-frequency sound on a composite domain. The field values at boundary points between the sub-regions were used to construct formulas for additional sound sources that were introduced to change the acoustic field in the sub-regions in the desired manner. It was observed that independently on each sub-region, the acoustic field can be fully or partially shielded from the sources located on the complementary sub-region. The results on the shielding of a given region from the sources located on the complementary region can also be obtained as a special case. The study also discussed problems related to the active control of sound on composite regions consisting of two or more sub-regions.