In the realm of power grids environmental protection, low-frequency harmonic noise radiated from transformers has always been the focus of attention for decades. The existing noise control technologies, such as traditional noise barriers, sound insulation enclosures, and damping panels, not only occupying a large space but also causing difficulties in heat dissipation and daily maintenance of transformers. Therefore, explorations on the theory and design of low-noise power transformers become particularly necessary. In this paper, we started from the concept of acoustic radiation efficiency and discussed the radiation efficiency of a typical distribution transformer with radiators. It is found that the overall radiation efficiency is reduced below 230Hz (low-frequency band) due to radiator barriers compared with that of the flat transformer tank. Furthermore, the phase effect of vibration distribution was also studied with a validated BEM code, inspired by the "acoustic short circuit" phenomenon. It is verified that the acoustic short circuit phenomenon truly exists for a typical transformer enclosure and affects its sound radiation. These supporting results might lead to a promising noise reduction technology from the perspective of radiation control of transformer tanks, i.e. acoustic metamaterials for noise source phase control.