An air core power reactor (10) having a noise mitigating sound shield (40). In one embodiment the sound shield includes a plurality of sound absorbing panels (42p) configured for positioning about an outermost reactor layer (12′) so that the panels reduce radiation of acoustic energy when the reactor coil layers carry current. One or more flexible members (48) are attached along the first side of each sound absorbing panel for contact with the outermost reactor layer. Sound barrier material (44) is positioned along the second side of each panel. When the flexible members are attached to a panel and the panel is installed about the outermost first layer of the reactor, the flexible members are positioned against the outermost first layer and the flexible members provide a gap between the first side of the panel and the outermost first layer of the reactor.