What are the audio implications within a dome?
This is not really related to spherical mirror projection. A solid (reflective) dome does have a focusing effect (focal point at 1/3 the dome radius). Inflatable domes have less of a problem since some sound is transmitted through and absorbed by the cloth (a good thick carpet floor also helps). Large planetariums solve this by using perforated metal mesh surfaces with the speakers on the outside of the dome.
This is not really related to spherical mirror projection. A solid (reflective) dome does have a focusing effect (focal point at 1/3 the dome radius). Inflatable domes have less of a problem since some sound is transmitted through and absorbed by the cloth (a good thick carpet floor also helps). Large planetariums solve this by using perforated metal mesh surfaces with the speakers on the outside of the dome.