Start with Super Sonic  on the sound test (bottom right) play sounds 04, 01, 02, 06. Start with Hyper Sonic  on the sound test (bottom right) play sounds 04, 01, 02, 06, 04, 01, 02, 06.

You have to enter them and complete the puzzle to get an emerald, 7 times. Now that you have super sonic, continue normally until mushroom hill zone. You should see knuckles walk out of a tunnel, so enter it and you should find a flashing big ring. Enter it and stand on one of the emeralds to start the challenge.