I also have this sound on my 2003 New Beetle Turbo S. It's the secondary air pump that forces air into the catalytic converter upon startup. (That is what found in a video on Youtube) On my 2013 Smart Brabus it sounds pretty muffled, on my Beetle it sounds like a jet engine which means it needs to be replaced. Once the Smart starts screeching, like my Beetle I will replace it too. Apparently, when the bearings in the pump go bad they get louder and louder. Eventually, it will throw a code in both cars. The pump for the Beetle is around $90.00, for the Smart they are $150.00.