I had a similar event after a auto launch last weekend. After release there was a weird vibration/buzz/whine/etc. and I figured it was the main wheel so squeezed the brake handle. No change. After landing just we rolled to a stop and the tail dropped back to earth I heard that sound again. Obviously it was the tail wheel spinning down, and in the case of the Duo XL that component is a heavy brass item (for cg) and takes a long time to unwind.

If your Duo has a brass tailwheel I'd bet that's what you heard.

KS