Flexible or perforated port tubing

Some time ago I found examples for bass reflex port tubing with holes (this is a german article but for reference: the first measurement compares the perforated and none perforated bass reflex tube) and for speakers using flexible material for the tubing (page 16-17), both to reduce overtones in the bass reflex tube. While both approaches are understandable in their concept I am missing further details to fully comprehend them. For instance in the german article it is pointed out that the length of the tube has to be longer by 2^0.5 when adding those holes. Wanting to dive deeper into the topic I tried to find some more articles and measurements. However, my search was unsuccessful.


I was hoping if someone of you could point me in the right direction. Is there no more research available or do I simply dont know the correct terms to search for?