At a Modeling workshop earlier this summer, I was given a “whirly tube”. When you swing it in a circle, it makes a low-pitched whistling sound. There are overtones as well. It’s a pretty interesting instance of the classic standing wave in a tube scenario.
The product is available from Steve Spangler’s store (click the image above).
I wrote up a bit of a physical exposition of what (I think is) is going on with the whirly tube.
Read the PDF
I’m not convinced this explanation is correct. Andy’s suggestion below seems good. I’d appreciate hearing from anyone with insight.
Teaching Danny... 
I’m not convinced that the frequency of oscillation matters. With smaller ones, all you have to do is blow over the top (no spinning needed). I think the corrugation is key.