An open pipe (organ pipe) has a narrow, high Q resonance. Is there any research out there for the effect on Q at different angles of end cut? If not I am going to get a carpet tube, a speaker and a saw ;-)
The organ pipe's Q will indeed decrease. Although I have never seen an equation which expresses this, a simple estimate can be made as follows:
The slanted end joins the tube at two places, where the tube length is different. Calculate the resonances corresponding to those two different "effective" tube lengths; these will furnish upper and lower bounds for the spread in resonances the tube will support.
Please report back when your experiments are completed so you can share the results!