Step 2: The Mouthpiece
PVC pipe comes with a variety of wall thicknesses. Schedule 40 is common, and is what I used. The 1/2" CPVC doesn't quite fit inside the 1/2" PVC, and the 1/2" PVC doesn't quite fit inside the 3/4" PVC. By sawing a slit down one side of the pipe, it can spring open and fit tightly on the next size pipe down.
My mouthpiece parts fit so tightly that no glue was needed.
I cut the 1/2" PVC channel and put it in place to mark the size of the rectangular sounding hole. Then I removed the 1/2" PVC, drilled the hole, and touched it up with an X-acto crafts knife. You need a narrow and sharp blade to get in the hole and carve out the wedge-shaped edge of the hole.
I put the wooden dowel plug right up to the start of the sounding hole. Setting it further back toward the mouth changes the pitch and allows some tuning. I used a metal drift pin and a hammer to set the plug inside the pipe.