The whistle is made from 1/2" and 1/8" thick pieces of wood. I used oak, which is a fairly porous wood. A denser closer-grained wood would probably be a better choice.
Exact dimensions are not critical. I drew concentric circles of the 1/2" thick body using 1-1/4" diameter and 1" diameter fender washers. The inside circle is used to align the Forstner bit. The 1-1/4" diameter fender washer was also used to draw the 1/8" thick side caps.
I have CAD captured the whistle, but did the drawing in metric. You can make a 1:1 printout of the drawings at left by downloading the eval version of my BigPrint program and just dragging the image at left onto the program. Or you can print the print the pdf. You can alslo download the whistle SketchUp model
The middle layer should be cut 13 mm thick, the two sides 3 mm thick.
Drill the body with a Forstner bit or cut it out with a scroll saw.
I used a scroll saw to cut the body and the side caps. The mouthpiece of the whistle is split lengthwise with a saw and the wind cutter at the other end of the opening is cut at a 60 deg angle.
Shorten the end of the top part of the mouthpiece, either by cutting or by sanding. Sand both inside faces of the mouthpiece (what will be the air slot) smooth. The inside of the body should be smooth. Maintain the sharp edge of the wind cutter.
Glue the top of the mouthpiece to one of the side caps.
Now is your opportunity to "tune" your whistle. Temporarily place the body of the whistle on the side cap, aligning the parts as shown with an approximate 1/16" slot between the top and bottom portions of the mouthpiece.
Place the second side cap into position and hold the parts together.
Blow on the whistle to test it.
Make sure your whistle is going to sound its best by adjusting the body position and the size of the air slot. When you are happy with the sound, glue the parts together. I filed and sanded everything smooth and radiused the edges.
I used a short piece of 3/8" dowel and concaved one side to fit the curvature of the body and glued it to the body. Then I drilled a hole in the center of that dowel for attaching a lanyard.
The oak was given a couple of coats of linseed oil (inside and outside) and it sounds fine. Sealing with varnish would also be good. Be careful not to plug up the air slot with varnish.
Experiment with the various dimensions of the whistle and you can probably reduce the size of the mouth enabling the use of a small ball or pellet inside the body, which will tumble around in the turbulent air when you blow on the whistle. The tumbling ball will disrupt the airflow creating pressure fluctuations within the body and the warbling sound we associate with a police whistle.
Enjoy your whistle!