Let's see. Prop-diam * 3.14159 * rpm gives inches per minute. Divide that by 63360 (inches per mile), giving miles per minute... then multiply that by 60 to give MPH. So, a 16" prop spinning at 15,000rpm is moving the tip at ~714mph. The speed of sound is ~740mph, but it varies quite a bit depending on things such as altitude.

Realize the prop tip doesn't have to go supersonic to make that noise. The air getting out of the way of the prop tip can go supersonic without the tip itself doing so.