At what rpm does the tip of a 54" propeller start to incur mach losses?
A 54 inch propeller would start to incur efficiency loss at approximately 4300 rpm.

At 4300 rpm a 54 inch propeller would have a tip speed of 691 mph which, relative to the 767 mph speed of sound, is about the maximum which still allows propeller efficiency. 

You can calculate the variables using this tool: WarpDriveProps.com Propeller Tip Speed Calculator