As an aside to this topic. Before Chuck Yeager broke the sound barrier in the Bell X-1. In fact just after WW11, tests were done in the UK and US with Piston Fighters ie. Spits and alike.
These tests were usually controlled high speed dives. During some of these flights Mach Tuck was experienced and unfortunately some of the test Airmen and Women lost their lives..
The centre of pressure as John Tullamrine says, moved rearwood on the Tail Plane rendering it useless due the shock obstruction of airflow over the elevators. Saw this on the box one night. I stand to be corrected ofcourse.