How does the pitching moment change as the speed of A/C approaches critical Mach number? In an aircraft performance course, I saw that pitching moment goes backwards as the speed of A/C approaches critical Mach number. In fact, that results in nose down pitching moment. But, according to my notes, there must be shock waves at the back of the A/C. In this situation, should not these waves behave as force pitching down? How can it be possible? And why?
Yes most aircraft which operate in the transonic zone experience a nose down pitch with increase in speed. The two main causes are : 


Rearward movement of centre of pressure
Because of supersonic acceleration at higher speed, pressure continues to decrease past the 50% chord point, thus increasing the amount of lift produced by mid chord part of wing.
Modification to airflow over the tailplane
Most tailplane work in a region of downwash from the mainplane, in case of swept aircraft the downwash can be considerable. The formation of shockwave on main plane modifies the flow such that the downwash is reduced and this will pitch aircraft nose down