# Vapour clouds and the speed of sound

I've been thinking about this question for a while and I didn't get to any conclusion yet.

When an aircraft flies faster than the speed of sound (specifically when it achieves it) a cloud of condensed water becomes visible. Like in the figure below:

I know that as the speed of the object increases to the sonic velocity (the local velocity of sound waves), these sound waves begin to pile up in front of the object, so the localised air pressure and air temperature around the object drops. If the temperature drops below the saturation temperature, a cloud forms.

Considering that after the cloud formation the aircraft still accelerates, will this effect happen again as the aircraft achieves a multiple of the sonic velocity? For instance the aircraft achieves the velocities $$2v_s$$, ..., $$n v_s$$, where $$v_s$$ is the sonic velocity .