As far as I remember from ATPL theory(I am not a pilot) speed of sound decreases because of temperature. It's like -50c up there. So you cannot fly the same IAS because you will reach the speed of sound. And you cannot fly conventional aircraft faster than the speed of sound...
I am not sure about the density... The density is the amount of molecules and the temperature is the energy:bigger temperature faster movement of molecules. So when you reach the spead of sound you reach the speed of air molecules and molecules cannot move out of your way... So you hit something like concrete wall.
(I think in hard materials sound moves quite different so it's difficult to compare gas and liquid ect...)
from wikipedia:
In fact, assuming an
ideal gas, the speed of sound
c depends on temperature only,
not on the pressure or
density (since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas.