My understanding is that a normal jet aircraft will have a real hard time approaching and breaking the speed of sound at whatever density, temperature it's at...
Basically, the drag (drag coefficient, C sub D, for the aerodynamic geeks among us) approximately triples as you go throught the speed of sound. Nobody will give an aircraft three times the power it needs otherwise unless going through the "sonic barrier" is a requirement. Once past it, it drops off again to about 50 percent higher than its subsonic value, so cruising at supersonic speeds is practical (though expensive, for a bunch of other reasons besides drag as well).