Did Felix Baumgartner produce a sonic boom during his jump? I really got to thinking about this.  The speed of sound is measured at 761.2 MPH  at sea level.  But how does this number change as air density decreases?  The lack of air density is what allowed his terminal velocity to much lower than say a jump at 5k feet high.  I am not disputing his maximum velocity (800+ MPH), but did Felix Baumgartner actually produce a sonic boom in the process?  I mean, I beleive most people subconsioulsy associate "sonic boom" and "faster than the speed of sound".
 A: Sonic boom refers to the explosive sound caused by the shock wave from an object traveling faster than the velocity of sound. Yes, It's actually spoken out as breaking the sound barrier.
Felix jumped from an altitude of 39,044 km (which is 128,097 ft.) and reached a peak speed of 833 mph. Yes, He did produce the Sonic boom. Most likely, we use the term Breaking the sound barrier while considering air-crafts like "Concorde" because they could be easily sensed. But in case of Felix, he produced

"It was Mach 1.24. Our ground recovery teams on four different locations heard the sonic boom," said Clark, a former high-altitude military parachutist and NASA doctor who worked on escape systems for space shuttle astronauts.

That "Mach 1.24" reading is comparable to the shock waves produced by Space shuttles...


But how does this number change as air density decreases?

Velocity variation of Sound: Indeed, Sound varies with Temperature and also with Density. Also, the state of matter (which refers again to density). It travels faster in liquids and even more faster in solids (like 5120 m/s in Iron)
In general, the speed of sound in a gas is given by Laplace correction of Newton's formula. For solids, see Wiki ('cause it's not necessary now...) $$v=\sqrt{\frac{\gamma P}{\rho}}$$
Applying Ideal gas law and using density of air ($\rho=1.293$ $kgm^{-3}$), we could find that the velocity of sound increases by 0.61 per degree celsius rise in temperature in air. Also, the velocity of sound in a gas is inversely proportional to the square root of its density. But, it's independent on Pressure (Don't believe in appearance of the formula). This is because increase in pressure, also increases the density of gas. This could be achieved by using different gas densities (at same volume & pressure).
Also, See the Atmospheric variation of sound's velocity.
