There are a lot of confusing statements out there, so let's start with the basics.
The speed of sound is defined by:
speed of sound = SQRT[(Specific heat of the gas)*(gas Constant R)*(Temperature)]
That tells us that the speed of sound is NOT a constant. The only variable that impacts the speed of sound is the specific heat , which is a property of the constituents of the gas itself and the temperature of the gas. So, that means that if we change the constituents of the atmosphere or if we cool or heat the atmosphere, we can change the speed of sound.
Anyone that watched Felix Baumgartner's jump should have noticed the temperature telemetry that was shown on screen. It was quite a bit cooler up there than it was at the surface. That means the speed of sound was lower at the altitude the Felix jumped than it was on the ground.
So, while the speed of sound on the ground was about 761 mph, the speed of sound up at 100,000 ft was about 690 mph.
Now let's talk about the physics of the jump. In a vacuum, we could use the following two equations:
v = vi + at (velocity equals initial velocity plus the acceleration multiplied by the time elapsed)
x = vi*t + 1/2(a*t^2) (distance traveled equals initial velocity times time elapsed plus half the acceleration times time elapsed squared)
We can assume initial velocity was about zero. That simplifies to:
v = at and x = 1/2(a*t^2)
Throw that into Excel, and we quickly see that at 32 seconds after jumping he would have fallen 16,461 feet and reached a speed of 701 mph. That would mean he would have exceeded the speed of sound at that altitude.
Now, where this can be confusing is that normally when we talk about things like sky-divers falling through the atmosphere, we talk of terminal velocity. A sky-diver with arms and legs stretched out has a terminal velocity of about 125 mph. With his arms and legs tucked in, that terminal velocity can get up to 200 mph. Terminal velocity means that as you fall, you will have two forces acting on you - gravity pushing you down and air resistance pushing you up. Eventually, you reach a point where the acceleration of gravity is canceled out by the acceleration of the air resistance - so you keep falling, but can't get any faster.
Air resistance is defined as: D = Cd*(rho*(V^2*A/2) where the coefficient of drag (Cd) is going to increase with air density (the lower we get the denser the air gets).
The key to Felix's jump was that in order to hit the sound barrier (which Joe Kittinger had not done in his record holding jump from 102,800 feet) was to jump from a higher point where the air would be even thinner, and the resistance less.
Red Bull reports that Baumgartner had a peak speed of 833 mph. So, yes, he definitely exceeded the speed of sound.More questions on Red Bull Stratos Mission (October 2012):