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".
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asked Oct 16, 2012 at 13:31
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$\begingroup$ Did felix Baumgartner produce a sonic boom? en.wikipedia.org/wiki/Sonic_boom $\endgroup$– Chad HarrisonOct 16, 2012 at 13:40
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$\begingroup$ Just a related point. Yes speed of sound is less at higher altitude. That's a problem in jet transports, because their true stall speed increases with altitude, and where the stall speed and the speed of sound come together is called the "coffin corner". That limits the altitude of subsonic aircraft unless they have low wing-loading, like the U2. $\endgroup$– Mike DunlaveyOct 16, 2012 at 19:35
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9$\begingroup$ If an adrenaline junkie breaks the sound barrier at 25,000 meters and there is no one around to hear it, does it make a boom? $\endgroup$– dmckee --- ex-moderator kittenOct 16, 2012 at 22:30
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1 Answer
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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.
answered Oct 16, 2012 at 13:49
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$\begingroup$ Using the Ideal Gas Law, the speed of sound can also be expressed a $$v=\sqrt{\gamma R T}$$ where $R=8.314$ $J/molK$. Obviates the need to independently track $P$ & ${\rho}$. $\endgroup$ Oct 16, 2012 at 15:23
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1$\begingroup$ This is a terrific answer. Any way you can let us know, in laymen's terms, where in his descent he hit that sonic boom and how fast, exactly he was going? $\endgroup$ Oct 24, 2012 at 4:58
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$\begingroup$ FYI: According to Jian Huang "The standard value of the speed of sound in air at 31,000 m [the distance from which Joseph Kittenger jumped in 1960] is 300 m/s (670 mph)" $\endgroup$ Oct 24, 2012 at 5:08
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$\begingroup$ @SamTheBrand: Hello Sam, Felix actually jumped at an altitude of about 39 km. At about 30 km, the velocity of sound is 305 m/s. At his height, it is further reduced. Anyways, he actually reached a speed of some 370s (Man, That's too BIG). See my other answer if you require anymore info. If you require anymore explanation regarding the topic, I'd definitely revise my answer for focusing the point :-) $\endgroup$ Oct 24, 2012 at 5:18
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1$\begingroup$ @CrazyBuddy: Should that be 370 m/s instead of 370s? $\endgroup$– EveryoneOct 28, 2012 at 17:33