John, if I'm not completely wrong take the following example:
You have an enclosed airmass with a certain temperature and you measure the
Speed of Sound. You increase now the temperature, so the pressure will also
rise and thus the density will remain the same. But still the Speed of Sound
is decreasing. The reference given in your message states this:
Quote "Temperature stabilizes at -69.7E F at 36,000 ft so the speed of sound
stabilizes there at 573 knots." unquote.
Although density still decreases with increasing altitude (above 36'000ft in
standard atmosphere) temperature will rise again and thus also Speed of
Sound will increase again. I remember a figure from Concorde at Mach 2.0
where the TAS at FL 45'000 was calculated to be 1163 KTS which would also
reflect this.
But I must also admit that my deeper knowledge in physics is gone in the
past years. So I'm not able to go too deep into this. Sorry!
Regards
Oskar