To first order, and then some, the speed of sound in the lower atmosphere of Earth depends on temperature and nothing else. In the old days they often made speed-record attempts in early jets flat on the deck on a hot day in summer, simply because under those conditions the speed of sound was high, and therefore the critical mach number for corresponded to a high actual speed.
T is temperature above absolute zero.
Multiplying all out and taking the square root, we have units of speed, which is encouraging, but not positive proof that I have gotten it right. A Mach indicator uses ram air pressure corrected for static pressure - there is no temp. Now, on the other hand, true air speed is ram air pressure corrected for altitude AND temp. Others I work with agree with this philosophy. Please show us the error of our ways as necessary.