Sonic velocity:
Small pressure disturbances within a specific control volume [a discrete region within an open thermodynamic system i.e a local environment enclosing your wave] propagate at sonic velocity 'a' in air [generally sonic velocity in any medium is 'c'] this discussion does not apply to blast waves and strong shock waves
if one were to imagine themselves as a stationary observer, observing the control volume that contains the propagating wave front within a pipe one would see a steady state process and would one see that sound waves move as a longitudinal wave comprised of a series of rarefactions and compressions....
Now if one were to travel with the wave--- assuming that wave propagates left to right then the air [fluid] at the right of the control volume would appear to be moving toward the wavefront at sonic velocity 'a' and the air to the left will b moving away from at a speed a-dv ( were 'v' is the velocity at which the wave moves to the left away from the observer)---a rarefaction
Since fluid is composed of matter and matter has mass....and matter cannot be created or destroyed.... the mass at the left of the wave must equal the mass at the right so we achieve as mass balance of ml=mr
I can write this as rhoAa=(rho+drho)A(a-dv) A is the cross sectional area of the control volume within the pipe...since it appears on both sides, it cancels and one is left with...
a*d(rho)-rhodv=0 ....1
So, one assumes that no heat or work crosses the wavefront boundary so there no change in potential energy within the propagating wave... so we achieve energy balance...if you recall the quantity 'H' from thermodynamics which represents total energy (U+e) where U=internal energy e is other types of energy and work---without going into the math--- energy balance Uleft =Uright...this is represented by dH-adv...which solves to
H+a^2/2 =(h+dh)+(a-dv)^2 ...2
due to negligible changes in pressure or temperature...the wave propagation is adiabatic AND isoentropic (assumed)....if you recall that dG =h-TdS where 'S' in the entropy...then you'll see that for an isoentropic flow TdS=0....one ends up with
dH =dP/rh0....3...the d is a script delta indicating partial differential equations...which I can't write here
Combining relations 1,2 and3 one obtains
a^2 =(dP/dRho)s the little 's' indicates an isoentropic process ....using "Maxwell relations" I can actually write this as a^2=k(dP/drho)
T where k=ratio of specific heats, so and of course recalling that P=rhoRT and using that to solve the highlighted differential equation a^2 =k(dP/drho)
T =k[ drhoRT/drho]
T.=kRT..note because this involves partial differential equations, I did not show the intermediate steps.... solving it one finally obtains
a =(kRT)^.5
this explains not only why the speed of sound depends solely on temperature but it also explains why an isoentropic flow is assumed...it really doesn't get any easier than this...QED! 
here's typical thermodynamics class...the lady exclaiming at the end is the one who got the 'A'
http://www.youtube.com/watch?v=ndVhgq1yHdA