Estimating the current speed of sound This question is not about the theory but about getting a moderately accurate (ideally 1%) estimate of the speed of sound in the current conditions.  The range of conditions that I am interested in are those in which humans can live without special support.  
I found this in Wikipedia:
$$c_{air} = 331.3 \sqrt{1 + \frac{\theta}{273.15}}$$
where $\theta$ is the temperature in Celsius.  
I am slightly surprised that the pressure does not feature.  Is this because the pressure is determined by the temperature alone?  My knowledge of meteorology is poor but I would have expected that it is possible to have the same temperature at different pressures and that this would affect the speed of sound.  
How about humidity?  
I want this for a light hearted experiment.  Some of my musical friends are able to judge small fractions of a semitone in musical intervals.  I want to see how accurately we can judge the speed of a vehicle by the Doppler shift in a sound that it is producing.  
For example, if the speed of sound is currently $343.2ms^{-1}$ (sea level at $20C$) and the apparent note drops by a (well tempered) minor third then the vehicle was travelling at $106.8kmh^{-1}$.  
I have not yet allowed for wind speed, that will be a later refinement.  
 A: If you take your equation:
$$ c_{air} = 331.3 \sqrt{1 + \frac{\theta}{273.15}} $$
We can rearrange it to get:
$$ c_{air} = 331.3 \sqrt{\frac{273.15 + \theta}{273.15}} = 20.05\sqrt{T}$$
Where now $T$ is the temperature in Kelvin. The formula for the speed of sound in an ideal gas is:
$$ v = \sqrt{\gamma\frac{P}{\rho}} \tag{1} $$
where $P$ is the pressure, $\rho$ is the density, and $\gamma$ is the adiabatic index. For an ideal gas we know:
$$ P = \frac{nRT}{V} \tag{2} $$
where $n$ is the number of moles of the gas, and the density is:
$$ \rho = \frac{nM}{V} $$
where $M$ is the molar mass in kilograms. The point of all this is that we can substitute for $n/V$ in equation (2) to get:
$$ \frac{P}{\rho} = \frac{RT}{M} $$
and substitute in equation (1) to get:
$$ v = \sqrt{\frac{\gamma RT}{M}} $$
For air $\gamma = 1.4$ and $M=0.0288$ kg/mol, and substituting these values into our equation for $v$ gives:
$$ v = 20.10 \sqrt{T} $$
which is the same as your equation give or take some rounding errors. That's how your equation was arrived at. As you suspected the pressure is involved, but the pressure and density cancel each other out in such a way that the speed depends only on temperature.
Humidity will have an effect because it changes the density of the air and it changes the average molecular weight. You can calculate this, but I would simply Google for empirical equations giving the speed as a function of both temperature and humidity.
