Effect of Temperature on Vsound in air
The frequency of a wave is determined by the frequency of the source, therefore the frequency is generally known or at least unchanged by the medium through which it is travelling.

The velocity of a sound wave travelling through air does not vary with the air pressure, but it does depend on the temperature of the air. The pressure of the air is caused by the velocity of the air molecules. The square of this velocity is proportional to the temperature in kelvins (i.e. in degrees measured with respect to absolute zero (0 deg.K = -273 deg.C) :

The velocity of a sound wave is thus proportional to the velocity of the molecules of the air through which the wave travels. Thus the velocity of a sound wave at a temperature T is

If v=344 m/s at 20 deg.C, then at temperature Tdeg. kelvin

where TA is the Absolute Temperature and the constant 20.1 is determined from the basic properties of air. Tk= TC + 273deg., where TC is the temperature in Centigrade. Thus for Fahrenheit temperatures (TF), Tk = 273 + 5/9(TF - 32).

In a cold medium molecules move more slowly and this reduces the velocity at which sound is transmitted.

Table 1.3 Effect of variations in temp on velocity of sound in air.

Table 1.4 Effect of different mediums on Vsound at 20deg. C.