Acoustic Environment:Temperature-Dependent Velocity

Temperature-Dependent Velocity

The velocity of sound is temperature dependent. The approximate formula for calculating velocity is

The Effect of Altitude on the Velocity of Sound in Air

The theoretical expression for the speed of sound, c, in an ideal gas (air, for example) is

It can be seen that the velocity is dependent only on the type of gas and the temperature and is independent of changes in pressure. This is true because both P and ρ decrease with increasing altitude and the net effect is that atmospheric pressure has only a very slight effect on sound velocity. Therefore the speed of sound at the top of a mountain would be the same as at the bottom of the mountain if the temperature is the same at both locations.