Variation of speed of sound

There is one small complication that must be introduced into the definition of Mach Number even at this stage. The speed of sound varies according to the temperature of the air, and therefore we must add to the definition the fact that the speed of sound must be that corresponding to the temperature of the air in which the aircraft is actually travelling. People are often surprised to hear that the speed of sound in air depends on temperature alone.

The actual relationship is that the speed of sound is proportional to the square root of the absolute temperature.

We have seen that temperature falls with height in the atmosphere, and in the stratosphere where the temperature is about — 60°C (213 K) the speed of sound will have fallen from about 340 m/s at sea-level to about 295 m/s.

Perhaps it should be emphasised again that this drop in the speed of sound is not really a function of the height at all; at a temperature of —60°C such as may occur at sea-level in, say, the North of Canada in winter, the speed of sound would also be about 290 m/s, while in tropical climates it might be well over 340 m/s even at considerable heights.

This variation of the speed of sound with temperature accounted for the rather surprising feature of speed record attempts of some years back in that the pilots waited for hot weather, or went to places where they expected hot weather, in order to make the attempts. Surprising because it had always been considered, and was in fact true, that high temperatures act against the performance of both aircraft and engine. The point, of course, is that the record breakers wanted to go as fast as possible while keeping as far away as possible from the speed of sound – so they wanted the speed of sound to be as high as possible. Nowadays in breaking speed records the aim of the pilot is just the opposite, i. e. to get through the speed of sound as quickly as possible – but we are anticipating.