Bev Pantry, of Carmel College, asks :-
Why does the speed of sound in air increase with temperature?
John Campbell, a physicist at the University of Canterbury, responded.
Sound is transmitted as a pressure wave which moves through the material by the atoms jostling their neighbours. Solids and liquids are almost incompressable, which means that the atoms/molecules are touching one another and cannot get much closer. Hence a sound wave travels much faster through solids and liquids than through a gas. For example, 5100 metres per second in aluminium, 1500 m/s in water but only 330 m/s in air.
A gas is easily compressible, as we know from our use of hand-operated cycle pumps. If you take a liquid and turn it into gas the volume increases by about 700 times. That is close enough to 1000 (10 times 10 times 10). So each gas molecule is about 10 atomic diameters apart from its neighbours. Before a gas molecule can pass the wave to a neighbouring atom it spends time in transit. Therefore sound travels slower in gases than in liquids or solids.
For most of the time a gas molecule is travelling between collisions, surprisingly at a speed faster than sound travels in the gas. Although the molecule is travelling very fast, its direction after a collision with another gas molecule can be in any direction, forwards, sideways or even backwards. So the speed with which it progressess in general in the direction of the sound wave, ie the speed of sound in the gas, is less than the average instantaneous speed of the molecule which can be travelling in any direction.
The average speed of a gas molecule depends on its temperature. The higher the temperature the higher the kinetic energy of the molecule and hence the faster it travels and the sooner the molecule reaches its neighbour. Therefore, the higher the temperature of the gas the faster the speed of sound is through it.
For air the speed of sound increases by 0.6 metre per second for each degree Celsius rise in temperature of the air.
I remember hearing about the early days of research into the nature of the high altitude atmosphere. In the 1940s and 50s these altitudes could be cheaply reached using small rockets. An early technique for measuring the temperature of the high altitude air was to eject a hand grenade from the rocket. The delayed explosion was used as a sound source to measure the speed of sound reaching the rocket, and hence the temperature of the air the sound passed through.