As a physical phenomenon, sound is a waveform propagated by the collisions of particles in the medium through which it travels. It is little wonder then that the speed of sound should depend mainly on the properties of the medium itself. Some of these properties are:
1. Elastic Modulus (and thus Pressure/Temperature)
The elastic modulus is a measure of the amount of deformation that a material undergoes temporarily when a force is applied to it. For solids, the elastic modulus used is the Shear Modulus, while for fluids i.e. liquids and gases, it is the Bulk Modulus.
Higher the elastic modulus, greater will be the speed of sound in that medium. For the mathematically inclined the relationship is “speed of sound” is directly proportional to the square root of the “elastic modulus”.
Also importantly, since the elastic modulus ties in with pressure and thus temperature, the “speed of sound” is also directly proportional to the square root of the “temperature”. For instance, the speed of sound in air in an icy 0 degrees Celsius is approximately 330 m/s; while in temperate zones at 20 degrees Celsius it is 340 m/s and in hot deserts at 45 degrees Celsius, it can be as much as 360 m/s. Speeds of sound also vary with altitudes for similar reasons.
Since density implies how closely packed the molecules of a medium are, it would suggest that more energy would be required to cause the molecules to vibrate a dense packing than would be required to cause a sparse packing to vibrate.
Thus, the speed of sound decreases with an increase in density of the medium and vice-versa. Or stated in mathematical parlance, the “speed of sound” is inversely proportional to square root of the “density” of the medium. For instance, although gold and aluminum have about the same elastic modulus, sound travels at half the speed in gold than it does in aluminum, since the density of gold is much higher than that of aluminum.
Although the above two properties are key, certain other factors can also have an impact. Amongst these are the frequency of the sound itself in dispersive mediums (such as water) and the composition of gaseous mediums where the transmission process is not necessarily adiabatic (i.e. no heat transfer in and out of the system). These factors are significant only when such mediums are specifically being considered for acoustic transmission.
Concluding, in everyday life we say that the speed of sound is affected by common environmental factors such as temperature, pressure, humidity and altitude. However on looking deeper at the science involved, these are in fact related to the “elastic modulus” and “density” of the medium- the two fundamental parameters that determine the speed of sound.