The intensity is proportional to the square of the amplitude as above defined.
It is also proportional to the square of the maximum velocity of the vibrating air-particles.
When sound issues from a small body in free air, the intensity diminishes as the square of the distance from the body increases.
If the wave of sound be confined in a tube with a smooth interior surface, it may be conveyed to great distances without sensible loss of intensity.
The velocity of sound in air depends on the elasticity of the air in relation to its density. The greater the elasticity the swifter is the propagation; the greater the density the slower is the propagation.
The velocity is directly proportional to the square root of the elasticity; it is inversely proportional to the square root of the density.
Hence, if elasticity and density vary in the same proportion, the one will neutralize the other as regards the velocity of sound.
That they do vary in the same proportion is proved by the law of Boyle and Mariotte; hence the velocity of sound in air is independent of the density of the air.
But that this law shall hold good, it is necessary that the dense air and the rare air should have the same temperature.
The intensity of a sound depends upon the density of the air in which it is generated, but not on that of the air in which it is heard.