Why can we not hear people talking when they are far away from us?
In reality, a sound wave originating at some source does not move in a straight line (a plane wave) but expands in a series of spherical wave fronts.
Huygens' wavelets. Originating along the fronts of (A) circular waves and (B) plane waves, wavelets recombine to produce the propagating wave front.
The average amount of energy passing through a unit area per unit of time in a specified direction is called the intensity of the wave. One of the most important properties of a sound wave is a decrease in energy, or intensity, as the wave propagates - i.e., sound waves lose energy as they travel. This happens for a number of reasons.
As a circular wave front expands, its intensity is distributed over an increasingly larger circumference. The intensity along the circumference of the circle, will therefore decrease in an inverse relationship with the growing radius of the circle, or distance from the source of the wave.
From a three dimensional perspective, the same thing happens. As a spherical wave front expands, its intensity is distributed over a larger and larger surface area. The intensity along the surface of the sphere decreases with the growing radius of the circle, or distance from the source of the wave.
Scientifically, this is called the Inverse Square Law.
Since the surface area of a sphere
= 4πr2,
the intensity of the wave is inversely proportional to the square of the radius
or inversely proportional to the square of the distance from the source.
In addition to the decrease in energy caused by the inverse square law, part of the energy of a sound wave is lost to the medium itself - i.e., it is absorbed by the medium. As sound waves move through a medium, the particles in the medium vibrate and transfer energy. A small part of this energy is lost to the medium as heat.