Why Sound dies away with Distance

Sound:
Since the last ball B is driven outward with a force nearly equal to that possessed by A, it would seem that the effect on the ear drum should be independent of distance and that a sound should be heard as distinctly when remote as when near. But we know from experience that this is not true, because the more distant the source of sound, the fainter the impression; and finally, if the distance between the source of sound and the hearer becomes too great, the sound disappears entirely and nothing is heard. The explanation of this well-known fact is found in a further study of the elastic balls. If A hits two balls instead of one, the energy possessed by A is given in part to one ball, and in part to the other, so that neither obtains the full amount. These balls, having each received less than the original energy, have less to transmit; each of these balls in turn meets with others, and hence the motion becomes more and more distributed, and distant balls receive less and less impetus. The energy finally given becomes too slight to affect neighboring balls, and the system comes to rest. This is what occurs in the atmosphere; a moving air particle meets not one but many adjacent air particles, and each of these receives a portion of the original energy and transmits a portion. When the original disturbance becomes scattered over a large number of air particles, the energy given to any one air particle becomes correspondingly small, and finally the energy becomes so small that further particles are not affected; beyond this limit the sound cannot be heard.

If an air particle transmitted motion only to those air particles directly in line with it, we should not be able to detect sound unless the ear were in direct line with the source. The fact that an air particle divides its motion among all particles which it touches, that is, among those on the sides as well as those in front, makes it possible to hear sound in all directions. A good speaker is heard not only by those directly in front of him, but by those on the side, and even behind him.

FIG. - When a ball meets more than one ball, it divides its motion.