Geoff, note the reference to a point source in the quote Ralph (Atmasphere) provided just above. The reason the amplitude of electromagnetic waves goes down in free space as distance increases is that they "spread out" to some degree. If they are emitted by a point source, and therefore are radiated essentially equally in all directions, the energy received at any given point will decrease in proportion to the square of the distance, since (as stated in the reference Ralph provided) "the surface area of a sphere increases with the square of the radius."
That is the same reason, btw, that the SPL produced by a relatively small box-type speaker (which from the perspective of a listener seated some distance in front of the speaker can be considered as roughly approximating a point source) drops off at 6 db per doubling of distance (putting aside the effects of room reflections). Planar speakers and line sources of course behave differently, and SPL falls off more slowly in those cases, as distance increases.
What makes communications with satellites and inter-planetary probes possible is that the antennas are designed to focus the RF energy much more sharply than a point source, so that the energy "spreads out" as little as possible as distance increases.
Consider the example of a flashlight being shined against a wall, in comparison to a laser pointer being shined against the wall. As distance increases, the diameter of the spot that is illuminated by the flashlight will INCREASE much more than in the case of the laser pointer. While the brightness of any given point within the spot that is illuminated by the flashlight will DECREASE much more, as distance increases, than in the case of the laser pointer.
Regards,
-- Al
