Rob525,
Good questions. Here is a link to a pretty comprehensive study done in recent times which attempts to correlate all the radio signals believed to be to or from Amelia Earhart following her 1937 disappearance:
The Post Loss Radio Signal Catalog, page 2
Radio wave theory has a lot of factors to consider which could account for the many reports of hearing Amelia after her plane would have no longer been in the air.
An aircraft cannot remain airborne for an indefinite time. When usable fuel runs out, the engines will quit and the plane will begin to descend on a glide and go to earth. Amelia certainly knew this, and was desperately seeking a place to land - if not on Howland Island, then any other island.
Amelia's plane was equipped with a then state-of-the-art radio which could transmit and receive in the High Frequency (HF) range. She had certain assigned frequencies to use. She also had a circular Direction Finder antenna which she could use to attempt to home in on a radio transmission from the Cutter Itasca (stationed off Howland Island).
During daylight hours, the sun creates a condition in which only direct line transmissions can be heard. There is a range (distance) that the radio can be detected based on the frequency, the power of the transmitter, the altitude and orientation of the antenna (aircraft), sensitivity of the receiving station, and other atmospheric conditions.
Day time transmissions from Amelia's plane would NOT have been powerful enough to have reached the Continental US, and would have been weak/attenuated by the time they reached the most distant stations which could pick her up. Because of all this, some stations could hear other stations calling Amelia, but not hear her reply. Others might have been close enough to hear Amelia, but not the station she heard.
Voice transmissions usually require a strong connection/signal to be heard, while Morse Code transmissions can be heard over longer ranges because it is simply dots and dashes, or (sometimes) interruptions in the carrier signal. A station far away might hear Amelia key her microphone, but not make out what she was saying.
At Night time, HF signals will bounce off the Ionosphere, bend back to earth, and then rise up to the Ionosphere further away, and repeat. This is referred to as "Skip" or sky wave signals. Think of a series of rings around a transmitter. If you are on one of those rings with a receiver, you could be able to pick up the signal. It is almost instantaneous. Atmospheric conditions, static, transmitter orientation, etc can cause the signal to fade in or out at the receiver site.
Another radio phenomenon is frequency "harmonics". These are higher frequencies which are related to the chosen transmission frequency. They occur in a predictable pattern, much like playing a chord on a musical instrument. When all is in tune, and conditions are right, you can hear other notes which are not actually being played on the instrument, but which are part of the harmonic make-up of the chord. The same is true of radio signals or other sound transmissions (like underwater sounds). What this means is that someone listening on a radio set tuned to a higher frequency than the one Amelia is transmitting on might be able to hear her if they happen to be on one of her station's harmonic frequencies.
The above link addresses a number of these issues. It attempts to match signal logs from various stations to those of other stations in an attempt to validate the communications. For example one remote receiver hears another station asking for Amelia to respond by keying her microphone, but hears no response. Another station reports hearing a series of microphone keyings at the same time, but did not hear the station requesting them. When all is assembled and studied in a single timeline, a clearer picture develops.
There were Hoaxes, certainly, with a number of people claiming to have heard Amelia on radios. But the hoaxes were easily eliminated because they were claimed to be at times outside of when a Skip signal might have been heard, or on frequencies that were not related to Amelia's.
But some of those reported signals DID have merit and were heard on night time signals which related to harmonic frequencies closely associated with Amelia's.
Reports of hearing Amelia (after her plane would have landed) were almost immediate. Early reports of her being missing included reports of various stations picking up her signals. This was the strongest clue that she may have made a successful landing, because her radios would not have worked in the water - only on land and with one engine operating.
There were probably attempts to fake Amelia's voice in transmissions, but that would have to have been done on some specialized transmission equipment to also fake her frequency.
I have heard stories about radio or TV signals being picked up which were transmitted days or even years before, but cannot verify them. The signals associated with Amelia are pretty well documented and occurred within days of her disappearance.
