The amateur frequencies available are segments of spectrum far more than just 3-to-30MHz. Modes range from voice (analog and multiple digital modes) to data to video to FAX/imaging, etc. An interesting and rewarding hobby.
For someone of my generation to be asked 'What is short wave' is just staggering. Where do you start? Even television started out on amateur frequencies in the 30's (no Leave It To Beaver! Just slow-scan. :^) }
Today younger folk ask about what I watched on TV when I was a child; we didn't have TV! Oh, a few folks had TV. I could walk up the railroad tracks to the highway where a lady lived; she had one of those TVs that the picture tube was mounted vertical {the neck of the tube was too long to mount horizontally without taking up half of the room}. One watched the picture through a mirror that set the picture right. I watched a little on that one day and wondered who would ever get involved with such a thing. I was about 7 years old.
But younger people who do not know what 'short wave' is may need to learn a bit about it - if all other communications are cut off. I just cannot teach a course here on the FR thread. :^)
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As for amateur freqs beyond 10 meters, first is the 11 meter CB band {27 MHz}, which became Babel; then there is the 2 meter amateur band {144 MHz to 148 MHz} which is mostly FM, not AM, but seems to be a little higher class of CB. Some of the equipment is worth over a thousand dollars - and up!
When I got my amateur license the idea was to build as much of your own equipment as possible; that is how slow-scan TV got started. Today one buys a few thousand dollars of digital equipment and puts up an antenna - perhaps with a loading coil to keep it short - and plugs it in and BOOM - you are an amateur operator.
All of my first amateur rigs, I either built or modified to do what I wanted. Today I do not even understand half of the technology being applied. sigh