simple RF audio transmission and reception

i have just started to understand how radios and RF transmission work. i think i have got the basics. my question is, is it possible to to hook up an amplified audio source to an inductor, to make a simple transmitter then connect a second inductor to another op amp to listen to the music being transmitted. By this setup, i understand that the range and quality would be limited but is it in any way possible?

Not really. If the inductors are VERY close together, like wrapped around the same metal core, you will have a transformer, which will transfer the signal from the primary (input inductor) to the secondary (output inductor). This is what audio transformers do. The signal is transferred by magnetic coupling, not electro-magnetic waves (as in RF). Magnetic coupling works better at low frequencies (like audio).

The antenna (inductor in your description) needs to be tuned to the frequency you are sending. It is theoretically possible to create an antenna tuned to 1KHz or so (audio band) but it will be BIG and will require lots of power to transmit.

Audio is transmitted over radio waves by attaching it to a higher frequency. The simplest method is Amplitude Modulation (AM). Frequency Modulation (FM) has also been used for a long time. Higher frequencies can transmit using a smaller antenna.

yes i understand that i will need a tuner i.e. a LC circuit. how is the demodulation of am different from fm? any easy understandable circuits?

The simplest AM demodulators are nothing more them a diode peak-detector. I think this is a pretty informative explanation.

I don't think there is a simple informative circuit or explanation for FM. I know that I can't explain it very well. FM starts with a base frequency (e.g. 105.9 FM). If there is no sound the frequency will be constant. The audio signal causes the frequency to shift higher or lower (instead of making the amplitude higher or lower). This makes for better signal reception (it doesn't get louder when you are closer to the transmitter) but also makes the receiver more complicate. All FM receivers have some kind of frequency tracking circuit that is a little 'slow' to respond. If the current signal is at a different frequency than the tracked frequency the difference is detected and converted to a voltage. I'll be honest with you, I understand them in concept, but not in enough detail to make one myself or explain it.