The basic principles are pretty straightforward.
The key idea is _superposition_ – basically, you can add two waves together, and they will create a new wave. An important observation is that you can also subtract a wave you know is there, and recover the other wave that was added.
From here it’s a pretty short step. The “radio frequency”, for example 101.1 MHz, is the frequency of what’s known as the _carrier wave_, the shared known base waveform between the sender and the receiver. The sender takes the sounds they want to transmit (which is a wave, of course), and then adds that wave to the carrier wave, which makes a new wave with tiny little changes to a certain aspect of the carrier wave. The receiver also knows the carrier wave, so they can subtract it out and recover the original wave.
The “tiny little changes” are done to one of the wave dimensions, either amplitude or frequency, hence the names AM (amplitude modulation) and FM (frequency modulation).
This of course hand-waves away an immense amount of engineering and technical detail required to actually “add” or “subtract” a sound wave and an electromagnetic wave, broadcast it at power, and output a coherent signal.
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