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I don't know what I misunderstood or what but I thought in FM and AM you can transfer your frequency characteristics of modulating signal anywhere you want but I find out that there is a range for each one :

AM : 550 to 1720 kHz

FM : 88 to 108 MHz

And also it's said that audio spectrum ranges from 20 to 20,000 Hz but FM and AM limit the upper modulating frequency to respectively 15 and 5 kHz .

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You are confusing radio services with types of radio modulation.

By law, in the United States (and I think all of North America), the AM and FM commercial broadcast bands are as you describe. The US example is contained in CFR Title 47 Part 73. These rules lay out what folks are allowed to do vis-a-vis radio broadcasting in the US.

You're leaving out all of the licensed and unlicensed RF bands, however. There's a whole range of amateur, commercial, and unlicensed RF frequencies that are available in the US and nearly any other country that regulates the airwaves. Pretty much every frequency has a service allocated to it, and that service has its own rules regarding whether the stations are channelized or not, what modulations (AM, FM, SSB, digital, etc.) are allowed, what power level the transmitters can operate at, etc.

So -- physically, you can do what you want. Legally, you need to operate inside the law (or at least don't bug your neighbors to the point that they complain) lest humorless agents of the Federal Government stop by your house and tell you to knock it off, on pain of fines, (very rarely) imprisonment, and the possibility of never being able to get a legal operator's license.

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With AM and FM modulation in general, which means modulating a carrier amplitude or frequency respectively; that you can do at any carrier frequency arbitrarily. However if we want to do it legally the FCC and other regulatory bodies limit what can be transmitted in each range of frequencies in terms of power level, bandwidth, out of band emissions, and licensing. This is the constraint the OP is referring to (regulatory constraint not a technical constraint).

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