Why does an AM radio channel require any bandwidth at all? Why can’t it just transmit on a single, precise frequency?
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Let’s say you want to transmit speech via AM. You take that audio signal and modulate it onto the “single, precise frequency” which is your carrier frequency. By doing that, which is adding the actual information you want to transmit to the carrier, you modify the waveform. The resulting waveform will look different from the unmodulated carrier if you “draw” it on paper, and that’s true for both a time diagram as for a frequency diagram. The resulting signal contains a range of frequencies depending on the frequency range of the audio signal transmitted. While it’s not the full mathematical picture, imagine modulating a 1000 Hz sine wave onto the carrier with AM: you’ll see the faster carrier changing amplitude in a sinusoidal fashion with the frequency of 1000 Hz. If you go look at the signal in the frequency domain, you don’t have only the carrier’s frequency, the 1000 Hz also need to show up in some form.
A single, precise frequency does not carry any information, or the other way around, transmitting information requires bandwidth.
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