Why does an AM radio channel require any bandwidth at all? Why can’t it just transmit on a single, precise frequency?
In: 95
Take a look at this: it’s the sum of two sine waves very closely spaced in frequency:
https://www.wolframalpha.com/input?i=sound+sin%282+pi+200+t%29+%2B+sin%282+pi+204+t%29
(You can look at the graph or click “play sound” to hear it.)
As time goes on, the two waves move in and out of phase, creating a [“beat frequency”](https://www.physicsclassroom.com/class/sound/Lesson-3/Interference-and-Beats): the sine wave’s amplitude changes over time.
So, two closely-spaced frequencies are mathematically identical to an amplitude-modulated sine wave. And this goes both ways: all amplitude-modulated waves must be constructed from two or more pure frequencies.
So modulating the amplitude of a sine wave inevitably “spreads out” its frequency distribution into nearby frequencies. You can prove mathematically that the rate of information transfer in your amplitude-modulated wave is proportional to the width of the frequency band it occupies.
https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem
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