Good question, and one which I did not address in the original article. For the answer, take a look at the image of the modulated vs. un-modulated signal.

Notice that the transmitter frequency is much higher than that of an audible frequency; in the above image, the audio tone imposed on the transmitter is spread out over eight cycles from the RF oscillator. This is important, because it allows variations in both the strength and the frequency of the audio tone to affect the modulated RF signal.

For example, if the audio tone were of a higher frequency, it might only cause an amplitude change in five of the oscillator’s cycles. In other words, the amplitude change in the transmitted signal will be shorter (amplitude changes will occur more frequency) or longer (amplitude changes will occur less frequently) depending on the frequency of the imposed audio tone. When these time variations in amplitude are converted back to an audio at the receiver, the audio wave will be respectively shorter or longer, thus re-producing the higher or lower frequency audio tone.

I’ve updated the article with this information, plus some corrections to other explanations. I will add some screen shots / videos of what the audio looks like on an oscilloscope later, which will hopefully make some of the explanations more clear.