Amplitude modulation (AM) indeed involves placing a lower frequency wave (known as the modulating signal) onto a higher frequency carrier wave by varying the amplitude of the carrier wave in accordance with the modulating signal. While it may seem that this process would result in a single frequency signal, AM actually occupies a bandwidth rather than a single frequency.
The reason for this is related to the properties of the modulating signal and the process of modulation itself. The modulating signal typically consists of a range of frequencies, such as an audio signal that contains a range of frequencies corresponding to the audible spectrum. When this signal is used to modulate the carrier wave, it imparts its frequency content onto the carrier wave.
The modulation process generates new frequencies that are the sum and difference of the original frequencies. Specifically, in AM, two sidebands are created on either side of the carrier frequency, and the bandwidth of the AM signal encompasses both the carrier frequency and the two sidebands.
The bandwidth of an AM signal is directly related to the maximum frequency contained within the modulating signal. According to the Carson's rule, the bandwidth of an AM signal is approximately twice the maximum frequency of the modulating signal. This means that a wider frequency range is required to accurately represent the modulating signal and recover it at the receiving end.
Therefore, even though AM is based on the modulation of a single carrier frequency, it requires a bandwidth that encompasses both the carrier frequency and the frequencies present in the modulating signal.