In Amplitude Modulation (AM), the instantaneous amplitude of the carrier wave is varied in accordance with the instantaneous amplitude of the modulating (message) signal. If the carrier is $C(t)=A_c\sin ({\omega }_{c}t)$ and message is $m(t)$, the AM wave is: $x_{AM}(t)=[A_c+m(t)]\sin ({\omega }_{c}t)$. The 'envelope' of the resulting wave follows the shape of the modulating signal.