Other comments gave a nice explanation of why AM does need a bandwidth, but here's the information theory explanation: https://en.m.wikipedia.org/wiki/Shannon%E

Other comments gave a nice explanation of why AM does need a bandwidth, but here's the information theory explanation: https://en.m.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem https://en.m.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theo... TL;DR: the information one can reliably send through a noisy channel (C) is proportional to the bandwidth of that channel.