Why is the bandwidth doubled with AM?
What you've observed is just the difference between baseband modulation (your original plot) and carrier modulation (the second plot). Note that for the AM case, since the signal that modulates the carrier is real, the resulting carrier-modulated signal is symmetric. This means that you can get away with only transmitting one of the sidebands. This approach is called single sideband (SSB) modulation. With an SSB system, the carrier-modulated signal only has the bandwidth of approximately one of the sidebands of the original baseband signal.