$($a$)$ A message signal $x(t)$ is to be sent into free space using AM or FM$.$ Which of the following waveforms corresponds to the amplitude modulated signal $s_{AM}(t)$ and which corresponds to the frequency modulated signal $S_{FM}(t)?$ Explain your reasoning.

$[6$ marks$]$

Figure Q$3$

$($b$)$ Determine the bandwidth of the FM signal $s_{FM}(t)$ if the bandwidth of $x(t)$ is $400ra\frac{d}{s}$ and the frequency modulation index is $m_f=6.$

$[3$ marks$]$