The audio signal voltage is given by Vm=2sin12π x 103t . The bandwidth and LSB if carrier waves has a frequency 3.14 x 106  rad/sec

Given : Vm=Amsinwmt here wm=2πfm=12πx103 ⇒fm=6x103 = 6 kHz and  wc=3.14 x106  rad/s  ⇒2πfc =3.14 x106  rad/s  ⇒fc=πx1062πHz=500 kHz  band width = 2fm=2 x 6 x 103 = 12 kHz LSB=fc−fm=500-6=494 kHz