The audio signal voltage is given by Vm=2sin12π×103t . The band width and LSB if carrier wave has a frequency 3.14×106rad/s

Given  : Vm=2sin12π×103t  Comparing with Vm=V0sinwmt   we get,  wm=12π×103 ⇒2πfm=12π×103 ⇒fm=6000Hz=6kHz  Also,  it is given that wc=2πfc=3.14×106 rad/s ⇒2πfc=π×106 ⇒fc=5×105Hz=500kHz  Now,  Band width  = (fc+fm)−(fc−fm)                                   =2fm=12kHz  and LSB = fc−fm = 500 - 6 = 494 kHz