A) \[{{f}_{c}}=200Hz;{{f}_{\omega }}=50Hz\]
B) \[{{f}_{c}}=150Hz;{{f}_{\omega }}=50Hz\]
C) \[{{f}_{c}}=150Hz;{{f}_{\omega }}=30Hz\]
D) \[{{f}_{c}}=200Hz;{{f}_{\omega }}=30Hz\]
Correct Answer: B
Solution :
[b]: Here, \[{{C}_{m}}(t)=25sin(300\pi t)+15(cos(200\pi t))-cos(400\pi t))\]Compare this equation with standard equation of amplitude modulated wave, \[{{C}_{m}}(t)={{A}_{c}}sin{{\omega }_{c}}t-\frac{\mu {{A}_{c}}}{2}\cos ({{\omega }_{c}}+{{\omega }_{m}})t\] \[+\frac{\mu {{A}_{c}}}{2}\cos ({{\omega }_{c}}-{{\omega }_{m}})t\] \[{{A}_{c}}=25V,{{\omega }_{c}}=300\pi \Rightarrow 2\pi {{f}_{c}}=300\pi \Rightarrow {{f}_{c}}=150Hz\]\[{{\omega }_{c}}-{{\omega }_{m}}=200\pi \Rightarrow {{f}_{c}}-{{f}_{\omega }}=100Hz\] \[\therefore \]\[{{f}_{\omega }}=150-100=50Hz\]
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