A) 178.5 and 171.5
B) 89.25 and 85.75
C) 1785 and 1715
D) 892.5 and 857.5
Correct Answer: B
Solution :
The equation for a amplitude modulated wave is \[y=(a\,\cos {{\omega }_{m}}t+A)sin{{\omega }_{c}}t\] Comparing it with given equation, \[{{\omega }_{c}}=5.5\times {{10}^{5}}Hz\] \[\Rightarrow \]\[{{f}_{c}}=\frac{{{\omega }_{c}}}{2\pi }=\frac{7\times 5.5\times {{10}^{5}}}{22\times 2}=87.5kHz\] \[{{\omega }_{m}}=2.2\times {{10}^{4}}Hz\] \[\Rightarrow \]\[{{f}_{m}}=\frac{{{\omega }_{m}}}{2\pi }=\frac{7\times 2.2\times {{10}^{4}}}{2\times 22}=3.50\,kHz\] So, the side band frequency, \[{{f}_{1}}={{f}_{c}}-{{f}_{m}}=87.5-3.500=84kHz\] \[{{f}_{2}}={{f}_{c}}+{{f}_{m}}=91.00kHz\]
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