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  • A sinusoidal wave <img alt="\mathrm{y(t)=40 \sin \left(10 \times 10^{6} \mathrm{\pi t}\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%28t%29%3D40%20%5Csin%20%5Cleft%281

A sinusoidal wave \mathrm{y(t)=40 \sin \left(10 \times 10^{6} \mathrm{\pi t}\right)} is amplitude modulated by anothet sinusoidal wave \mathrm{x(t)=20 \sin (1000 \pi t)}. The amplitude of minimum frequency component of modulated signal is :

Option: 1

0.5


Option: 2

0.25


Option: 3

20


Option: 4

10


Answers (1)

best_answer

\mathrm{y(t)=40 \sin \left(10 \times 10^{7} \mathrm{\pi t}\right)}
\mathrm{x(t)=20 \sin (1000\, \pi t)}
\mathrm{\omega_{c}=10^{7}\pi}
\mathrm{\omega_{m}=10^{3} \pi}
\mathrm{A_{c}= 40}
\mathrm{A_{m}= 20}

Equation of modulated \mathrm{=\left ( A_{c}+A_{m}\sin \omega _{m}t \right ) \left ( \sin \omega_{c} t \right )}
                                       \mathrm{=A_{c}\left(1+\frac{A_{m}}{A_{c}} \sin \omega_{m} t\right) \sin \omega_{c} t}
                                       \mathrm{=A_{c} \left ( 1+\mu \sin \omega_{m}t \right )\sin \omega_{c}t}
                                       \mathrm{=A_{c} \sin \omega_{c}t+\frac{u A_{c}}{2}\left[\cos \left(\omega_{c}-\omega_{m}\right) t-\cos \left (\omega_{c}+\omega_{m} \right )t\right]}  
 

Amplitude of minimum frequency
\mathrm{=\frac{\mu A_{c}}{2}=\left(\frac{1}{2}\right) \times \frac{40}{2}=10}
The correct option is (4)
 


                                         

Posted by

Devendra Khairwa

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