Question

A carrier signal $C\left(t\right)=25\sin (2.512\times {10}^{10}t)$ is amplitude modulated by a message signal $m\left(t\right)=5\sin (1.57\times {10}^{8}t)$ and transmitted through an antenna. What will be the bandwidth of the modulated signal?

• A. $1987.5MHz$
• B. $2.01GHz$
• C. $50MHz$
• D. $8GHz$

Answer 1

The correct option is C

$50MHz$

Step 1: Given data

Carrier signal, $C\left(t\right)=25\sin (2.512\times {10}^{10}t)$

Message signal, $m\left(t\right)=5\sin (1.57\times {10}^{8}t)$

Step 2: Find frequency of message signal, $f_{m\left(t\right)}$

Standard message signal is given by

$m\left(t\right)=Asin\left({\omega }_{m}t\right)$

On comparing it with given message signal, we have,

$$\begin{gathered} {\omega }_m=1.57\times {10}^8 \\ {f}_{m\left(t\right)}=\omega /2\mathrm{\pi } \\ \Rightarrow {\mathrm{f}}_{\mathrm{m}\left(\mathrm{t}\right)}=1.57\times {10}^8/2\mathrm{\pi } \end{gathered}$$

Step 3: Find the bandwidth of the modulated signal

For amplitude modulated signal, Bandwidth of modulated signal is given by

$$\begin{gathered} \beta =2f_{m\left(t\right)} \\ \beta =2\times \left\{(1.57\times {10}^8)/2\pi \right\} \\ \beta =50MHz \end{gathered}$$

Hence, option C is correct.