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 bandwidth of the modulated signal?

• A. $1987.5\text{MHz}$
• B. $2.01\text{GHz}$
• C. $50\text{MHz}$
• D. $8\text{GHz}$

Answer 1

The correct option is C $50\text{MHz}$

Bandwidth of modulated signal is given by,
$$\beta =2f_{m\left(t\right)}$$ Where $f_m$ is frequency of message signal.
Given, ${\omega }_m=1.57\times {10}^8\text{rad/s}$
$\beta =2\times \frac{1.57\times {10}^8}{2\pi }$
$\beta =50\text{MHz}$