Question

A signal wave of frequency $12kHz$ is modulated with a carrier wave of frequency $2.51MHz$. The upper and lower sideband frequencies are respectively

• A. $2512kHz$and $2508kHz$
• B. $2522kHz$and $2488kHz$
• C. $2502kHz$ and $2498kHz$
• D. $2522kHz$ and $2498kHz$
• E. $2512kHz$ and $2488kHz$

Answer 1

The correct option is D

$2522kHz$ and $2498kHz$

Step 1. Given data

Signal wave frequency $v_s=12kHz$

Carrier wave frequency $v_c=2.51MHz=2510kHz$

Step 2. Finding upper and lower sideband frequencies

We know that upper sideband frequency is given by $v_u=v_c+v_s$

$$\begin{gathered} v_u=(2510+12)kHz \\ =2522kHz \end{gathered}$$

Similarly, lower sideband frequency is given by $v_l=v_c-v_s$

$$\begin{gathered} v_l=(2510-12)kHz \\ =2498kHz \end{gathered}$$

Hence, the correct option is (D)