Question

Statement I: A speech signal of $2kHz$ is used to modulate a carrier signal of $1MHz$. The bandwidth requirement for the signal is $4kHz$.

Statement II: The sideband frequencies are $1002kHz$ and $998kHz$. In the light of the above statements, choose the correct answer from the options given below:

• A. Both statement I and statement II are false
• B. Statement I is false but statement II is true
• C. Statement I is true but statement II is false
• D. Both statement I and statement II are true

Answer 1

The correct option is D

Both statement I and statement II are true

Step 1: Given data

Frequency of speech signal $\left(f_m\right)=2KHz$

Frequency of carrier signal $\left(f_c\right)=1MHz=1000KHz$

Step 2: Formula used:

The bandwidth will be given as-

$\mathrm{Bandwidth}=2f_m$

Side frequencies will be given as-

$f_c\pm f_m$

Where, $f_m$ is modulation frequency or signal frequency

$f_c$ is carrier frequency

Step 3: Calculating the bandwidth

First, check the bandwidth of the signal

Using the formula,

$\mathrm{Bandwidth}=2f_m$

$$\begin{gathered} \Rightarrow 2f_m \\ \Rightarrow 2\times 2 \\ \Rightarrow 4kHz \end{gathered}$$

Thus, statement I is correct.

Step 4: Determine the side frequencies

Using the formula of side frequency,

The side frequencies will be

$\left(f_c+f_m\right)and\left(f_c-f_m\right)$.

So,

$$\begin{gathered} \left(1000+2\right)and\left(1000-2\right) \\ 1002KHzand998KHz \end{gathered}$$

Thus, statement II is also correct.

So, both statements I and II are correct.

Hence, option D is the correct answer.