Given below are two statements :

Question:

Given below are two statements :

Statement I : A speech signal of $2 \mathrm{kHz}$ is used to modulate a carrier signal of $1 \mathrm{MHz}$.

The bandwidth requirement for the signal is $4 \mathrm{kHz}$.

Statement II : The side band frequencies are $1002 \mathrm{kHz}$ and $998 \mathrm{kHz}$. In the light of the above statements, choose the correct answer from the options given below :

  1. (1) Both statement I and statement II are false

  2. (2) Statement I is false but statement II is true

  3. (3) Statement I is true but statement II is false

  4. (4) Both statement I and statement II are true


Correct Option: , 4

Solution:

Side band $=\left(f_{c}-f_{m}\right)$ to $\left(f_{c}+f_{m}\right)=(1000-2) \mathrm{KHz}$ to $(1000+2) \mathrm{KHz}$

$=998 \mathrm{KHz}$ to $1002 \mathrm{kHz}$

Band width $=2 \mathrm{f}_{\mathrm{m}}$

$=2 \times 2 \mathrm{KHz}$

$=4 \mathrm{KHz}$

Both statements are true

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