Question

Given below are two statements : Statement I : A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz. Statement II : The side band frequencies are 1002 kHz and 998 kHz. In the light of the above statements, choose the correct answer :

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

Hint:

In Amplitude Modulation (AM), the information is contained in the sidebands, and the total bandwidth is always double the message frequency.

Answer 1

The Correct Option is A

To solve the question and validate the given statements, we need to understand the concepts of signal modulation, bandwidth, and sidebands in communication systems.

1. Understanding Statement I:
   • A speech signal with a frequency of 2 kHz is used to modulate a carrier signal of 1 MHz.
   • In amplitude modulation (AM), the bandwidth (BW) of the modulated signal is given by BW = 2 \times \text{modulating frequency}.
   • Thus, the bandwidth required is BW = 2 \times 2 \text{ kHz} = 4 \text{ kHz}.
   • This confirms that Statement I is true.
2. Understanding Statement II:
   • In AM, the sidebands are generated at frequencies f_c \pm f_m, where f_c is the carrier frequency and f_m is the modulating frequency.
   • Here, f_c = 1 \text{ MHz} = 1000 \text{ kHz} and f_m = 2 \text{ kHz}.
   • The sidebands are at:
     • Upper sideband (USB): 1000 \text{ kHz} + 2 \text{ kHz} = 1002 \text{ kHz}
     • Lower sideband (LSB): 1000 \text{ kHz} - 2 \text{ kHz} = 998 \text{ kHz}
   • This confirms that Statement II is true.
3. Conclusion:
   • Both the bandwidth requirement and the sideband frequencies are correctly outlined in the statements.
   • Therefore, the correct answer is: Both Statement I and Statement II are true.