Question

A signal wave of frequency 12 kHz is modulated with a carrier wave of frequency 2.51 MHz. What are the frequencies of the upper and lower sidebands?
A. 2512 kHz and 2508 kHz
B. 2522 kHz and 2488 kHz
C. 2502 kHz and 2498 kHz
D. 2522 kHz and 2498 kHz
E. 2512 kHz and 2488 kHz

Answer 1

Hint: Before we proceed with the problem, it is important to know about the carrier wave, upper sideband, and lower sideband. A carrier wave is defined as continuous electromagnetic radiation which is of constant amplitude and frequency. If the frequency of the band is above the carrier frequency is known as the upper sideband and if the frequency of the band is above the carrier frequency is known as the lower sideband.

Formula Used:
The formula to find the upper sideband and lower sideband frequencies are given by,
Upper sideband frequency = \[{\nu _C} + {\nu _S}\]
Lower sideband frequency = \[{\nu _C} - {\nu _S}\]
Where, \[{\nu _C}\] is frequency of the carrier wave and \[{\nu _S}\] is frequency of the signal wave.

Complete step by step solution:
The frequency of the signal wave is 12 kHz and the frequency of the carrier wave is 2.51 MHz (2510 KHz). We have,
Upper sideband frequency = \[{\nu _C} + {\nu _S}\] = (12+2510) = 2522 KHz
Similarly,
Lower sideband frequency = \[{\nu _C} - {\nu _S}\]= (2510-12) = 2498 KHz
Therefore, the frequencies of the upper and lower sidebands are 2522 KHz and 2498 KHz.

Hence, option D is the correct answer

Note: The carrier wave can be modulated as the voice or music, that is to be transmitted. It is used to carry the signals from one location to another on the surface of the earth. For distant communication carrier waves of higher frequencies are used because high-frequency carrier waves travel with the speed of light and do not require a material medium to propagate.