Question

A signal wave of frequency \(12 \mathrm{KHz}\) is modulated with a carrier wave of frequency \(2.51 \mathrm{MHz}\). The upper and lower side band frequency are respectively. (A) \(2512 \mathrm{~Hz}\) and \(2508 \mathrm{KHz}\) (B) \(2522 \mathrm{KHz}\) and \(2488 \mathrm{KHz}\) (C) \(2502 \mathrm{KHz}\) and \(2498 \mathrm{KHz}\) (D) \(2522 \mathrm{KHz}\) and \(2498 \mathrm{KHz}\)

Short answer

The upper and lower sideband frequencies are 2522 KHz and 2498 KHz, respectively. So the correct answer is (D).

Step-by-step solution

Convert frequencies to the same unit

Convert the signal frequency to MHz and the carrier frequency to KHz, or both to Hz. In this case, we will convert both to KHz. Signal frequency = 12 KHz (already in KHz) Carrier frequency = 2.51 MHz = 2510 KHz

Calculate the upper sideband frequency

Add the signal frequency to the carrier frequency to calculate the upper sideband frequency. Upper sideband frequency = Carrier frequency + Signal frequency = 2510 KHz + 12 KHz = 2522 KHz

Calculate the lower sideband frequency

Subtract the signal frequency from the carrier frequency to calculate the lower sideband frequency. Lower sideband frequency = Carrier frequency - Signal frequency = 2510 KHz - 12 KHz = 2498 KHz

Identify the correct answer

Now that we have calculated the upper and lower sideband frequencies, we can compare our results to the given options and determine the correct answer. The upper sideband frequency is 2522 KHz, and the lower sideband is 2498 KHz. Comparing these values to the given options, we see that the correct answer is: (D) 2522 KHz and 2498 KHz