Question

A \(5\) kHz frequency signal is amplitude modulated on a carrier wave of frequency \(2\) MHz. - One possible frequency of the resultant signal is

• A. \(1995 \, \text{kHz}\)
• B. \(1985 \, \text{kHz}\)
• C. \(1975 \, \text{kHz}\)
• D. \(1965 \, \text{kHz}\)

Hint:

In amplitude modulation (AM), the resultant signal contains the carrier frequency \( f_c \) and two sidebands at: \[ f_{\text{upper}} = f_c + f_m, \quad f_{\text{lower}} = f_c - f_m \] Always use these formulas to determine possible frequencies in AM signals.

Answer 1

The Correct Option is A

Step 1: Understanding Amplitude Modulation In amplitude modulation (AM), the resultant signal consists of the carrier frequency and sidebands. The sideband frequencies are given by: \[ f_{\text{upper}} = f_c + f_m \] \[ f_{\text{lower}} = f_c - f_m \] where: 
- \( f_c = 2000 \) kHz = \(2\) MHz (carrier frequency), 
- \( f_m = 5 \) kHz (modulating signal frequency). 

Step 2: Calculating Sideband Frequencies \[ f_{\text{upper}} = 2000 + 5 = 2005 \, \text{kHz} \] \[ f_{\text{lower}} = 2000 - 5 = 1995 \, \text{kHz} \] Since the question asks for one possible frequency, the correct answer is: \[ \mathbf{1995 \, \text{kHz}} \] Thus, the correct answer is \( \mathbf{(1)} \ 1995 \, \text{kHz} \).