Question

A carrier wave of frequency \(2\,MHz\) and peak voltage \(15\,V\) is used to modulate a message signal of frequency \(20\,kHz\) and peak voltage \(8\,V\). The frequencies of side bands produced are

• A. \(2000\,kHz,\,20\,kHz\)
• B. \(2020\,kHz,\,1980\,kHz\)
• C. \(2040\,kHz,\,1960\,kHz\)
• D. \(2020\,kHz,\,2000\,kHz\)

Hint:

In amplitude modulation: \[ \text{Side bands}=f_c\pm f_m \] Always keep carrier and message frequencies in same units before substitution.

Answer 1

The Correct Option is B

Step 1: Recall the side band formulas.
When a carrier is amplitude modulated, two new frequencies appear on either side. \[ f_{USB} = f_c + f_m,\qquad f_{LSB} = f_c - f_m \] Here $f_c$ is the carrier and $f_m$ is the message frequency.

Step 2: Match the units.
Convert the carrier to kilohertz so both are in the same unit. \[ f_c = 2\,\text{MHz} = 2000\,\text{kHz} \] \[ f_m = 20\,\text{kHz} \]
Step 3: Note the unused numbers.
The peak voltages $15$ V and $8$ V affect how strong the signal is, not the side band frequencies, so we ignore them here.
Step 4: Upper side band.
\[ f_{USB} = 2000 + 20 = 2020\,\text{kHz} \]
Step 5: Lower side band.
\[ f_{LSB} = 2000 - 20 = 1980\,\text{kHz} \]
Step 6: State the side bands.
\[ \boxed{2020\,\text{kHz},\ 1980\,\text{kHz}} \]