Question

An information signal of frequency 10 kHz is modulated with a carrier wave of frequency 3.61 MHz. The upper side and lower side frequencies are:

• A. 3650 kHz and 3590 kHz
• B. 3620 kHz and 3600 kHz
• C. 3610 kHz and 3580 kHz
• D. 3600 kHz and 3620 kHz

Hint:

In amplitude modulation, the carrier frequency is shifted by the information signal frequency to generate the upper and lower side frequencies. The USF is the sum and the LSF is the difference of the carrier and signal frequencies.

Answer 1

The Correct Option is B

To find the upper and lower side frequencies when an information signal is modulated with a carrier wave, we use the following formulas:

• Upper Side Frequency (USF): \( f_c + f_m \)
• Lower Side Frequency (LSF): \( f_c - f_m \)

where \( f_c \) is the carrier frequency and \( f_m \) is the frequency of the information signal.

Given:

• Carrier frequency (\( f_c \)) = 3.61 MHz = 3610 kHz
• Information signal frequency (\( f_m \)) = 10 kHz

We can calculate as follows:

Upper Side Frequency:

\( f_c + f_m = 3610 \text{ kHz} + 10 \text{ kHz} = 3620 \text{ kHz} \)

Lower Side Frequency:

\( f_c - f_m = 3610 \text{ kHz} - 10 \text{ kHz} = 3600 \text{ kHz} \)

Thus, the solution is that the upper side and lower side frequencies are 3620 kHz and 3600 kHz, respectively.

Answer 2

Given: 
- Information signal frequency \( f_m = 10 \, {kHz} \) 
- Carrier frequency \( f_c = 3.61 \, {MHz} = 3610 \, {kHz} \) When an information signal is modulated, the upper side frequency (USF) and lower side frequency (LSF) are given by the following formulas: \[ {USF} = f_c + f_m \quad {and} \quad {LSF} = f_c - f_m \] Substituting the given values: \[ {USF} = 3610 \, {kHz} + 10 \, {kHz} = 3620 \, {kHz} \] \[ {LSF} = 3610 \, {kHz} - 10 \, {kHz} = 3600 \, {kHz} \] Thus, the upper side frequency and lower side frequency are \( 3620 \, {kHz} \) and \( 3600 \, {kHz} \), respectively.