Question

If the frequencies of the carrier wave and message signal are $1$ MHz and $28$ kHz respectively, then the frequencies of the side bands are

• A. $1014$ kHz, $986$ kHz
• B. $1028$ kHz, $972$ kHz
• C. $29$ kHz, $27$ kHz
• D. $514$ kHz, $486$ kHz

Hint:

In Amplitude Modulation (AM), a carrier wave of frequency $f_c$ is modulated by a message signal of frequency $f_m$. This process generates two sideband frequencies: the Upper Sideband Frequency ($f_c + f_m$) and the Lower Sideband Frequency ($f_c - f_m$). The bandwidth of the AM signal is $2f_m$.

Answer 1

The Correct Option is B

Step 1: Identify the frequencies and the modulation type.
The problem involves a carrier wave ($f_c$) and a message signal ($f_m$), and asks for the sideband frequencies. This is an Amplitude Modulation (AM) scenario. Carrier frequency: $f_c = 1 \text{ MHz}$. Message frequency: $f_m = 28 \text{ kHz}$.

Step 2: Convert all frequencies to a single unit (kHz).
Since $1 \text{ MHz} = 1000 \text{ kHz}$: $f_c = 1000 \text{ kHz}$. $f_m = 28 \text{ kHz}$.

Step 3: State the formulas for the sideband frequencies.
In Amplitude Modulation (AM), two sideband frequencies are generated: an Upper Sideband Frequency ($f_{USB}$) and a Lower Sideband Frequency ($f_{LSB}$). \[ f_{USB} = f_c + f_m. \] \[ f_{LSB} = f_c - f_m. \]

Step 4: Calculate the sideband frequencies.
Upper Sideband Frequency: \[ f_{USB} = 1000 \text{ kHz} + 28 \text{ kHz} = 1028 \text{ kHz}. \] Lower Sideband Frequency: \[ f_{LSB} = 1000 \text{ kHz} - 28 \text{ kHz} = 972 \text{ kHz}. \] The frequencies of the sidebands are $1028 \text{ kHz}$ and $972 \text{ kHz}$.