A single of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/are :-

Options

A. 2005 kHz, and 1995 kHz
B. 2005 kHz, 2000 kHz and 1995 kHz
C. 2000 kHz and 1995 kHz
D. 2 MHz only

Answer

To solve the problem of finding the frequencies of the resultant signal when a 5 kHz signal is amplitude modulated on a carrier wave of frequency 2 MHz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Frequencies:**
- Frequency of the modulating signal (source frequency, \( f_m \)): 5 kHz
- Frequency of the carrier wave (\( f_c \)): 2 MHz

2. **Convert Units:**
- Convert 2 MHz to kHz for consistency:
\[ f_c = 2 \text{ MHz} = 2000 \text{ kHz} \]

3. **Calculate the Upper Side Frequency (\( f_{u} \)):**
- The upper side frequency is calculated using the formula:
\[ f_{u} = f_c + f_m \]
- Substitute the values:
\[ f_{u} = 2000 \text{ kHz} + 5 \text{ kHz} = 2005 \text{ kHz} \]

4. **Calculate the Lower Side Frequency (\( f_{l} \)):**
- The lower side frequency is calculated using the formula:
\[ f_{l} = f_c - f_m \]
- Substitute the values:
\[ f_{l} = 2000 \text{ kHz} - 5 \text{ kHz} = 1995 \text{ kHz} \]

5. **List the Frequencies of the Resultant Signal:**
- The frequencies of the resultant signal are:
- Lower side frequency: 1995 kHz
- Upper side frequency: 2005 kHz
- The original modulating frequency: 5 kHz (which is equivalent to 0.005 MHz)

6. **Final Answer:**
- The frequencies of the resultant signal are:
- 1995 kHz, 2005 kHz, and 5 kHz.

### Summary of Result:
The frequencies of the resultant signal are: **1995 kHz, 2005 kHz, and 5 kHz.**