A speech signal of `3 kHz` is used to modulate a carrier signal of frequency `1 MHz`, using amplitude modulation. The frequencies of the side bands will be

Options

A. 1.003 MHz and 0.997 MHz
B. 3001 kHz and 2997 kHz
C. 1003 kHz and 1000 kHz
D. 1 MHz and 0.997 MHz

Explanation

To find the frequencies of the sidebands in amplitude modulation, we can follow these steps:

### Step 1: Identify the frequencies
- Given:
- Frequency of the carrier signal, \( f_c = 1 \text{ MHz} = 1 \times 10^6 \text{ Hz} \)
- Frequency of the speech signal, \( f_s = 3 \text{ kHz} = 3 \times 10^3 \text{ Hz} \)

### Step 2: Calculate the sideband frequencies
- In amplitude modulation, the sidebands are calculated using the following formulas:
- Lower Sideband (LSB) frequency: \( f_{LSB} = f_c - f_s \)
- Upper Sideband (USB) frequency: \( f_{USB} = f_c + f_s \)

### Step 3: Substitute the values into the formulas
- For the Lower Sideband (LSB):
\[ f_{LSB} = f_c - f_s = 1 \text{ MHz} - 3 \text{ kHz} = 1 \times 10^6 \text{ Hz} - 3 \times 10^3 \text{ Hz} = 997 \text{ kHz} = 0.997 \text{ MHz} \]

- For the Upper Sideband (USB):
\[ f_{USB} = f_c + f_s = 1 \text{ MHz} + 3 \text{ kHz} = 1 \times 10^6 \text{ Hz} + 3 \times 10^3 \text{ Hz} = 1003 \text{ kHz} = 1.003 \text{ MHz} \]

### Step 4: Final results
- The frequencies of the sidebands are:
- Lower Sideband (LSB): \( 0.997 \text{ MHz} \)
- Upper Sideband (USB): \( 1.003 \text{ MHz} \)

### Summary of the results:
- Lower Sideband (LSB): \( 0.997 \text{ MHz} \)
- Upper Sideband (USB): \( 1.003 \text{ MHz} \)

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