Audio sine waves of 3 kHz frequency are used to amplitude modulate a carrier signal of 1.5 MHz. Which of the following statements are true?

Options

A. The sideband frequencies are 1506 kHz and 1494 kHz.
B. The bandwidth required foe amplitude modulation is 6 kHz.
C. The bandwidth required for amplitude modulation is 3 MHz
D. The sideband frequencies are 1503 kHz and 1494 kHz

Explanation

To solve the problem, we need to analyze the given information about amplitude modulation (AM) and calculate the sideband frequencies and bandwidth. Here’s a step-by-step solution:

### Step 1: Identify the given frequencies
- The frequency of the audio sine wave (modulating signal) is \( f_m = 3 \, \text{kHz} = 3 \times 10^3 \, \text{Hz} \).
- The frequency of the carrier signal is \( f_c = 1.5 \, \text{MHz} = 1.5 \times 10^6 \, \text{Hz} \).

### Step 2: Calculate the lower sideband frequency
The lower sideband frequency (\( f_{LSB} \)) can be calculated using the formula:
\[ f_{LSB} = f_c - f_m \]
Substituting the values:
\[ f_{LSB} = 1.5 \times 10^6 - 3 \times 10^3 = 1.497 \times 10^6 \, \text{Hz} = 1497 \, \text{kHz} \]

### Step 3: Calculate the upper sideband frequency
The upper sideband frequency (\( f_{USB} \)) can be calculated using the formula:
\[ f_{USB} = f_c + f_m \]
Substituting the values:
\[ f_{USB} = 1.5 \times 10^6 + 3 \times 10^3 = 1.503 \times 10^6 \, \text{Hz} = 1503 \, \text{kHz} \]

### Step 4: Calculate the bandwidth required
The bandwidth (BW) required for amplitude modulation is given by:
\[ \text{BW} = 2 f_m \]
Substituting the value of \( f_m \):
\[ \text{BW} = 2 \times 3 \, \text{kHz} = 6 \, \text{kHz} \]

### Step 5: Evaluate the options
Now, we need to evaluate the statements based on our calculations:
1. Sideband frequencies are 1506 kHz and 1494 kHz. **(False)**
2. Bandwidth is 600 kHz. **(False)**
3. Bandwidth required for amplitude is 3 MHz. **(False)**
4. Sideband frequencies are 1503 kHz and 1494 kHz. **(False)**

The only correct statement is that the bandwidth is 6 kHz, which is not listed in the options.

### Conclusion
From the calculations, the only true statement is that the bandwidth required for amplitude modulation is 6 kHz.

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