A sinusoidal carrier voltage of frequency 10 MHz and amplitude 200 volts is amplitude modulated by a sinusoidal voltage of frequency 10 kHz producing 40% modulation. Calculate the frequency of upper and lower sidebands.

Options

A. 10010 kHz, 9990 kHz
B. 1010kHz, 990 kHz
C. 10100 Hz,9990 Hz
D. 1010 MHz, 990 MHz

Explanation

To solve the problem of calculating the frequencies of the upper and lower sidebands for an amplitude-modulated signal, we can follow these steps:

### Step 1: Identify the given values
- **Carrier frequency (Fc)** = 10 MHz = 10,000 kHz (since 1 MHz = 1,000 kHz)
- **Modulating frequency (Fm)** = 10 kHz
- **Modulation index (m)** = 40% = 0.4 (not directly needed for calculating sidebands, but it's good to note)

### Step 2: Calculate the frequency of the upper sideband (USB)
The frequency of the upper sideband can be calculated using the formula:
\[ \text{USB} = F_c + F_m \]

Substituting the values:
\[ \text{USB} = 10,000 \text{ kHz} + 10 \text{ kHz} = 10,010 \text{ kHz} \]

### Step 3: Calculate the frequency of the lower sideband (LSB)
The frequency of the lower sideband can be calculated using the formula:
\[ \text{LSB} = F_c - F_m \]

Substituting the values:
\[ \text{LSB} = 10,000 \text{ kHz} - 10 \text{ kHz} = 9,990 \text{ kHz} \]

### Step 4: Present the final results
- **Upper Sideband Frequency (USB)** = 10,010 kHz
- **Lower Sideband Frequency (LSB)** = 9,990 kHz

### Summary
Thus, the frequencies of the upper and lower sidebands are:
- Upper Sideband: 10,010 kHz
- Lower Sideband: 9,990 kHz

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