A signal wave of frequency 12 kHz is modulated with a carrier wave of frequency 2-51 MHz. The upper and lower side band frequencies are respectively.

Options

A. 2512 KHz and 2508KHz
B. 2522KHz and 2488KHz
C. 2502KHz and 2498KHz
D. 2522KHz and 2498KHz

Explanation

To find the upper and lower sideband frequencies for a modulated signal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Frequencies:**
- Signal frequency (fm) = 12 kHz
- Carrier frequency (fc) = 2.51 MHz

2. **Convert Frequencies to the Same Unit:**
- Convert the carrier frequency from MHz to kHz:
\[ fc = 2.51 \text{ MHz} = 2.51 \times 1000 \text{ kHz} = 2510 \text{ kHz} \]

3. **Calculate the Upper Sideband Frequency (USB):**
- The formula for the upper sideband frequency is:
\[ USB = fc + fm \]
- Substitute the values:
\[ USB = 2510 \text{ kHz} + 12 \text{ kHz} = 2522 \text{ kHz} \]

4. **Calculate the Lower Sideband Frequency (LSB):**
- The formula for the lower sideband frequency is:
\[ LSB = fc - fm \]
- Substitute the values:
\[ LSB = 2510 \text{ kHz} - 12 \text{ kHz} = 2498 \text{ kHz} \]

5. **Final Results:**
- Upper Sideband Frequency (USB) = 2522 kHz
- Lower Sideband Frequency (LSB) = 2498 kHz

### Summary:
- The upper sideband frequency is **2522 kHz**.
- The lower sideband frequency is **2498 kHz**.