An oscillator is producing FM waves of requency `2kHz` with a variation of `10kHz`. What is modulating index?

Options

A. `0.20`
B. `5.0`
C. `0.67`
D. `1.5`

Answer

To find the modulating index for the given frequency modulation waves, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Modulating frequency (ν) = 2 kHz
- Frequency variation (Δf) = 10 kHz

2. **Convert the Values to Hertz:**
- Since the modulating index formula requires the frequencies to be in Hertz, we need to convert kilohertz to hertz.
- Modulating frequency (ν) = 2 kHz = 2 × 10^3 Hz = 2000 Hz
- Frequency variation (Δf) = 10 kHz = 10 × 10^3 Hz = 10000 Hz

3. **Use the Formula for Modulating Index (m):**
- The modulating index (m) is given by the formula:
\[ m = \frac{\Delta f}{ν} \]
- Where Δf is the frequency variation and ν is the modulating frequency.

4. **Substitute the Values into the Formula:**
- Now, substituting the values we have:
\[ m = \frac{10000 \text{ Hz}}{2000 \text{ Hz}} \]

5. **Calculate the Modulating Index:**
- Performing the division:
\[ m = \frac{10000}{2000} = 5 \]

6. **Conclusion:**
- Therefore, the modulating index (m) is 5.

### Final Answer:
The modulating index is **5**.

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