*Question E1C09:
[97.307] What is the highest modulation index permitted at the highest modulation frequency for angle modulation below 29.0 MHz?*  

*Correct Answer is  B: 1.0*  

### AI Response: (may contain errors)  

In the context of FCC regulations for amateur radio, the modulation index is a measure of the extent of modulation applied to a carrier signal in angle modulation, which includes both frequency modulation (FM) and phase modulation (PM).

### Explanation:

1. **Correct Answer: 1.0**

   - The modulation index is defined as the ratio of the frequency deviation to the modulation frequency. For angle modulation below 29.0 MHz, the FCC limits the modulation index to a maximum of 1.0. This means that the frequency deviation should not exceed the modulation frequency.
   - A modulation index of 1.0 ensures that the signal remains within the allocated bandwidth and minimizes interference with adjacent channels.

2. **Why Other Choices Are Incorrect:**

   - **Choice A: 0.5**
     - A modulation index of 0.5 is more restrictive than necessary. While it would comply with the regulations, it does not utilize the full allowable modulation depth, potentially reducing the effectiveness of the transmission.
   
   - **Choice C: 2.0**
     - A modulation index of 2.0 exceeds the FCC limit for frequencies below 29.0 MHz. This could lead to excessive bandwidth usage and interference with adjacent channels, violating FCC rules.
   
   - **Choice D: 3.0**
     - Similarly, a modulation index of 3.0 is well above the permitted limit, leading to even greater potential for interference and non-compliance with FCC regulations.

### Useful Formula:

The modulation index ($m$) for frequency modulation is given by:

$$
m = \frac{\Delta f}{f_m}
$$

where:
- $\Delta f$ = frequency deviation
- $f_m$ = modulation frequency

For compliance below 29.0 MHz, ensure $m \leq 1.0$. This keeps the signal within the required bandwidth and adheres to FCC regulations.