*Question T9A08:
What is the approximate length, in inches, of a quarter-wavelength vertical antenna for 146 MHz?*  

*Correct Answer is  C: 19*  

### AI Response: (may contain errors)  

To determine the approximate length of a quarter-wavelength vertical antenna for 146 MHz, we can use the formula for the wavelength ($\lambda$) in meters:

$$
\lambda = \frac{300}{f}
$$

where:
- $f$ = frequency in MHz

For 146 MHz, we calculate the wavelength as follows:

$$
\lambda = \frac{300}{146} \approx 2.05 \text{ meters}
$$

Since we want the length of a quarter-wavelength antenna, we divide the wavelength by 4:

$$
L = \frac{\lambda}{4} = \frac{2.05}{4} \approx 0.5125 \text{ meters}
$$

To convert this to inches (since 1 meter = 39.37 inches):

$$
L \approx 0.5125 \times 39.37 \approx 20.2 \text{ inches}
$$

Rounding to the nearest whole number gives us approximately 19 inches, which corresponds to the correct answer.

### Explanation of Choices:
- **Correct Answer: C: 19**
  - This is the correct calculation for a quarter-wavelength antenna at 146 MHz.

- **Choice A: 112**
  - This length is far too long for a quarter-wavelength antenna at this frequency. It may be confused with a full-wavelength calculation.

- **Choice B: 50**
  - This length is also too long and does not correspond to a quarter-wavelength at 146 MHz.

- **Choice D: 12**
  - This length is too short and does not match the calculated quarter-wavelength.

### Summary:
- The formula for wavelength is crucial for determining antenna lengths.
- The correct length for a quarter-wavelength vertical antenna at 146 MHz is approximately 19 inches.