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

To determine the approximate length of a quarter-wavelength vertical antenna for 146 MHz, it is important to understand the relationship between frequency and wavelength. The formula for calculating the wavelength in meters is:

[ \text{Wavelength (meters)} = \frac{300}{\text{Frequency (MHz)}} ]

Substituting the frequency of 146 MHz into this formula gives:

[ \text{Wavelength} = \frac{300}{146} \approx 2.05 \text{ meters} ]

Since a quarter-wavelength antenna is one fourth of this full wavelength:

[ \text{Quarter-wavelength} = \frac{2.05}{4} \approx 0.5125 \text{ meters} ]

To convert this length from meters to inches (since there are approximately 39.37 inches in a meter):

[ 0.5125 \text{ meters} \times 39.37 \text{ inches/meter} \approx 20.2 \text{ inches} ]

It appears that the approximate length in inches for the antenna should round to around 20 inches. However, when provided with the answer choices, the closest and most reasonable estimate based on practical antenna design considerations