To determine the length of an antenna operating at a specific frequency, we can use the formula:
Length of antenna (in meters) = (Speed of light) / (Frequency)
The speed of light in a vacuum is approximately 299,792,458 meters per second.
Let's calculate the length of an antenna operating at 4 MHz (4 million hertz):
Length of antenna = (299,792,458 m/s) / (4,000,000 Hz) ≈ 74.948 meters
So, the length of the antenna operating at 4 MHz would be approximately 74.948 meters.
As for the fractions you mentioned, 1/16 or 1/512 of the wavelength, these fractions can be used as guidelines for antenna design, especially when considering the "quarter-wave" or "half-wave" principles. In the case of a quarter-wave antenna, the length of the antenna is approximately one-fourth (1/4) of the wavelength, while for a half-wave antenna, the length is approximately one-half (1/2) of the wavelength. These principles help in optimizing the antenna's performance and impedance matching.
However, it's important to note that the fractions you mentioned, 1/16 or 1/512, do not correspond to any specific principle for antenna length calculation. These fractions might not align with the optimal lengths for efficient radiation and reception at the given frequency. It's generally recommended to adhere to the quarter-wave or half-wave principles for antenna design, or consult specific antenna design guidelines and simulations for the desired frequency range.