The U. S. Navy has long proposed the construction of extremely low frequency (ELF waves) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency 71 Hz.

The length of the antenna would be L = 1056 km

Explanation:

Given:-

- The frequency of ELF, f = 71 Hz

- The speed of EM wave, c = 3.00 * 10^8 m/s

Find:-

Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves

Solution:-

- We will first determine the wavelength (λ) of the ELF waves with frequency (f) generated by the transmitter. The relationship that holds true for all types of EM waves is:

λ = c / f

λ = (3.00*10^8 m/s) / (71 Hz)

λ = 4225352.11267 m

- The antenna of the transmitter is to be designed such that its length (L) is 1/4-wavelength of ELF generated. So:

L = 0.25*λ

L = 0.25*4225352.11267

L = 1056 km