Question

The ideal size (most efficient) for a broadcast antenna with one end on the ground is one-fourth the wavelength (λ/4) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band?

a) 1.5 MHz (AM)
b) 3.0 MHz (FM)
c) 4.0 MHz (AM)
d) 6.0 MHz (FM)

Answer 1

A 50.0 meter high antenna broadcasts most efficiently at a frequency of 1.5 MHz, which is in the AM radio band.

Step-by-step explanation:

To determine the most efficient broadcast frequency for a radio station with an antenna that is 50.0 m high, we assume the ideal antenna size is one-fourth the wavelength (λ/4) of the electromagnetic radiation. The height of the antenna (50.0 m) represents λ/4, so one full wavelength (λ) would be 4 times the height of the antenna (200.0 m).

The speed of electromagnetic waves, which includes radio waves, is the speed of light (c), approximately 3 x 108 m/s. Therefore, the frequency (f) can be calculated using the formula c = fλ. Substituting the values, we find f = c / λ = (3 x 108 m/s) / (200 m) = 1.5 x 106 Hz or 1.5 MHz.

This frequency of 1.5 MHz falls within the range of the AM (Amplitude Modulation) radio band, which typically ranges from 530 kHz to 1700 kHz (or 1.7 MHz). Therefore, the most efficient broadcast frequency for the 50.0 m high antenna is 1.5 MHz and it is in the AM band. As such, the answer to the student's question is (a) 1.5 MHz (AM).