Two radio antennas are 120 m apart on a north-south line.The two antennas radiate in phase at a frequency of 5.6 MHz.All radio measurements are made far from the antennas.What is the smallest angle,reckoned north of east from midway between the antennas,at which destructive interference of the two radio waves occurs? (c = 3.00 × 10⁸ m/s) A)13° B)6.4° C)9.7° D)16° E)19°

Question

Quizplus · Accepted Answer

The smallest angle at which destructive interference occurs is when the path length difference between the two waves is half a wavelength. The path length difference is 120 m, so the wavelength is 240 m. The frequency is 5.6 MHz, so the wavelength is c/f = 3.00 × 10^8 m/s / 5.6 × 10^6 Hz = 53.6 m. Therefore, the smallest angle at which destructive interference occurs is sin^-1(120 m / 240 m) = 13°.

Two Radio Antennas Are 120 M Apart on a North-South