Two radio antennas are 120 m apart on a north-south line, and they radiate in phase at a frequency of 3.4 MHz. All radio measurements are made far from the antennas. If the east-west reference line passes midway between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s) A) 43° B) 22° C) 68° D) 47° E) 30°

Question

Quizplus · Accepted Answer

The path difference for constructive interference is given by $ d \sin \theta = m \lambda $, where $ d = 120 \, \text{m} $, $ \lambda = \frac{c}{f} = \frac{3.00 \times 10^8 \, \text{m/s}}{3.4 \times 10^6 \, \text{Hz}} \approx 88.24 \, \text{m} $, and $ m = 1 $ for the smallest angle. Solving for $ \theta $, we get $ \theta \approx 47^\circ $.

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