Double-slit interference: 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 wavelength λ is calculated using λ = c/f = (3.00 × 10^8 m/s) / (3.4 × 10^6 Hz) = 88.24 m. For constructive interference, the path difference must be an integer multiple of the wavelength. Using the formula for double-slit interference, d sin(θ) = mλ, where d = 120 m and m = 1 for the smallest angle, we solve for θ: sin(θ) = λ/d = 88.24/120. Solving gives θ ≈ 47°.

Double-Slit Interference: Two Radio Antennas Are 120 M Apart on a North-South