Physics quiz question: constructive interference from two radio transmitters

Physics 205B Quiz 3, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 25.1

A radio antenna receives a constructive interference signal of wavelength 320 m from two coherent transmitters, located 1.75 km away from one transmitter, and 1.91 km away from the other transmitter. The two transmitters are broadcasting signals __________ with each other.
(A) in phase.
(B) out of phase.
(C) somewhere in-between in phase and out of phase.
(D) (Not enough information given.)

Correct answer (highlight to unhide): (B)

The path length difference ∆l is | 1.91 km – 1.75 km | = 0.16 km = 160 m, which is one-half of a wavelength. Since the receiving antenna detects constructive interference, the two transmitters must be broadcasting out of phase.

Section 30882
Exam code: quiz03gR7L
(A) : 6 students
(B) : 17 students
(C) : 4 students
(D) : 0 students

Success level: 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.29