Physics quiz question: out of phase radio tower interference

Physics 205B Quiz 3, fall semester 2010
Cuesta College, San Luis Obispo, CA

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

Two coherent radio transmitters broadcast out of phase signals of wavelength 150 m. A radio antenna receives signals from both transmitters, and is located 1.55 km away from one transmitter, and 2.00 km away from the other transmitter. The receiving antenna will detect __________ interference.
(A) constructive.
(B) destructive.
(C) something in-between constructive and destructive.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

The two transmitters are out of phase, such that for destructive interference the path difference ∆l must be m·λ, while for constructive interference the path difference must be (m + 1/2)·λ, where m is any integer.

The path difference between the waves that are emitted by these towers is ∆l = (2.00 km – 1.55 km) = 0.45 km = 450 m, which is equal to 3·λ, making this destructive interference.

Student responses
Section 70856
(A) : 4 students
(B) : 5 students
(C) : 2 students
(D) : 0 students

Success level: 45%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42

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Physics quiz question: in-phase radio tower interference (spring semester 2010).