Physics quiz question: interference from two in-phase radio transmitters

Physics 205B Quiz 3, spring semester 2017
Cuesta College, San Luis Obispo, CA

A radio antenna receives signals from two in-phase transmitters at the same wavelength of 30 m. This diagrams is not drawn to scale. The radio antenna receives __________ interference signal.
(A) a constructive.
(B) a destructive.
(C) something in-between a constructive and destructive.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

Radio waves from the transmitter at x = 0 travel 45 m to get to the receiver. Radio waves from the transmitter at x = +180 m travel 135 m to get to the receiver. The path length difference ∆l is 135 m – 45 m = 90 m, which is (90 m)/(30 m) = three times the wavelength of 30 m. Since there is a whole number (here, 3) wavelength path length difference, the receiving antenna detects constructive interference from these two in-phase transmitters.

Sections 30882, 30883
Exam code: quiz03d3St
(A) : 11 students
(B) : 15 students
(C) : 2 students
(D) : 0 students

Success level: 39%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.12