Physics quiz question: wavelength for destructively interfering radio transmitters

Physics 205B Quiz 3, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 25.3

A radio antenna receives a destructive interference signal from two transmitters, one located 750 m away, and the other located 890 m away. The two transmitters broadcast in phase at the same wavelength. The maximum value for the wavelength broadcast by the two transmitters is:
(A) 70 m.
(B) 140 m.
(C) 210 m.
(D) 280 m.

Correct answer (highlight to unhide): (D)

For in phase sources, the condition for destructive interference is given by:

∆l = (m + 1/2)·λ,

where the difference in path lengths is ∆l = 890 m - 750 m = 140 m, and solving for λ yields:

140 m = (m + 1/2)·λ,

λ = (140 m)/(m + 1/2).

To find the maximum possible value for λ, we set m = 0, and:

λ = (140 m)/((0) + 1/2) = 2·(140 m) = 280 m.

(Response (A) is ∆l/2; response (B) is ∆l; and response (C) is (3/2)·∆l.)

Section 30882
Exam code: quiz03rD1o
(A) : 3 students
(B) : 12 students
(C) : 5 students
(D) : 12 students

Success level: 37%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.47