20170601

Physics final exam problem: destructive interference angles in one quadrant

Physics 205B Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA

Two vertical radio transmitters broadcast in phase at the same wavelength of 1.2 m, and are spaced a certain apart along the east-west direction. A Physics 205B student holding a receiver starts from due south of the transmitters, and detects three different locations with destructive interference signals before finally reaching due east of the transmitters. (Assume that each of the distances from the transmitters to the receiver are very large.) Determine a plausible separation distance (in m) between the transmitters. Explain your reasoning using the properties of source phases, path lengths, and interference.

Solution and grading rubric:
  • p:
    Correct. Discusses/demonstrates that three minima locations will be found in the range θ = 0° (due south) to 90° (due west) by using one of two approaches:
    1. using the destructive interference condition d⋅sinθ = (m + 1/2)⋅λ, where m = 0, 1, 2, ..., finds a plausible separation distance d such that the third minima (m = 2) will be within θ = 90°, but the fourth minima (m = 3) is outside of θ = 90° (i.e., 3.0 m ≤ d ≤ 4.8 m); or
    2. using the constructive interference condition d⋅sinθ = m⋅λ, where m = 0, 1, 2, ..., finds the separation distance d such that the third maxima (m = 3) will be at θ = 90°; which allows for the m = 0, 1, and 2 minima to exist within that range (i.e., d = 3.6 m).
  • r:
    Nearly correct, but includes minor math errors. May have claimed equally spaced minima angles at θ = 30°, 60° and 90° to find a plausible separation distance d using θ = 30° for the first minima angle.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Garbled attempt at applying properties of source phases, path lengths, and interference.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying properties of source phases, path lengths, and interference.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 30882, 30883
Exam code: finalmR3x
p: 3 students
r: 4 students
t: 6 students
v: 7 students
x: 4 students
y: 2 students
z: 0 students

A sample "p" response (from student 0428), finding the maximum possible separation distance:

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