Physics midterm question: interference of out-of-phase radio transmitters

Physics 205B Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

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

Two vertical radio transmitters broadcast at the same wavelength of 1.2 m, and are spaced 4.8 m apart along the east-west direction. A receiver held by a Physics 205B student located to the east of both transmitters detects a destructive interference signal. Discuss whether a receiver held by another Physics 205B student located to the south will detect a constructive, destructive, or something in-between a constructive and destructive signal. Explain your reasoning using the properties of source phases, path lengths, and interference.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates:
  1. that the radio transmitters are out of phase, as the difference in path lengths to the student located to the east is four times the wavelength, which would be constructive interference for in phase sources, but destructive interference (as is the case here) for out of phase sources;
  2. there is zero difference in path lengths to the student located to the south, which means that the out of phase sources will interfere destructively in that direction as well.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. At least discusses how (1) transmitters are out of phase, but does not sufficiently explain (2) the destructive interference for the south receiver.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Only (1) or (2) is complete, typically understands that difference in path lengths to the south receiver is zero.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at discussing source phases, path lengths, and interference.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of discussing source phases, path lengths, and interference.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01p34K
p: 20 students
r: 7 students
t: 13 students
v: 7 students
x: 0 student
y: 0 students
z: 0 student

A sample "p" response (from student 5425):
A sample "t" response (from student 1107):