Physics midterm question: moving interfering transmitters back from receiver

Physics 205B Midterm 1, spring semester 2014
Cuesta College, San Luis Obispo, CA

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

A radio antenna receives a destructive interference signal from two transmitters that broadcast in phase at the same wavelength. Discuss why the radio antenna will still receive a destructive interference signal if both of the two transmitters are each moved one-half of a wavelength farther away from their current distances from the radio antenna. Explain your reasoning by using the properties of waves and interference.

Solution and grading rubric:

• p:
  Correct. Recognizes that (a) the two waves from in phase sources interfere destructively, so the path length difference ∆l = (m + 1/2)∙λ, and (b) demonstrates by either drawings or explicit math how extending both paths by half a wavelength will not affect the path length difference, thus the interference will still be destructive as stated.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically recognizes that ∆l will not be affected by moving both transmitters by half a wavelength, but does not explicitly demonstrate how this is so.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01b0w7
p: 14 students
r: 14 students
t: 11 students
v: 1 student
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 5297):
Another sample "p" response (from student 3420):