Physics final exam problem: direct wave and phase-shifted askew reflection interference

Physics 205B Final Exam, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Review and Synthesis Problem 10, p. 963

[20 points.] A radio wave with a wavelength of 350 m follows two paths to a receiver that is 1,600 m away. One path goes directly to the receiver and the other reflects from an airplane that is flying above the point that is exactly halfway between the transmitter and receiver. There is a 180° phase change when the wave reflects off the airplane. If the receiver experiences destructive interference, what is the minimum (non-zero) altitude for the airplane? Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Recognizes (a) 180° phase change reflection off of airplane causes destructive condition to be Δl = m*λ; (b) the path difference is 2·hypotenuse - 1,600 m; and solves for the non-zero height of the airplane.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least recognizes correct destructive interference condition, and some attempt at solving for height of airplane.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at applying interference condition and height of airplane.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30882
Exam code: finalsM0k
p: 7 students
r: 1 student
t: 5 students
v: 8 students
x: 1 student
y: 2 students
z: 0 students

A sample "p" response (from student 4027):
Another sample "p" response (from student 1990):
A sample "y" response (from student 0524):