Physics midterm problem: out-of-phase source interference

Physics 205B Midterm 1, spring semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 25.1, 25.3

[20 points.] A radio transmitter sends a signal of wavelength 0.18 km to a receiver 1.22 km away. 
The signal also travels to the receiver by another path where it reflects with a 180° phase shift from a metal skyscraper, as shown at right. As a result, there is a destructive signal at the receiver. Find the shortest possible distance between the skyscraper and the receiver. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Sets up proper destructive interference condition for out-of-phase sources (∆l = m·λ), where ∆l = (1.30 km - x) - 1.22 km, and solves for x, the distance from the skyscraper to the receiver using m = 1 to obtain the shortest possible skyscraper-receiver distance.
  
• 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.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• 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: midterm01g74S
p: 2 students
r: 0 students
t: 4 students
v: 0 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 2414):