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:
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):