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):