Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 25.31
A commercially available wireless router[*] broadcasts at a 0.12 m wavelength from two vertical antennae spaced 0.18 m apart. Assume that the two antennae are in phase. Determine how many destructive interference (minima) directions there will be (if any) in the 360° range of all possible directions. Show your work and explain your reasoning using the properties of source phases, path lengths, and interference.
[*] Linksys WRT54GL wireless router, 802.11b channel 1 (2412 MHz), overall width 200 mm, downloads.linksys.com/downloads/WRT54GL_V11_DS_NC-WEB,0.pdf
Solution and grading rubric:
Correct. Approximates two in-phase antennae as a double slit, and equates path length difference approximation dsinθ with destructive interference (minima) condition for in-phase sources to find θ = 19° and 90° as measured counterclockwise from the θ = 0° south direction, such that there are six unique directions of destructive interference in the 360° range of all possible directions. Okay if minima directions in the south-east quadrant are not correctly mapped via symmetry to find all minima directions, if at least the two unique θ = 19° and 90° directions in the southeast quadrant are found.
Nearly correct, but includes minor math errors. Only specifically searches over the cardinal directions, and finds of these that only east and west have destructive interference.
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying path length differences and interference.
Irrelevant discussion/effectively blank.
Sections 30882, 30883
Exam code: finalLd0c
p: 4 students
r: 13 students
t: 5 students
v: 11 students
x: 4 students
y: 3 students
z: 3 students
A sample "p" response (from student 5246):
A sample "r" response (from student 0104):