Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 25.1
A radio antenna receives a constructive interference signal from two transmitters that broadcast in phase at the same wavelength. Discuss why the radio antenna will still receive a constructive interference signal if one transmitter were moved one-half of a wavelength closer to the radio antenna, while the other transmitter was moved one-half of a wavelength farther from the radio antenna. Explain your reasoning by using the properties of waves and interference.
Solution and grading rubric:
Correct. Shows either by a diagram or explicit demonstration of how Δl = |l1 - l2| is a whole number of wavelengths (where l1' = l1 + λ/2 and l2' = l2 - λ/2 results in Δl' still being equal to a whole number of wavelengths) that constructive interference still results.
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
Nearly correct, but argument has conceptual errors, or is incomplete.
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some attempt at using interference, phase/path lengths differences.
Implementation/application of ideas, but credit given for effort rather than merit.
Irrelevant discussion/effectively blank.
Sections 30882, 30883
Exam code: finalEL7a
p: 20 students
r: 3 students
t: 7 students
v: 4 students
x: 1 student
y: 0 students
z: 0 students
A sample "p" response (from student 0001), using the path-length difference equation:
Another sample "p" response (from student 0007), using a diagram:
Another sample "p" response (from student 7810), using both the path-length difference equation and a diagram: