Physics final exam question: speed of waves along standing wave strings

Physics 205A Final Exam, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Questions 11.3, 11.4, Multiple-Choice Questions 11.5, 11.6, 11.8

A string has its tension set by a hanging mass, and resonates at its fundamental frequency. If a shorter length of the string is used with the same hanging mass (which changes its fundamental frequency), discuss why the speed of waves along this string does not change. (Ignore stretching in the string.) Explain your reasoning using the properties of wave speeds, periodic waves, and standing waves.

Solution and grading rubric:
  • p:
    Correct. Understands that (1) wave speed depends on tension and linear mass density, and (2) since neither of these are changed by using a shorter portion of this same string (with the same mass hanging from it), then the wave speed remains constant.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least understands the relationship between wave parameters.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 70854, 70855, 73320
Exam code: finaln0M3
p: 17 students
r: 25 students
t: 7 students
v: 9 students
x: 3 students
y: 0 students
z: 0 students

A sample "p" response (from student 7810):

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