Physics midterm question: comparable transverse wave speeds

Physics 205A Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

“Transverse wave travel along a bungee cord”
The Orchard - 果樹園
youtu.be/g49mahYeNgc

A transverse wave pulse is created by plucking one end such that it travels down along a cable or a wire. The cable and the wire are made of the same material, but the cable is thicker than the wire. The cable is shorter than the wire, and has more mass hanging off the end. Discuss how it is possible that waves could travel with the same speed along the cable and the wire. Explain your reasoning using the properties of waves.

Solution and grading rubric:

• p:
  Correct. The thicker cable has more tension (F) and a greater linear mass density (m/L) than the thinner wire, which has less tension and a lesser linear mass density. Transverse wave speeds depend on the square root of tension/linear mass density, such that it is plausible that wave can travel at the same speed if the ratio of the numerator and denominator in the square root is the same for cable and wire. (The length of the cable and wire does not directly influence wave speeds, given that the ratio of mass per unit length of the cable and of the wire cannot be changed by using different lengths.)
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May involve length-dependence in linear mass density term as affecting wave speed.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Claims that for the cable, the greater mass (whether due to the thickness of the cable, or the mass hanging off of it) is compensated by its shorter length; while for the wire less mass is compensated by its longer length, and since the tension is the same (whether assumed, implied, or ascribed to the same amount of "pluck" in creating a transverse wave pulse), then the wave speeds are the same for the cable and wire.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of relating wave speeds with tensions and linear mass densities.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02h4W6
p: 38 students
r: 3 students
t: 18 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 2820):