20170106

Physics final exam question: longer string, more tension fundamental standing wave

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

A Physics 205A student builds a standing wave experiment with a mass hanging over a pulley to create tension in a string, which has a fundamental frequency of 20 Hz. The length of string used is increased by a factor of two, and the amount of mass hanging off of the string is also increased by a factor of two. (Ignore stretching in the string.) Discuss why the longer string with a greater hanging mass will have a fundamental frequency lower than 20 Hz. Explain your reasoning using the properties of wave speeds, and standing waves.

• p:
Correct. Understands that:
1. the fundamental standing wave frequency f1 depends on the wave speed v (set by the tension) and the physical length L of string between the ends; and
2. the hanging mass increases by a factor of two, increasing the tension F in the string by a factor of, which increases the wave speed v by a factor of √2, and thus increases the fundamental standing wave frequency f1 by a factor of √2; and
3. doubling the length L between the ends halves the fundamental standing wave frequency f1; such that the overall change in the fundamental standing wave frequency f1 will be such that it is lower, by a factor of (√2)/2, or 0.70 times the original value of f1.
• 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. Only recognizes one of the arguments (2)-(3) as affecting f1.
• v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying standing wave frequency parameters.
• x:
Implementation/application of ideas, but credit given for effort rather than merit. Approach other than applying standing wave frequency parameters.
• y:
Irrelevant discussion/effectively blank.
• z:
Blank.
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 11 students
r: 3 students
t: 27 students
v: 7 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 0424):