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.
Solution and grading rubric:
Correct. Understands that:
- 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
- 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
- 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.
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. Only recognizes one of the arguments (2)-(3) as affecting f1.
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.
Implementation/application of ideas, but credit given for effort rather than merit. Approach other than applying standing wave frequency parameters.
Irrelevant discussion/effectively 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):