Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 11.49, Review & Synthesis 14 (p. 454).
A string with a length of 0.80 m between supports is stretched by a 2.3 kg mass hanging from one end. A device oscillates the n = 3 mode at 84 Hz. Find the mass that should hang off of this string such that the same 84 Hz frequency vibrates the n = 2 mode. Show your work and explain your reasoning using the properties of wave speeds, periodic waves, and standing waves.
Solution and grading rubric:
Correct. Mass m of the string is not provided. However:
f3 = 84 Hz = ((3/(2·L))·sqrt(M·g/(m/L)),
where the hanging mass M = 2.3 kg, (m/L) is the linear mass density of the string; and:
f2' = 84 Hz = ((2/(2·L))·sqrt(M'·g/(m/L)),
where M' is the new mass that hangs off of the string when vibrating in the n = 2 mode. Equating:
f2' = f3,
and cancelling common factors results in:
M' = M·(3/2)2 = 5.2 kg.
And/or may have solved for quantities such as wave speed along each string, linear mass density, etc., in intermediate steps.
Nearly correct, but includes minor math errors.
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Typically calculates linear mass density (m/L) as (2.3 kg)/(0.80 m) = 5.6 kg/m, and/or confounds (m/L) with hanging mass M, tension force F with frequency f, etc., but still has systematic attempt at finding linear mass density from original n = 3 case, and then feeds (erroneous) (m/L) and/or other factors into the n = 2 case, along with other algebraic or nomenclature errors.
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at manipulating standing wave frequency equations.
Implementation of ideas, but credit given for effort rather than merit.
Irrelevant discussion/effectively blank.
Sections 70854, 70855
Exam code: finalB0xs
p: 9 students
r: 5 students
t: 23 students
v: 6 students
x: 1 student
y: 2 students
z: 2 students
A sample "p" response (from student 1124):
A sample "t" response (from student 3389):
Kudos (from student 0415):