Physics clicker question: changing tension of a rope wave

Physics 205A, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

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

Students were asked the following clicker question (Classroom Performance System, einstruction.com) in the middle of their learning cycle:

Cord tension F = 75 N
Wave speed v = 140 m/s
Frequency f = 20 Hz (from a vibrating source)

Which wave parameter(s) increase if the cord were made more taut?
(A) Wave speed v.
(B) Wavelength lambda.
(C) Period T.
(D) (More than one of above choices.)
(E) (None of above choices.)
(F) (I'm lost, and don't know how to answer this.)

Sections 30880, 30881
(A) : 7 students
(B) : 5 students
(C) : 2 students
(D) : 19 students
(E) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. No comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Sections 30880, 30881
(A) : 4 students
(B) : 0 students
(C) : 0 students
(D) : 27 students
(E) : 0 students

Correct answer: (D)

The frequency f of a wave is determined solely by the properties of the source, while the wave speed v is determined solely by the properties of the medium (thus frequency and wave speed are said to be the independent wave parameters). For rope waves:

v = sqrt(F/mu),

where F is the tension in the rope, while mu is the linear mass density (mass per unit length) of the rope.

The wavelength is the dependent wave parameter that is determined by both the source and medium, given by:

lambda = v/f or v*T,

where T is the period (which is the inverse of frequency). So if tension F increases, the wave speed v will increase (while the frequency remains constant), and also the wavelength will increase as result of the increase in v.

Pre- to post- peer-interaction gains:
pre-interaction correct = 58%
post-interaction correct = 87%
Hake, or normalized gain = 70%

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