Physics quiz question: frequency of standing wave on a string

Physics 205A Quiz 6, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 11.4, Multiple-Choice Question 11.5

A viola's A-string[*],[**] has a length of 0.37 m and is stretched to a tension of 53 N. It vibrates at a fundamental frequency of 440 Hz. In order to increase the fundamental frequency of this viola string, which of the following should be done?
(A) Press a finger on the string, such that a shorter length of it vibrates.
(B) Increase the tension of the string.
(C) (Both of the above choices.)
(D) (Neither of the above choices.)

[*] theviolaworkshop.com/page16.html.
[**] gamutmusic.squarespace.com/viola-tensions/.

Correct answer (highlight to unhide): (C)

The fundamental frequency of a standing wave on a string is given by:

f₁ = (1/(2·L))·sqrt(F/(m/L)),

such that either decreasing the length L of the string, or increasing the tension F of the string would both result in an increase in f₁.

Sections 70854, 70855
Exam code: quiz06w4VE
(A) : 13 students
(B) : 13 students
(C) : 26 students
(D) : 2 students

Success level: 49%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.73