Physics quiz question: increasing tension of piano wire

Physics 205A Quiz 6, fall semester 2012
Cuesta College, San Luis Obispo, CA

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

The lowest note on a Charles Howes & Son CH162 grand piano [*],[**] is played on a wire that has a length of 1.195 m and vibrates at a fundamental frequency of 27.5 Hz. If the tension in the piano wire is increased, its fundamental frequency would:
(A) decrease.
(B) remain constant.
(C) increase.
(D) (Not enough information is given.)

[*] charleshowespianos.com/grand_pianos.htm.
[**] wki.pe/Piano_key_frequencies.

Correct answer (highlight to unhide): (C)

The speed of waves along the string is given by:

v = √(F/(m/L)),

such that increasing the tension F of the string (without affecting the linear mass density (m/L)) would increase the speed of waves that travel along the string.

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

f₁ = v/(2·L),

and since increasing the tension F of the string would increase the wave speed v, this would result in an increase in the f₁ frequency.

Sections 70854, 70855
Exam code: quiz06How3
(A) : 4 students
(B) : 6 students
(C) : 36 students
(D) : 0 students

Success level: 78%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.40