Physics midterm question: standing wave in warm closed-open pipe

Physics 205A Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Questions 12.1, 12.2, Problem 12.21

If the temperature of the air inside a closed-open pipe were to heat up, the speed of sound in the pipe would __________, while its fundamental frequency would __________.
(A) remain constant; remain constant.
(B) remain constant; change.
(C) change; remain constant.
(D) change; change.

Correct answer (highlight to unhide): (D)

The fundamental frequency of a standing sound wave in a closed-open pipe is given by:

f₁ = v/(4·L),

and the speed of sound waves is given by:

v = (331 m/s)·sqrt(T/(273 K)),

such that a temperature increase would increase the speed of sound, resulting in a higher fundamental frequency. (While the frequency of a sound wave already resonating in the pipe would not be affected by the change in speed due to the increase in temperature, this existing sound wave frequency would no longer be able to cause resonance in the pipe due to the change in the pipe's fundamental frequency requirement.)

Sections 70854, 70855
Exam code: midterm02fR3q
(A) : 7 students
(B) : 7 students
(C) : 9 students
(D) : 30 students

Success level: 55%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.22