Physics midterm question: converting open-open pipe to closed-open pipe

Physics 205A Midterm 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Questions 12.1, 12.2

If a cap were put on one end of the open-open pipe, this would become a closed-open pipe that would resonate for a sound wave in air with a fundamental frequency that is __________ the fundamental frequency of the original open-open pipe.
(A) lower than.
(B) the same as.
(C) higher than.
(D) (Not enough information is given.)

Correct answer: (A)

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

f₁ = v/(2·L).

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

f₁ = v/(4·L).

The length L of the pipe is unchanged, such that converting it from an open-open pipe to a close-open pipe would decrease its resonate fundamental frequency by a factor of 2.

Sections 70854, 70855
Exam code: midterm02gL0u
(A) : 35 student
(B) : 2 students
(C) : 17 students
(D) : 0 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.55