Physics midterm question: flute temperature compensation

Physics 205A Midterm 2, fall semester 2014
Cuesta College, San Luis Obispo, CA

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

"Flute Closeup with Sheet Music in Monochrome"
D. Mitchell Photography
flic.kr/p/oMfzip

An online tutorial[*] advises how to keep a flute in tune under certain conditions.

When a flute gets hotter in temperature, the pitch of the flute goes sharper. Flutes are subjected to hotter spaces when heating is turned too high, performance spaces are filled with audiences, sun shines on outdoor performance, hot lights onstage, etc. To correct this gradually pull out your headjoint [to extend the length of the flute].

Discuss why the length of the flute (which can be approximated as an open-open tube) must be extended to compensate for warmer air temperatures. Explain your reasoning using the properties of sound waves, temperatures, and standing waves.

[*] Jennifer Cluff, "Flute Tuning 'How-to,'" jennifercluff.com/begtune.htm#temp.

Solution and grading rubric:

• p:
  Correct. The standing wave frequencies for a flute are proportional to the velocity of sound waves in air (which depends on the air temperature), and inversely proportional to the length of the flute. Since a rise in temperature will increase the speed of sound waves in air, which would increase the fundamental frequency, increasing the length of the flute would decrease the fundamental frequency, compensating for the increase in temperature to keep the fundamental frequency of the flute constant.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of relating sound waves and standing waves.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02veR1
p: 44 students
r: 6 students
t: 14 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 5323):