Physics quiz question: swaying electrical transmission lines

Physics 205A Quiz 6, fall semester 2013
Cuesta College, San Luis Obispo, CA

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

"Swaying Power Lines.mpg"
lmwilliams100
youtu.be/US6iayPoBdM

An electrical transmission line in Northeast Arkansas covered with ice[*] sways back and forth at a fundamental frequency of 0.80 Hz, hanging from utility poles[**] with a spacing of 38 m. If the transmission line was no longer covered with ice (and assuming that the tension and length are relatively unchanged) the fundamental frequency would be __________ 0.80 Hz.
(A) lower than.
(B) equal to.
(C) higher than.
(D) (Not enough information is given.)

[*] youtu.be/US6iayPoBdM.
[**] wki.pe/Utility_pole.

Correct answer (highlight to unhide): (C)

The fundamental frequency f₁ of a string of length L is given by:

f₁ = v/(2·L),

where the speed v of transverse waves along the string depends on the tension F and the linear mass density (mass per unit length) (m/L):

v = sqrt(F/(m/L)).

If the transmission line was no longer covered by ice, and given that the tension and the length would be relatively unchanged, then there will be a decrease in mass per length of transmission line, such that (m/L) decreases, increasing v, and thus increasing the fundamental frequency f₁ that the transmission lines will sway back and forth.

Sections 70854, 70855, 73320
Exam code: quiz06wR3k
(A) : 7 students
(B) : 24 students
(C) : 33 students
(D) : 0 students

Success level: 52%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.51