If a transmission line in a cold climate collects ice, the increased diameter tends to cause vortex formation in a passing wind. The air pressure variations in the vortexes tend to cause the line to oscillate (gallop), especially if the frequency of the variations matches a resonant frequency of the line. In long lines, the resonant frequencies are so close that almost any wind speed can set up a resonant mode vigorous enough to pull down support towers or cause the line to short out with an adjacent line. If a transmission line has a length of 347 m, a linear density of 3.35 kg/m, and a tension of 65.2 MN, what are (a) the frequency of the fundamental mode and (b) the frequency difference between successive modes?

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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If a transmission line in a cold climate collects ice, the
increased diameter tends to cause vortex formation in a passing
wind. The air pressure variations in the vortexes tend to cause the
line to oscillate (gallop), especially if the frequency of the variations
matches a resonant frequency of the line. In long lines, the
resonant frequencies are so close that almost any wind speed can
set up a resonant mode vigorous enough to pull down support towers
or cause the line to short out with an adjacent line. If a transmission
line has a length of 347 m, a linear density of 3.35 kg/m, and a
tension of 65.2 MN, what are (a) the frequency of the fundamental
mode and (b) the frequency difference between successive modes?

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