Question

Guy wires used to support tall radio antennae often need to be kept at a specific tension or else the antennae may bend or buckle. The tension tends to decrease over time as the wire ages (and stretches) but on cold days, when the wire contracts, the tension increases. So, to keep the tension within tolerances, the tension in the wire is checked regularly and adjusted if it is found to be outside of tolerances. One way to check the wire tension is to cause it to vibrate at different frequencies and find the frequencies of the wires harmonics. Suppose that a 200 m long guy wire has a total mass of 450 kg. To properly support the antenna it is attached to it needs to be under a tension of 2 . 0 × 10 5 N. The tension should not be allowed to exceed 2 . 1 × 10 5 N or fall below 1 . 9 × 10 5 N. One day it is found that the wire will sustain vibrations at frequencies of 3.164 Hz, 3.955 Hz and 4.746 Hz, but not at any frequencies between these. (a) What is the fundamental frequency of the wire under its current tension? (b) Which harmonics are 3.164 Hz, 3.955 Hz and 4.746 Hz? Draw the standing waves that would form on the wire at each of these frequencies. (c) What is the wave propagation speed on the wire under its current tension? (d) What is the tension in the wire? Should the wire be loosened or tightened

Answer 1

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