In moderate winds, high-tension power lines sometimes “sing” or hum as a result of transverse waves on the lines that winds can generate. The cables that carry high-voltage electricity are made of aluminum with a steel core added for strength. The cross sectional areas of the steel and aluminum in the line are 39 mm2 and 220 mm2, respectively. The cable is 1.8 cm in diameter and is under a tension of 4.9 × 104 N. Typically, the towers are placed about 0.20 km apart. (See Figure P12.71.)
(a) What is the fundamental frequency of such a power line? (The densities of steel and aluminum are given in Table 10.1.)
(b) The wind can induce vibrations when flowing around a cylinder. The frequency of the vibrations induced this way is modeled well by the equation
where vwind is the speed of the wind and d is the diameter of the cylinder. The wind will induce vibration this way only if the frequency of the induced oscillation matches a natural frequency of the power line. It is found that the power line hums when the wind blows at a steady 6.7 m/s. What harmonic of the line is this induced vibration exciting?
(c) If the line is humming at the 152nd harmonic, how fast is the wind blowing?
Figure P12.71
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