You can sometimes hear a low-frequency “moaning” noise when strong winds blow through power lines strung between two poles. The wind is exciting a particular standing wave mode on the wire between its fixed ends at the poles; in this example, the wire is observed to have the shape shown in the diagram below at a particular instant in time. (a) If, for this mode (or harmonic), the frequency you hear is 20 Hz (near the lower threshold of human hearing), the tension of the wire is 1600 N, and the mass per unit length of the wire if 0.040 kg/m, how far apart are the poles assuming that, at equilibrium, the wire between the poles is horizontal? (b) What order harmonic is shown in the illustration below? (c) What is the wavelength of this sound in air? The speed of sound in air is 340 m/s. (d) Suppose there is a second wire strung between the poles, identical in every respect to the wire in part (a) except that its mass per unit length is 30% larger (i.e., it is 0.052 kg/m). If both wires are vibrating at the same harmonic (shown in the diagram), what beat frequency would you hear?
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