The Humming Power Line · AI Generator #GEN-2AF0490E

Physics

Problem

On a windy day, electrical power lines can produce an audible humming sound due to a phenomenon called "aeolian vibration." When wind flows across a cylindrical wire, it creates alternating vortices that cause the wire to vibrate transversely. A power transmission line consists of aluminum cable with linear mass density μ=1.2  kg/m\mu = 1.2\;\text{kg/m} stretched between two towers L=300  mL = 300\;\text{m} apart. The cable is under tension T=8000  NT = 8000\;\text{N}. On this particular day, the wind causes the cable to vibrate in its fundamental mode (first harmonic), producing a clearly audible tone. What frequency does the humming power line produce?

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