Sometimes, when the wind blows across a long wire, a low-frequency \"moaning\" s

Question

Sometimes, when the wind blows across a long wire, a low-frequency "moaning" sound is produced. The sound arises because a standing wave is set up on the wire, like a standing wave on a guitar string. Assume that a wire (linear density = 0.0165 kg / m ) sustains a tension of 380 N because the wire is stretched between two poles that are 15.18 m apart. The lowest frequency that an average, healthy human ear can detect is 20.0 Hz. What is the lowest harmonic number n that could be responsible for the "moaning" sound?

Explanation / Answer

first calculate the speed of the wave along the wire

(I'm not sure about the first equation but the rest are good)

v = sqrt(tension/density) = sqrt(380/0.0185) = 143 m/s

then the length of the wire = 0.5 wavelength (node at each end)

so wavelength = 21.5 m

so fundamental frequency = wavespeed/wavelength = 6.66 Hz

so 20 Hz is the 20/6.66 = 3rd harmonic.

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