To review the concepts that play roles in this problem, consult Multiple-Concept

Question

To review the concepts that play roles in this problem, consult Multiple-Concept Example 4. Sometimes, when the wind blows across a long wire, a low-frequency "moaning" sound is produced. This 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 = 0.0195 kg/m) sustains a tension of 136 N because the wire is stretched between two poles that are 8.35 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(136/0.0195) = 83.51 m/s
then the length of the wire = 0.5 wavelength (node at each end)
so wavelength = 16.70 m
so fundamental frequency = wavespeed/wavelength = 83.51/16.70 = 5.00 Hz
so 20 Hz is the 20/5.00 = 4rd harmonic is the lowest harmonic number n that could be responsible for the "moaning" sound

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