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

Question

Sometimes, when a 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. Assume that a wire of linear density = 0.157 kg/m sustains a tension of 340 N as it is being stretched between two poles that are 18.4 m apart. Assume also that one end of the wire is fixed to one pole, while the other is connected to a ring which is free to slide on the other pole (mostly without friction).

What is the lowest resonance frequency produced by the wire?
Hz
What is the next lowest resonant frequency?
Hz
Assuming that the lowest frequency that the human ear can hear is 20 Hz, what is the lowest harmonic number n that could be responsible for the "moaning" sound?

Explanation / Answer

speed of wave on string, v = sqrt(T/mue) (here T is tension and mue is linear mass density)

= sqrt(340/0.157)

= 46.54 m/s

the lowest resonance frequency produced by the wire, fo = v/(2*L)

= 46.54/(2*18.4)

= 1.26 Hz

the next lowest resonant frequency, f2 = 2*fo

= 2*1.26

= 2.52 hz

let n is the lowest harmonic number

20 = n*fo

==> n = 20/fo

= 20/1.26

= 15.87

here we should take closest integer.
so, n = 16

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