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. 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 = 0.0115 kg / m ) sustains a tension of 365 N because the wire is stretched between two poles that are 17.82 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

Given,
Linear density of wire, = 0.0115 kg/m

Tension, T = 365 N

Distance, l = 17.82 m

The fundamental frequency of the guitar string is given by,

            f = [1/(2l)] (T/)

= [1/(2 x 17.82 m)] ((365 N)/(0.0115 kg/m))

f = 5.00 Hz

The lowest harmonic number n that could be responsible for the ' moaning sound' is,

n = F/ f

n = (20.0 Hz)/(5 Hz)

n = 4

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