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 om the wire, like a standing wave on a guitar string.

Assume that a wire (linear density = 0.0140 kg/m) sustains a tension of 323 N because the wire is stretched between two poles that are 7.60 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

The tension in the string is T = 323 N The linear density of the string is = 0.0140 kg/m The length of the string (distance between the poles) L = 7.6 m The frequency of the fundamental vibration of the wave in a string is f = 1/2L (T/) Where L is the legth of vibrating segment             T is the applied tension              is the linear density f = 1/2(7.6 m) (323 N / 0.014 kg/m) f = 9.99 Hz f ˜ 10 Hz The lowest possible requency a human ear can hear is f' = 20 Hz The number of the harmonic which produces the required frequency is n = 20 Hz/10 Hz n = 2 The second harmonic of the string will produce the moaning sound in the string The second harmonic of the string will produce the moaning sound in the string

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