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 = 0.0160 kg / m ) sustains a tension of 341 N because the wire is stretched between two poles that are 18.25 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

v=sqrt(341/0.0160) = 145.98m/s

For standing waves on a string , the relation for the n-th harmonic is
n lambda/2 = L.

Indeed v = 145.98m/s

v = f lamda

But n lambda/2 = L

So

n= f 2 L / v

Now it is given that f>= 20.0 /s, therefore

n >= 20.0/s * 2*18.25m / 145.98m/s
n >= 0.50
The smallest integer n therefore is n = 0.50

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