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 = 0.0200 kg/m) sustains a tension of 79.9 N because the wire is stretched between two poles that are 6.32 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 relation for the n-th harmonic is =

n*lambda/2 = L.
Indeed v = sqrt(79.9/0.02) = 63.2 m/s
v = f*lamda
n*lambda/2 = L
n= f*2*L/v
Now it is given that f>= 20.0 Hz, therefore
n >= 20.0 Hz*2*6.32m / 63.2m/s
n >= 4.00
The smallest integer n therefore is n = 4

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