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 = 0.0140 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?

Respuesta :

Answer:

2

Explanation:

m = Linear density = [tex]0.014\ kg/m[/tex]

T = Tension = [tex]323\ N[/tex]

f = Frequency = 20 Hz

l = Length of the wire = 7.6 m

The harmonic number is given by

[tex]n=f2l\sqrt{\dfrac{m}{T}}\\\Rightarrow n=20\times 2\times 7.6\times \sqrt{\dfrac{0.014}{323}}\\\Rightarrow n=2.00141126679\approx 2[/tex]

The lowest harmonic number n is 2