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 = 0.0140 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?

Answer 1

2

Step-by-step explanation:

m = Linear density =
`0.014\ kg/m`

T = Tension =
`323\ N`

f = Frequency = 20 Hz

l = Length of the wire = 7.6 m

The harmonic number is given by

`n=f2l\sqrt{(m)/(T)}\\\Rightarrow n=20* 2* 7.6* \sqrt{(0.014)/(323)}\\\Rightarrow n=2.00141126679\approx 2`

The lowest harmonic number n is 2