Calculate the wavelength of a wave on a cable

Question

A steel cable with total length 34 m

 and mass 120 kg

 is connected to two poles. The tension in the cable is 4,128 N, and the wind makes the cable vibrate with a frequency of 2 Hz. Calculate the wavelength of the resulting wave on the cable.

Answer 1

Let

L = 34 m be the length of the cable,

m = 120 kg be the mass of the cable,

T = 4128 N be the tension on the cable,

f = 2 Hz be the frequency,

λ (to be calculated) be the wavelength.

Here are the relevant formulas:

v = λf, where v is the speed of wave propagation

v = √(T/μ), where μ = m/L is the linear density

From the above two equations

λ = v/f = √(TL/m)/f

Substituting actual numbers

λ = √(4128×34/120)/2 = 17 m