Calculate the wavelength of the resulting wave on the cable

Question

A steel cable with total length 75 m

 and mass 150 kg

 is connected to two poles. The tension in the cable is 2,204 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

Use the relationship v =√(T/μ) where T= tension and μ = linear density to find the speed along the wire. For this problem μ = 150kg /75m =2kg/m and T/μ = 2204 kgm/sec² /2kg/m which gives 1102 m²/sec² So v=√1104 and v= 33.23m/sec now use v=fλ where f=frequency and λ= wavelength. So λ =33.23m/sec/2/sec and λ = 16.61 m.