Question

A 90-m-long high-voltage cable is suspended between two towers. The mass of the 90-m cable is 100 kg. If the tension in the cable is 25 000 N, what is the lowest frequency at which this cable can oscillate?

Answer 1

Answer:

Explanation:

Given

Length of cable $L=90\ m$

mass of cable $m=100\ kg$

Tension in the cable $T=25,000\ N$

The lowest frequency observed is given by

$\nu =\frac{1}{2L}\cdot \sqrt{\frac{T}{\mu }}$

where $\nu =frequency$

$\mu =mass\ density(kg/m)$

$\mu =\frac{100}{90}=\frac{10}{9}\ kg/m$

$\nu =\frac{1}{2\times 90}\cdot \sqrt{\frac{25,000}{\frac{10}{9}}}$

$\nu =\frac{5\times 10\times 3}{2\times 90}$

$\nu =0.833\ Hz$