$8\mathrm{.}10*$ The cable between two electric transmission towers has a length of $2000$ m $.$ It is clamped at

its ends under a tension $P($Fig$.8\mathrm{.}24).$ The density of the cable material is $8890k\frac{g}{m^3}.$ If the

first four natural frequencies are required to lie between $0$ and $20$ Hz $,$ determine the neces$-$

sary cross$-$sectional area of the cable and the initial tension.

FIGURE $8\mathrm{.}24$