Question

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the
tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20${}^{\circ }C$( v = 343 m)$s^{-1}$:

Answer 1

Length of the steel wire, $l=12m$
Mass of the steel wire, $m=2.10kg$
Velocity of the transverse wave, $v=343m/s$
Mass per unit length, $\mu =m/l=2.10/12=0.175kg{m}^{-1}$
For Tension T, velocity of the transverse wave can be obtained using the relation:
$v=\sqrt{\frac{T}{\mu }}$
$\therefore$ $T=v^2\mu$
$=(343{)}^2\times 0.175=20588.575\simeq 2.06\times {10}^{4}N$.