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 ${20}^{\circ }C=343m{s}^{-1}$

Answer 1

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