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 °C = 343 m 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, $μ=\frac{m}{l}=\frac{2.10}{12}=0.175\,kg,m^{-1}$

For tension T, velocity of the transverse wave can be obtained using the relation:

$v=\sqrt\frac{T}{μ}$

$\therefore\,T=v^2μ$

= (343)2 × 0.175 = 20588.575≈ 2.06 × 104 N