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 = m/l = 2.10/12 = 0.175 kg m^-1 

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