Q.3:- 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.
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:
v = √T/µ
∴ T = vu
= (343)2 × 0.175 = 20588.575 ≈ 2.06 × 104 N.