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 ms^-1

Given:

Mass of the steel wire, M = 2.10 Kg

Length of the string, L = 12 m

Mass per unit length, m = M/L

⇒ m = 2.10 Kg/ 12m

⇒ m = 0.175 Kgm^-1

Velocity of the transverse wave, V = 343ms^-1

The Tension, T in transverse wave in the string is given by,

T = V²m …(1)

Where,

T = tension in the string

m = mass per unit length

V = velocity of wave

By putting the given data in equation (1), we get,

T = (343ms^-1)²× 0.175Kgm^-1

⇒ T = 20588.5 N