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