15.3 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.
15.3 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 = 2.1 kg
Velocity of the transverse wave, v = 343 m/s
Mass per unit length, = = = 0.175 kg/m
The velocity (v) of the transverse wave in the string is given by the relation:
, where T is the tension
T = = = 20588.575 N = 2.06 N
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