Steel wire has a length of 12.0 \mathrm{~m} and a mass of 2.10 \mathrm{~kg} . What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at 20^{\circ} \mathrm{C}=343 \mathrm{~m} \mathrm{~s}^{-1}
Steel wire has a length of 12.0 \mathrm{~m} and a mass of 2.10 \mathrm{~kg} . What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at 20^{\circ} \mathrm{C}=343 \mathrm{~m} \mathrm{~s}^{-1}

Length of the steel wire is given as I=12 \mathrm{~m}

Mass of the steel wire is given as \mathrm{m}=2.0 \mathrm{~kg}

Velocity of the transverse wave is given as \mathrm{v}=343 \mathrm{~m} / \mathrm{s}

Mass per unit length is given as

\mu=\mathrm{M} / \mathrm{l}=2.10 / 12=0.175 \mathrm{~kg} / \mathrm{m}
As we know,

Expression for velocity of the transverse wave, \mathrm{v}=\sqrt{\frac{T}{\mu}}

Therefore, \mathrm{T}=\mathrm{v}^{2} \mu

=343^{2} \times 0.175=2.06 \times 10^{4} \mathrm{~N}