A steel wire has a length of 12 m and a mass of 2.10 kg. What should be the tension in the wire, that the…
A steel wire has a length of 12 m and a mass of 2.10 kg. What should be the tension in the wire, that the speed of a transverse wave on the wire equals to speed of sound in dry air at 20°C (= $343\ \mathrm{ms}^{-1}$)?
Solution
Sol. Given, speed of sound in air, $v = 343\ \mathrm{ms}^{-1}$
Length of the wire, $l = 12.0\ \mathrm{m}$
Total mass of the wire, $M = 2.10\ \mathrm{kg}$
Therefore, mass per unit length of the wire,
$\alpha = \dfrac{M}{l} = \dfrac{2.10}{12.0} = 0.175\ \mathrm{kgm}^{-1}$
Now, $v = \sqrt{\dfrac{T}{\alpha}}$
or $T = v^{2}\alpha = (343)^{2} \times 0.175 = 20588.6\ \mathrm{N} = 2.06 \times 10^{4}\ \mathrm{N}$
Answer: $2.06 \times 10^{4}\ \mathrm{N}$