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

Question

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 the speed of a transverse wave on the wire equals the speed of sound in dry air at $20^\circ	ext{C}$ (343 m/s)?

Professor PC Thomas Classes · Answer

$\mu = m/L = 2.10 / 12.0 = 0.175$ kg/m. Since $v = \sqrt{T/\mu}$, we have $T = v^2 \mu = (343)^2 	imes 0.175 = 2.06 	imes 10^4$ N.