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 speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C = 343 m s–1.​

Answer 1

Explanation:

Length of the steel wire, l = 12 m

Mass of the steel wire, m = 2.10 kg

Velocity of the transverse wave, v = 343 m/s

Mass per unit length, µ = m/l = 2.10/12 = 0.175 kg m-1

For Tension T, velocity of the transverse wave can be obtained using the relation:

v = √T/µ

∴ T = vu

= (343)2 × 0.175 = 20588.575 ≈ 2.06 × 104 N.

Answer 2

Answer:

The tension in the wire when the speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C will be equal to 2.06 ×10⁴N.

Explanation:

Given that for a steel wire:

length, $l= 12m$  and   mass, $m= 2.10 kg$

Here the mass per unit length, $\mu =\frac{m}{l}=\frac{2.10}{12}=0.175kgm^{-1}$

The speed of the transverse wave, $v=343ms^{-1}$

We know     $v=\sqrt{\frac{T}{\mu } }$

⇒               $T=v^{2}\mu$

Put the values of ν and μ in above equation:

  ∴           $T=(343ms^{-1})^{2}(0.172kgm^{-1})\\T= 2.06 *10^{4}kgms^{-2}\\T= 2.06*10^{4}N$

Therefore the tension in the wire equals to 2.06 ×10⁴N.