Waves

Question : 3 of 27

Marks: +1, -0

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 to the speed of sound in dry air at 20 °C = 343

\mathrm{m}\,\mathrm{s}^{-1}

Solution:

Here,

l = 12.0

m, M = 2.10 kg, T = ?, v = 343

\mathrm{m}\,\mathrm{s}^{-1}

Mass per unit length, µ

= \frac{M}{l}= \frac{2.10}{12.0}=0.175\,\frac{\mathrm{kg}}{\mathrm{m}^{-1}}

As,

v=\sqrt{\frac{T}{\mu}}

\therefore T=v^{2}.\,\mu=(343)^{2}\times 0.175

=2.06\times 10^{4}\,\mathrm{N}

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