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  • 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.

Q.15.3 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^{o}C = 343 \; m\; s^{-1}.

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Mass per unit length od the wire is

\\\mu =\frac{M}{l}\\ =\frac{2.10}{12}\\ =0.175\ kg\ m^{-1}

The speed of a transverse wave in a wire is given by

\\v=\frac{T}{\mu }\\ 343=\sqrt{\frac{T}{01.175}}\\ T=343^{2}\times 0.175\\ T=2.059\times 10^{4}\ N

The tension in the wire should be 2.059\times 10^{4}\ N such that the speed of the transverse wave in it is equal to 343 m s-1.

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Sayak

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